Tide

Tide

Overview
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

 and the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 and the rotation of the Earth.

Most places in the ocean usually experience two high tides and two low tides each day (semi-diurnal tide), but some locations experience only one high and one low tide each day (diurnal tide). The times and amplitude of the tides at the coast are influenced by the alignment of the sun and moon, by the pattern of tides in the deep ocean (see figure 4) and by the shape of the coastline and near-shore bathymetry
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

 (see figure 7).

Tides vary on timescales ranging from hours to years due to numerous influences.
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Encyclopedia
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

 and the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 and the rotation of the Earth.

Most places in the ocean usually experience two high tides and two low tides each day (semi-diurnal tide), but some locations experience only one high and one low tide each day (diurnal tide). The times and amplitude of the tides at the coast are influenced by the alignment of the sun and moon, by the pattern of tides in the deep ocean (see figure 4) and by the shape of the coastline and near-shore bathymetry
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

 (see figure 7).

Tides vary on timescales ranging from hours to years due to numerous influences. To make accurate records, tide gauge
Tide gauge
A tide gauge is a device for measuring sea level and detecting tsunamis.Sensors continuously record the height of the water level with respect to a height reference surface close to the geoid...

s at fixed stations measure the water level over time. Gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to the reference (or datum) level usually called mean sea level.

While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to forces such as wind and barometric pressure changes, resulting in storm surge
Storm surge
A storm surge is an offshore rise of water associated with a low pressure weather system, typically tropical cyclones and strong extratropical cyclones. Storm surges are caused primarily by high winds pushing on the ocean's surface. The wind causes the water to pile up higher than the ordinary sea...

s, especially in shallow seas and near coasts.

Tidal phenomena are not limited to the oceans, but can occur in other systems whenever a gravitational field that varies in time and space is present. For example, the solid part of the Earth is affected by tides, though this is not as easily seen as the water tidal movements.

Characteristics



Tide changes proceed via the following stages:
  • Sea level rises over several hours, covering the intertidal zone; flood tide.
  • The water rises to its highest level, reaching high tide.
  • Sea level falls over several hours, revealing the intertidal zone; ebb tide.
  • The water stops falling, reaching low tide.


Tides produce oscillating currents known as tidal streams. The moment that the tidal current ceases is called slack water
Slack water
Slack water, which used to be known as 'The stand of the tide', is a short period in a body of tidal water either side of high water or low water essentially when the water is completely unstressed, and therefore with no rise or fall of the tide and no movement either way in the tidal stream, and...

 or slack tide. The tide then reverses direction and is said to be turning. Slack water usually occurs near high water and low water. But there are locations where the moments of slack tide differ significantly from those of high and low water.

Tides are most commonly semi-diurnal (two high waters and two low waters each day), or diurnal (one tidal cycle per day). The two high waters on a given day are typically not the same height (the daily inequality); these are the higher high water and the lower high water in tide table
Tide table
A tide table, sometimes called a tide chart, is used for tidal prediction and shows the daily times and height of high water and low water for a particular location...

s. Similarly, the two low waters each day are the higher low water and the lower low water. The daily inequality is not consistent and is generally small when the moon is over the equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

.

Tidal constituents


Tidal changes are the net result of multiple influences that act over varying periods. These influences are called tidal constituents. The primary constituents are the Earth's rotation, the positions of moon and the sun relative to Earth, the moon's altitude (elevation) above the Earth's equator, and bathymetry
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

.

Variations with periods of less than half a day are called harmonic constituents. Conversely, cycles of days, months, or years are referred to as long period constituents.

The tidal forces affect the entire earth
Earth tide
Earth tide is the sub-meter motion of the Earth of about 12 hours or longer caused by Moon and Sun gravitation, also called body tide which is the largest contribution globally. The largest body tide contribution is from the semidiurnal constituents, but there are also significant diurnal...

, but the movement of the solid Earth is only centimeters. The atmosphere is much more fluid and compressible so its surface moves kilometers, in the sense of the contour level of a particular low pressure in the outer atmosphere.

Principal lunar semi-diurnal constituent


In most locations, the largest constituent is the "principal lunar semi-diurnal", also known as the M2 (or M2) tidal constituent. Its period is about 12 hours and 25.2 minutes, exactly half a tidal lunar day, which is the average time separating one lunar zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...

 from the next, and thus is the time required for the Earth to rotate once relative to the moon. Simple tide clock
Tide clock
A tide clock is a specially designed clock that keeps track of the Moon's apparent motion around the Earth. Along many coastlines the Moon contributes the major part of the combined lunar and solar tides....

s track this constituent. The lunar day is longer than the Earth day because the moon orbits in the same direction the Earth spins. This is analogous to the minute hand on a watch crossing the hour hand at 12:00 and then again at about 1:05 (not at 1:00).

The moon orbits the Earth in the same direction as the Earth rotates on its axis, so it takes slightly more than a day—about 24 hours and 50 minutes—for the moon to return to the same location in the sky. During this time, it has passed overhead (culmination
Culmination
In astronomy, the culmination of a planet, star, constellation, etc. is the altitude reached when the object transits over an observer's meridian....

) once and underfoot once (at an hour angle
Hour angle
In astronomy and celestial navigation, the hour angle is one of the coordinates used in the equatorial coordinate system to give the position of a point on the celestial sphere....

 of 00:00 and 12:00 respectively), so in many places the period of strongest tidal forcing is the above mentioned, about 12 hours and 25 minutes. The moment of highest tide is not necessarily when the moon is nearest to zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...

 or nadir
Nadir
The nadir is the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous...

, but the period of the forcing still determines the time between high tides.

Because the gravitational field created by the moon weakens with distance from the moon, it exerts a slightly stronger tidal force
Tidal force
The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...

 on the side of the Earth facing the moon than on the opposite side. The moon thus tends to "stretch" the Earth slightly along the line connecting the two bodies. The solid Earth deforms a bit, but ocean water, being fluid, is free to move much more in response to the tidal force, particularly horizontally. As the Earth rotates, the magnitude and direction of the tidal force at any particular point on the Earth's surface change constantly; although the ocean never reaches equilibrium—there is never time for the fluid to "catch up" to the state it would eventually reach if the tidal force were constant—the changing tidal force nonetheless causes rhythmic changes in sea surface height.

Semi-diurnal range differences


When there are two high tides each day with different heights (and two low tides also of different heights), the pattern is called a mixed semi-diurnal tide.

Range variation: springs and neaps



The semi-diurnal range (the difference in height between high and low waters over about a half day) varies in a two-week cycle. Approximately twice a month, around new moon
New moon
In astronomical terminology, the new moon is the lunar phase that occurs when the Moon, in its monthly orbital motion around Earth, lies between Earth and the Sun, and is therefore in conjunction with the Sun as seen from Earth...

 and full moon
Full moon
Full moon lunar phase that occurs when the Moon is on the opposite side of the Earth from the Sun. More precisely, a full moon occurs when the geocentric apparent longitudes of the Sun and Moon differ by 180 degrees; the Moon is then in opposition with the Sun.Lunar eclipses can only occur at...

 when the sun, moon and Earth form a line (a condition known as syzygy
Syzygy (astronomy)
In astronomy, a syzygy is a straight line configuration of three celestial bodies in a gravitational system. The word is usually used in reference to the Sun, the Earth and either the Moon or a planet, where the latter is in conjunction or opposition. Solar and lunar eclipses occur at times of...

) the tidal force
Tidal force
The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...

 due to the sun reinforces that due to the moon. The tide's range is then at its maximum: this is called the spring tide, or just springs. It is not named after the season
Spring (season)
Spring is one of the four temperate seasons, the transition period between winter and summer. Spring and "springtime" refer to the season, and broadly to ideas of rebirth, renewal and regrowth. The specific definition of the exact timing of "spring" varies according to local climate, cultures and...

 but, like that word, derives from an earlier meaning of "jump, burst forth, rise" as in a natural spring
Spring (hydrosphere)
A spring—also known as a rising or resurgence—is a component of the hydrosphere. Specifically, it is any natural situation where water flows to the surface of the earth from underground...

.

When the moon is at first quarter or third quarter, the sun and moon are separated by 90° when viewed from the Earth, and the solar tidal force partially cancels the moon's. At these points in the lunar cycle, the tide's range is at its minimum: this is called the neap tide, or neaps (a word of uncertain origin). Spring tides result in high waters that are higher than average, low waters that are lower than average, 'slack water
Slack water
Slack water, which used to be known as 'The stand of the tide', is a short period in a body of tidal water either side of high water or low water essentially when the water is completely unstressed, and therefore with no rise or fall of the tide and no movement either way in the tidal stream, and...

' time that is shorter than average and stronger tidal currents than average. Neaps result in less extreme tidal conditions. There is about a seven-day interval between springs and neaps.

Lunar altitude



The changing distance separating the moon and Earth also affects tide heights. When the moon is at perigee
Perigee
Perigee is the point at which an object makes its closest approach to the Earth.. Often the term is used in a broader sense to define the point in an orbit where the orbiting body is closest to the body it orbits. The opposite is the apogee, the farthest or highest point.The Greek prefix "peri"...

, the range increases, and when it is at apogee, the range shrinks. Every 7½ lunation
Lunation
Lunation is the mean time for one lunar phase cycle .  It is on average 29.530589 days, or 29 days 12 hours 44 minutes and 3 seconds...

s (the full cycles from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range. If a storm happens to be moving onshore at this time, the consequences (property damage, etc.) can be severe.

Bathymetry


The shape of the shoreline and the ocean floor changes the way that tides propagate, so there is no simple, general rule that predicts the time of high water from the moon's position in the sky. Coastal characteristics such as underwater bathymetry
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

 and coastline shape mean that individual location characteristics affect tide forecasting; actual high water time and height may differ from model predictions due to the coastal morphology's effects on tidal flow. However, for a given location the relationship between lunar altitude and the time of high or low tide (the lunitidal interval
Lunitidal interval
The lunitidal interval, measures the time lag from the moon passing overhead, to the next high or low tide. It is also called the high water interval /Tides are known to be mainly caused by the moon's gravity...

) is relatively constant and predictable, as is the time of high or low tide relative to other points on the same coast. For example, the high tide at Norfolk, Virginia
Norfolk, Virginia
Norfolk is an independent city in the Commonwealth of Virginia in the United States. With a population of 242,803 as of the 2010 Census, it is Virginia's second-largest city behind neighboring Virginia Beach....

, predictably occurs approximately two and a half hours before the moon passes directly overhead.

Land masses and ocean basins act as barriers against water moving freely around the globe, and their varied shapes and sizes affect the size of tidal frequencies. As a result, tidal patterns vary. For example, in the U.S., the East coast has predominantly semi-diurnal tides, as do Europe's Atlantic coasts, while the West coast predominantly has mixed tides.

Other constituents


These include solar gravitational effects, the obliquity (tilt) of the Earth's equator and rotational axis, the inclination of the plane of the lunar orbit and the elliptical shape of the Earth's orbit of the sun.

A compound tide (or overtide) results from the shallow-water interaction of its two parent waves.

Phase and amplitude



Because the M2 tidal constituent dominates in most locations, the stage or phase of a tide, denoted by the time in hours after high water, is a useful concept. Tidal stage is also measured in degrees, with 360° per tidal cycle. Lines of constant tidal phase are called cotidal lines, which are analogous to contour lines of constant altitude on topographical maps. High water is reached simultaneously along the cotidal lines extending from the coast out into the ocean, and cotidal lines (and hence tidal phases) advance along the coast. Semi-diurnal and long phase constituents are measured from high water, diurnal from maximum flood tide. This and the discussion that follows is precisely true only for a single tidal constituent.

For an ocean in the shape of a circular basin enclosed by a coastline, the cotidal lines point radially inward and must eventually meet at a common point, the amphidromic point
Amphidromic point
An amphidromic point is a point within a tidal system where the tidal range is almost zero. The tidal range is zero at the amphidromic point and increases with distance from this point...

. The amphidromic point is at once cotidal with high and low waters, which is satisfied by zero tidal motion. (The rare exception occurs when the tide encircles an island, as it does around New Zealand
New Zealand
New Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...

, Iceland
Iceland
Iceland , described as the Republic of Iceland, is a Nordic and European island country in the North Atlantic Ocean, on the Mid-Atlantic Ridge. Iceland also refers to the main island of the country, which contains almost all the population and almost all the land area. The country has a population...

 and Madagascar
Madagascar
The Republic of Madagascar is an island country located in the Indian Ocean off the southeastern coast of Africa...

.) Tidal motion generally lessens moving away from continental coasts, so that crossing the cotidal lines are contours of constant amplitude (half the distance between high and low water) which decrease to zero at the amphidromic point. For a semi-diurnal tide the amphidromic point can be thought of roughly like the center of a clock face, with the hour hand pointing in the direction of the high water cotidal line, which is directly opposite the low water cotidal line. High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. This rotation is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere, and is caused by the Coriolis effect
Coriolis effect
In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right...

. The difference of cotidal phase from the phase of a reference tide is the epoch. The reference tide is the hypothetical constituent equilibrium tide on a landless Earth measured at 0° longitude, the Greenwich meridian.

In the North Atlantic, because the cotidal lines circulate counterclockwise around the amphidromic point, the high tide passes New York Harbor approximately an hour ahead of Norfolk Harbor. South of Cape Hatteras the tidal forces are more complex, and cannot be predicted reliably based on the North Atlantic cotidal lines.

History of tidal physics


Tidal physics was important in the early development of heliocentrism
Heliocentrism
Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around a stationary Sun at the center of the universe. The word comes from the Greek . Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center...

  and celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...

, with the existence of two daily tides being explained by the moon's gravity. Later the daily tides were explained more precisely by the interaction of the moon's gravity and the sun's gravity to cause the variation of tides.

An early explanation of tides was given by Galileo Galilei in his 1632 Dialogue Concerning the Two Chief World Systems
Dialogue Concerning the Two Chief World Systems
The Dialogue Concerning the Two Chief World Systems was a 1632 Italian language book by Galileo Galilei comparing the Copernican system with the traditional Ptolemaic system. It was translated to Latin as Systema cosmicum in 1635 by Matthias Bernegger...

, whose working title was Dialogue on the Tides. However, the resulting theory was incorrect – he attributed the tides to water sloshing due to the Earth's movement around the sun, hoping to provide mechanical proof of the Earth's movement – and the value of the theory is disputed, as discussed there. At the same time Johannes Kepler
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...

 correctly suggested that the moon caused the tides, based upon ancient observation and correlations, an explanation which was rejected by Galileo. It was originally mentioned in Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...

's Tetrabiblos
Tetrabiblos
The Tetrabiblos , also known under the Latin title Quadripartitum , is a text on the philosophy and practice of astrology, written in the second century AD by the Alexandrian scholar Claudius Ptolemy ....

 as being derived from ancient observation.

Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 (1642–1727) was the first person to explain tides by the gravitational attraction of masses. His explanation of the tides (and many other phenomena) was published in the Principia
Philosophiae Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726...

 (1687). and used his theory of universal gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

 to account for the tide-generating forces as due to the lunar and solar attractions.
Newton and others before Pierre-Simon Laplace
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...

 worked with an equilibrium theory, largely concerned with an approximation that describes the tides that would occur in a non-inertial ocean evenly covering the whole Earth. The tide-generating force (or its corresponding potential
Scalar potential
A scalar potential is a fundamental concept in vector analysis and physics . The scalar potential is an example of a scalar field...

) is still relevant to tidal theory, but as an intermediate quantity rather than as a final result; theory has to consider also the Earth's accumulated dynamic tidal response to the force, a response that is influenced by bathymetry
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

, Earth's rotation, and other factors.

In 1740, the Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides. Daniel Bernoulli
Daniel Bernoulli
Daniel Bernoulli was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics...

, Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...

, Colin Maclaurin
Colin Maclaurin
Colin Maclaurin was a Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series, a special case of the Taylor series, are named after him....

 and Antoine Cavalleri shared the prize.

Maclaurin used Newton’s theory to show that a smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is a prolate spheroid (essentially a three dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth's rotational effects
Coriolis effect
In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right...

 on motion. Euler realized that the tidal force's horizontal component (more than the vertical) drives the tide. In 1744 Jean le Rond d'Alembert
Jean le Rond d'Alembert
Jean-Baptiste le Rond d'Alembert was a French mathematician, mechanician, physicist, philosopher, and music theorist. He was also co-editor with Denis Diderot of the Encyclopédie...

 studied tidal equations for the atmosphere which did not include rotation.

Pierre-Simon Laplace formulated a system of partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. The Laplace tidal equations are still in use today. William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...

, rewrote Laplace's equations in terms of vorticity which allowed for solutions describing tidally driven coastally trapped waves, known as Kelvin wave
Kelvin wave
A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the phase speed of the wave crests is equal to the...

s.

Others including Kelvin and Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...

 further developed Laplace's theory. Based on these developments and the lunar theory
Lunar theory
Lunar theory attempts to account for the motions of the Moon. There are many irregularities in the Moon's motion, and many attempts have been made over a long history to account for them. After centuries of being heavily problematic, the lunar motions are nowadays modelled to a very high degree...

 of E W Brown
Ernest William Brown
Ernest William Brown FRS was a British mathematician and astronomer, who spent the majority of his career working in the United States....

 describing the motions of the moon, Arthur Thomas Doodson
Arthur Thomas Doodson
-Biography:He was born at Boothstown, Salford, the son of cotton-mill manager Thomas Doodson. He was educated at Rochdale secondary school and then in 1908 entered Liverpool University, graduating in both chemistry and mathematics . He was profoundly deaf and found it difficult to get a job but...

 developed and published in 1921 the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies. Some of his methods remain in use.

Forces


The tidal force
Tidal force
The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...

 produced by a massive object (moon, hereafter) on a small particle located on or in an extensive body (Earth, hereafter) is the vector difference between the gravitational force exerted by the moon on the particle, and the gravitational force that would be exerted on the particle if it were located at the Earth's center of mass. Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).
The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the sun is on average 389 times farther from the Earth, its field gradient is weaker. The solar tidal force is 46% as large as the lunar. More precisely, the lunar tidal acceleration (along the moon-Earth axis, at the Earth's surface) is about 1.1 × 10−7 g, while the solar tidal acceleration (along the sun-Earth axis, at the Earth's surface) is about 0.52 × 10−7 g, where g is the gravitational acceleration
Standard gravity
Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...

 at the Earth's surface. Venus has the largest effect of the other planets, at 0.000113 times the solar effect.

Tidal forces can also be analysed this way: each point of the Earth experiences the moon's radially decreasing gravity differently; they are subject to the tidal forces of Figure 6, which dominate. Finally, most importantly, only the tidal forces' horizontal components actually tidally accelerate the water particles since there is small resistance. The tidal force on a particle equals about one ten millionth that of Earth's gravitational force.

The ocean's surface is closely approximated by an equipotential surface, (ignoring ocean currents) commonly referred to as the geoid
Geoid
The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest , and extended through the continents . According to C.F...

. Since the gravitational force is equal to the potential's gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

, there are no tangent
Tangent
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

ial forces on such a surface, and the ocean surface is thus in gravitational equilibrium. Now consider the effect of massive external bodies such as the moon and sun. These bodies have strong gravitational fields that diminish with distance in space and which act to alter the shape of an equipotential surface on the Earth. This deformation has a fixed spatial orientation relative to the influencing body. The Earth's rotation relative to this shape causes the daily tidal cycle. Gravitational forces follow an inverse-square law
Inverse-square law
In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....

 (force is inversely proportional to the square of the distance), but tidal forces are inversely proportional to the cube
Cube (arithmetic)
In arithmetic and algebra, the cube of a number n is its third power — the result of the number multiplying by itself three times:...

 of the distance. The ocean surface moves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, which occurs on the part of the Earth nearest to and furthest from the moon. When the tidal equipotential changes, the ocean surface is no longer aligned with it, so that the apparent direction of the vertical shifts. The surface then experiences a down slope, in the direction that the equipotential has risen.

Laplace's tidal equations


Ocean depths are much smaller than their horizontal extent. Thus, the response to tidal forcing can be modelled using the Laplace tidal equations which incorporate the following features:
  1. The vertical (or radial) velocity is negligible, and there is no vertical shear
    Wind shear
    Wind shear, sometimes referred to as windshear or wind gradient, is a difference in wind speed and direction over a relatively short distance in the atmosphere...

    —this is a sheet flow.
  2. The forcing is only horizontal (tangent
    Tangent
    In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

    ial).
  3. The Coriolis effect
    Coriolis effect
    In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right...

     appears as a fictitious lateral forcing proportional to velocity.
  4. The surface height's rate of change is proportional to the negative divergence of velocity multiplied by the depth. As the horizontal velocity stretches or compresses the ocean as a sheet, the volume thins or thickens, respectively.


The boundary conditions dictate no flow across the coastline and free slip at the bottom.

The Coriolis effect steers waves to the right in the northern hemisphere and to the left in the southern allowing coastally trapped waves. Finally, a dissipation term can be added which is an analog to viscosity.

Amplitude and cycle time


The theoretical amplitude of oceanic tides caused by the moon is about 54 centimetres (21.3 in) at the highest point, which corresponds to the amplitude that would be reached if the ocean possessed a uniform depth, there were no landmasses, and the Earth were rotating in step with the moon's orbit. The sun similarly causes tides, of which the theoretical amplitude is about 25 centimetres (9.8 in) (46% of that of the moon) with a cycle time of 12 hours. At spring tide the two effects add to each other to a theoretical level of 79 centimetres (31.1 in), while at neap tide the theoretical level is reduced to 29 centimetres (11.4 in). Since the orbits of the Earth about the sun, and the moon about the Earth, are elliptical, tidal amplitudes change somewhat as a result of the varying Earth–sun and Earth–moon distances. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the moon and ±5% for the sun. If both the sun and moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach 93 centimetres (36.6 in).

Real amplitudes differ considerably, not only because of depth variations and continental obstacles, but also because wave propagation across the ocean has a natural period of the same order of magnitude as the rotation period: if there were no land masses, it would take about 30 hours for a long wavelength surface wave to propagate along the equator halfway around the Earth (by comparison, the Earth's lithosphere
Lithosphere
The lithosphere is the rigid outermost shell of a rocky planet. On Earth, it comprises the crust and the portion of the upper mantle that behaves elastically on time scales of thousands of years or greater.- Earth's lithosphere :...

 has a natural period of about 57 minutes). Earth tide
Earth tide
Earth tide is the sub-meter motion of the Earth of about 12 hours or longer caused by Moon and Sun gravitation, also called body tide which is the largest contribution globally. The largest body tide contribution is from the semidiurnal constituents, but there are also significant diurnal...

s, which raise and lower the bottom of the ocean, and the tide's own gravitational self attraction are both significant and further complicate the ocean's response to tidal forces.

Dissipation


Earth's tidal oscillations introduce dissipation at an average
Average
In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....

 rate of about 3.75 terawatt.
About 98% of this dissipation is by marine tidal movement.
Dissipation arises as basin-scale tidal flows drive smaller-scale flows which experience turbulent dissipation. This tidal drag creates torque on the moon that gradually transfers angular momentum to its orbit, and a gradual increase in Earth–moon separation. The equal and opposite torque on the Earth correspondingly decreases its rotational velocity. Thus, over geologic time, the moon recedes from the Earth, at about 3.8 centimetres (1.5 in)/year, lengthening the terrestrial day.
Day length has increased
Tidal acceleration
Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite , and the primary planet that it orbits . The "acceleration" is usually negative, as it causes a gradual slowing and recession of a satellite in a prograde orbit away from the primary, and a corresponding...

 by about 2 hours in the last 600 million years. Assuming (as a crude approximation) that the deceleration rate has been constant, this would imply that 70 million years ago, day length was on the order of 1% shorter with about 4 more days per year.

History


From ancient times, tidal observation and discussion has increased in sophistication, first marking the daily recurrence, then tides' relationship to the sun and moon. Pytheas
Pytheas
Pytheas of Massalia or Massilia , was a Greek geographer and explorer from the Greek colony, Massalia . He made a voyage of exploration to northwestern Europe at about 325 BC. He travelled around and visited a considerable part of Great Britain...

 travelled to the British Isles
British Isles
The British Isles are a group of islands off the northwest coast of continental Europe that include the islands of Great Britain and Ireland and over six thousand smaller isles. There are two sovereign states located on the islands: the United Kingdom of Great Britain and Northern Ireland and...

 about 325 BC and seems to be the first to have related spring tides to the phase of the moon.

In the 2nd century BC, the Babylonian astronomer, Seleucus of Seleucia
Seleucus of Seleucia
Seleucus of Seleucia was a Hellenistic astronomer and philosopher. Coming from Seleucia on the Tigris, the capital of the Seleucid empire, or, alternatively, Seleukia on the Red Sea, he is best known as a proponent of heliocentrism and for his theory of the origin of tides.- Heliocentric theory...

, correctly described the phenomenon of tides in order to support his heliocentric
Heliocentrism
Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around a stationary Sun at the center of the universe. The word comes from the Greek . Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center...

 theory. He correctly theorized that tides were caused by the moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

, although he believed that the interaction was mediated by the pneuma
Pneuma
Pneuma is an ancient Greek word for "breath," and in a religious context for "spirit" or "soul." It has various technical meanings for medical writers and philosophers of classical antiquity, particularly in regard to physiology, and is also used in Greek translations of the Hebrew Bible and in...

. He noted that tides varied in time and strength in different parts of the world. According to Strabo
Strabo
Strabo, also written Strabon was a Greek historian, geographer and philosopher.-Life:Strabo was born to an affluent family from Amaseia in Pontus , a city which he said was situated the approximate equivalent of 75 km from the Black Sea...

 (1.1.9), Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the moon's position relative to the sun.

In China, Wang Chong
Wang Chong
Wang Chong , courtesy name Zhongren , was a Chinese philosopher active during the Han Dynasty. He developed a rational, secular, naturalistic and mechanistic account of the world and of human beings and gave a materialistic explanation of the origin of the universe. His main work was the Lùnhéng...

 (27–100 AD) correlated tide to the moon's movement in the book entitled Lunheng
Lunheng
The Lunheng is a wide-ranging Chinese classic text containing critical essays by Wang Chong on natural science, Chinese mythology, philosophy, and literature.-Title:...

. He noted that "tide's rise and fall follow the moon and vary in magnitude."

The Naturalis Historia of Pliny the Elder
Pliny the Elder
Gaius Plinius Secundus , better known as Pliny the Elder, was a Roman author, naturalist, and natural philosopher, as well as naval and army commander of the early Roman Empire, and personal friend of the emperor Vespasian...

 collates many tidal observations, e.g., the spring tides are a few days after (or before) new and full moon and are highest around the equinoxes, though Pliny noted many relationships now regarded as fanciful. In his Geography, Strabo described tides in the Persian Gulf
Persian Gulf
The Persian Gulf, in Southwest Asia, is an extension of the Indian Ocean located between Iran and the Arabian Peninsula.The Persian Gulf was the focus of the 1980–1988 Iran-Iraq War, in which each side attacked the other's oil tankers...

 having their greatest range when the moon was furthest from the plane of the equator. All this despite the relatively small amplitude of Mediterranean basin tides. (The strong currents through the Strait of Messina
Strait of Messina
The Strait of Messina is the narrow passage between the eastern tip of Sicily and the southern tip of Calabria in the south of Italy. It connects the Tyrrhenian Sea with the Ionian Sea, within the central Mediterranean...

 and between Greece
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....

 and the island of Euboea
Euboea
Euboea is the second largest Greek island in area and population, after Crete. The narrow Euripus Strait separates it from Boeotia in mainland Greece. In general outline it is a long and narrow, seahorse-shaped island; it is about long, and varies in breadth from to...

 through the Euripus puzzled Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

). Philostratus
Philostratus
Philostratus or Lucius Flavius Philostratus , , called "the Athenian", was a Greek sophist of the Roman imperial period. His father was a minor sophist of the same name. He was born probably around 172, and is said by the Suda to have been living in the reign of emperor Philip the Arab . His death...

 discussed tides in Book Five of The Life of Apollonius of Tyana
Apollonius of Tyana
Apollonius of Tyana was a Greek Neopythagorean philosopher from the town of Tyana in the Roman province of Cappadocia in Asia Minor. Little is certainly known about him...

. Philostratus mentions the moon, but attributes tides to "spirits". In Europe around 730 AD, the Venerable Bede
Bede
Bede , also referred to as Saint Bede or the Venerable Bede , was a monk at the Northumbrian monastery of Saint Peter at Monkwearmouth, today part of Sunderland, England, and of its companion monastery, Saint Paul's, in modern Jarrow , both in the Kingdom of Northumbria...

 described how the rising tide on one coast of the British Isles coincided with the fall on the other and described the time progression of high water along the Northumbrian coast.

In the 9th century, the Arabian earth-scientist
Islamic geography
Geography and cartography in medieval Islam refers to the advancement of geography, cartography and the earth sciences in the medieval Islamic civilization....

, Al-Kindi
Al-Kindi
' , known as "the Philosopher of the Arabs", was a Muslim Arab philosopher, mathematician, physician, and musician. Al-Kindi was the first of the Muslim peripatetic philosophers, and is unanimously hailed as the "father of Islamic or Arabic philosophy" for his synthesis, adaptation and promotion...

 (Alkindus), wrote a treatise entitled Risala fi l-Illa al-Failali l-Madd wa l-Fazr (Treatise on the Efficient Cause of the Flow and Ebb), in which he presents an argument on tides which "depends on the changes which take place in bodies owing to the rise and fall of temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

." He describes a precise laboratory
Laboratory
A laboratory is a facility that provides controlled conditions in which scientific research, experiments, and measurement may be performed. The title of laboratory is also used for certain other facilities where the processes or equipment used are similar to those in scientific laboratories...

 experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

 that proved his argument.

The first tide table in China
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...

 was recorded in 1056 AD primarily for visitors wishing to see the famous tidal bore
Tidal bore
A tidal bore is a tidal phenomenon in which the leading edge of the incoming tide forms a wave of water that travel up a river or narrow bay against the direction of the river or bay's current...

 in the Qiantang River
Qiantang River
The Qiantang River is a southeast Chinese river that originates in the borders of Anhui and Jiangxi provinces and passes through Hangzhou, the capital of Zhejiang province, before flowing into the East China Sea through Hangzhou Bay....

. The first known British tide table is thought to be that of John Wallingford, who died Abbot of St. Albans in 1213, based on high water occurring 48 minutes later each day, and three hours earlier at the Thames mouth than upriver at London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...

.

William Thomson (Lord Kelvin)
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...

 led the first systematic harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...

 of tidal records starting in 1867. The main result was the building of a tide-predicting machine
Tide-predicting machine
A tide-predicting machine was a special-purpose mechanical analog computer of the late 19th and early 20th centuries, constructed and set up to predict the ebb and flow of sea tides and the irregular variations in their heights – which change in mixtures of rhythms, that never repeat...

 using a system of pulleys to add together six harmonic time functions. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machines were used until the 1960s.

The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary
Thames Estuary
The Thames Mouth is the estuary in which the River Thames meets the waters of the North Sea.It is not easy to define the limits of the estuary, although physically the head of Sea Reach, near Canvey Island on the Essex shore is probably the western boundary...

. Many large ports had automatic tide gage stations by 1850.

William Whewell
William Whewell
William Whewell was an English polymath, scientist, Anglican priest, philosopher, theologian, and historian of science. He was Master of Trinity College, Cambridge.-Life and career:Whewell was born in Lancaster...

 first mapped co-tidal lines ending with a nearly global chart in 1836. In order to make these maps consistent, he hypothesized the existence of amphidromes where co-tidal lines meet in the mid-ocean. These points of no tide were confirmed by measurement in 1840 by Captain Hewett, RN, from careful soundings in the North Sea.

Timing



There is a delay between the phases of the moon and the effect on the tide. Springs and neaps in the North Sea
North Sea
In the southwest, beyond the Straits of Dover, the North Sea becomes the English Channel connecting to the Atlantic Ocean. In the east, it connects to the Baltic Sea via the Skagerrak and Kattegat, narrow straits that separate Denmark from Norway and Sweden respectively...

, for example, are two days behind the new/full moon and first/third quarter moon. This is called the tide's age.

The local bathymetry
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

 greatly influences the tide's exact time and height at a particular coast
Coast
A coastline or seashore is the area where land meets the sea or ocean. A precise line that can be called a coastline cannot be determined due to the dynamic nature of tides. The term "coastal zone" can be used instead, which is a spatial zone where interaction of the sea and land processes occurs...

al point. There are some extreme cases: the Bay of Fundy
Bay of Fundy
The Bay of Fundy is a bay on the Atlantic coast of North America, on the northeast end of the Gulf of Maine between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine...

, on the east coast of Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

, features the world's largest well-documented tidal ranges, 17 metres (55.8 ft) because of its shape. Some experts believe Ungava Bay
Ungava Bay
Ungava Bay is a large bay in northeastern Canada separating Nunavik from Baffin Island. The bay is shaped like a rounded square with a side length of about and has an area of approximately...

 in northern Quebec
Quebec
Quebec or is a province in east-central Canada. It is the only Canadian province with a predominantly French-speaking population and the only one whose sole official language is French at the provincial level....

 to have even higher tidal ranges, but it is free of pack ice for only about four months every year, while the Bay of Fundy rarely freezes.

Southampton
Southampton
Southampton is the largest city in the county of Hampshire on the south coast of England, and is situated south-west of London and north-west of Portsmouth. Southampton is a major port and the closest city to the New Forest...

 in the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

 has a double high water caused by the interaction between the region's different tidal harmonics, caused primarily by the east/west orientation of the English Channel
English Channel
The English Channel , often referred to simply as the Channel, is an arm of the Atlantic Ocean that separates southern England from northern France, and joins the North Sea to the Atlantic. It is about long and varies in width from at its widest to in the Strait of Dover...

 and the fact that when it is high water at Dover
Strait of Dover
The Strait of Dover or Dover Strait is the strait at the narrowest part of the English Channel. The shortest distance across the strait is from the South Foreland, 6 kilometres northeast of Dover in the county of Kent, England, to Cap Gris Nez, a cape near to Calais in the French of...

 it is low water at Land's End
Land's End
Land's End is a headland and small settlement in west Cornwall, England, within the United Kingdom. It is located on the Penwith peninsula approximately eight miles west-southwest of Penzance....

 (some 300 nautical miles distant) and vice versa. This is contrary to the popular belief that the flow of water around the Isle of Wight
Isle of Wight
The Isle of Wight is a county and the largest island of England, located in the English Channel, on average about 2–4 miles off the south coast of the county of Hampshire, separated from the mainland by a strait called the Solent...

 creates two high waters. The Isle of Wight is important, however, since it is responsible for the 'Young Flood Stand', which describes the pause of the incoming tide about three hours after low water.

Because the oscillation modes of the Mediterranean Sea
Mediterranean Sea
The Mediterranean Sea is a sea connected to the Atlantic Ocean surrounded by the Mediterranean region and almost completely enclosed by land: on the north by Anatolia and Europe, on the south by North Africa, and on the east by the Levant...

 and the Baltic Sea
Baltic Sea
The Baltic Sea is a brackish mediterranean sea located in Northern Europe, from 53°N to 66°N latitude and from 20°E to 26°E longitude. It is bounded by the Scandinavian Peninsula, the mainland of Europe, and the Danish islands. It drains into the Kattegat by way of the Øresund, the Great Belt and...

 do not coincide with any significant astronomical forcing period, the largest tides are close to their narrow connections with the Atlantic Ocean. Extremely small tides also occur for the same reason in the Gulf of Mexico
Gulf of Mexico
The Gulf of Mexico is a partially landlocked ocean basin largely surrounded by the North American continent and the island of Cuba. It is bounded on the northeast, north and northwest by the Gulf Coast of the United States, on the southwest and south by Mexico, and on the southeast by Cuba. In...

 and Sea of Japan
Sea of Japan
The Sea of Japan is a marginal sea of the western Pacific Ocean, between the Asian mainland, the Japanese archipelago and Sakhalin. It is bordered by Japan, North Korea, Russia and South Korea. Like the Mediterranean Sea, it has almost no tides due to its nearly complete enclosure from the Pacific...

. Elsewhere, as along the southern coast of Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

, low tides can be due to the presence of a nearby amphidrome (see figure 4).

Analysis



Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's theory of gravitation first enabled an explanation of why there were generally two tides a day, not one, and offered hope for detailed understanding. Although it may seem that tides could be predicted via a sufficiently detailed knowledge of the instantaneous astronomical forcings, the actual tide at a given location is determined by astronomical forces accumulated over many days. Precise results require detailed knowledge of the shape of all the ocean basins—their bathymetry
Bathymetry
Bathymetry is the study of underwater depth of lake or ocean floors. In other words, bathymetry is the underwater equivalent to hypsometry. The name comes from Greek βαθύς , "deep", and μέτρον , "measure"...

 and coastline shape.

Current procedure for analysing tides follows the method of harmonic analysis introduced in the 1860s by William Thomson. It is based on the principle that the astronomical theories of the motions of sun and moon determine a large number of component frequencies, and at each frequency there is a component of force tending to produce tidal motion, but that at each place of interest on the Earth, the tides respond at each frequency with an amplitude and phase peculiar to that locality. At each place of interest, the tide heights are therefore measured for a period of time sufficiently long (usually more than a year in the case of a new port not previously studied) to enable the response at each significant tide-generating frequency to be distinguished by analysis, and to extract the tidal constants for a sufficient number of the strongest known components of the astronomical tidal forces to enable practical tide prediction. The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component. Because astronomical frequencies and phases can be calculated with certainty, the tide height at other times can then be predicted once the response to the harmonic components of the astronomical tide-generating forces has been found.

The main patterns in the tides are
  • the twice-daily variation
  • the difference between the first and second tide of a day
  • the spring–neap cycle
  • the annual variation

The Highest Astronomical Tide is the perigean spring tide when both the sun and the moon are closest to the Earth.

When confronted by a periodically varying function, the standard approach is to employ Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...

, a form of analysis that uses sinusoidal functions as a basis set, having frequencies that are zero, one, two, three, etc. times the frequency of a particular fundamental cycle. These multiples are called harmonics of the fundamental frequency, and the process is termed harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...

. If the basis set of sinusoidal functions suit the behaviour being modelled, relatively few harmonic terms need to be added. Orbital paths are very nearly circular, so sinusoidal variations are suitable for tides.

For the analysis of tide heights, the Fourier series approach has in practice to be made more elaborate than the use of a single frequency and its harmonics. The tidal patterns are decomposed into many sinusoids having many fundamental frequencies, corresponding (as in the lunar theory) to many different combinations of the motions of the Earth, the moon, and the angles that define the shape and location of their orbits.

For tides, then, harmonic analysis is not limited to harmonics of a single frequency. In other words, the harmonies are multiples of many fundamental frequencies, not just of the fundamental frequency of the simpler Fourier series approach. Their representation as a Fourier series having only one fundamental frequency and its (integer) multiples would require many terms, and would be severely limited in the time-range for which it would be valid.

The study of tide height by harmonic analysis was begun by Laplace, William Thomson (Lord Kelvin), and George Darwin
George Darwin
Sir George Howard Darwin, FRS was an English astronomer and mathematician.-Biography:Darwin was born at Down House, Kent, the second son and fifth child of Charles and Emma Darwin...

. A.T. Doodson
Arthur Thomas Doodson
-Biography:He was born at Boothstown, Salford, the son of cotton-mill manager Thomas Doodson. He was educated at Rochdale secondary school and then in 1908 entered Liverpool University, graduating in both chemistry and mathematics . He was profoundly deaf and found it difficult to get a job but...

 extended their work, introducing the Doodson Number notation to organise the hundreds of resulting terms. This approach has been the international standard ever since, and the complications arise as follows: the tide-raising force is notionally given by sums of several terms. Each term is of the form
A·cos(w·t + p)

where A is the amplitude, w is the angular frequency usually given in degrees per hour corresponding to t measured in hours, and p is the phase offset with regard to the astronomical state at time t = 0 . There is one term for the moon and a second term for the sun. The phase p of the first harmonic for the moon term is called the lunitidal interval
Lunitidal interval
The lunitidal interval, measures the time lag from the moon passing overhead, to the next high or low tide. It is also called the high water interval /Tides are known to be mainly caused by the moon's gravity...

 or high water interval. The next step is to accommodate the harmonic terms due to the elliptical shape of the orbits. Accordingly, the value of A is not a constant but also varying with time, slightly, about some average figure. Replace it then by A(t) where A is another sinusoid, similar to the cycles and epicycles of Ptolemaic theory
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...

. Accordingly,
A(t) = A·(1 + Aa·cos(wa·t + pa)) ,

which is to say an average value A with a sinusoidal variation about it of magnitude Aa , with frequency wa and phase pa . Thus the simple term is now the product of two cosine factors:
A·[1 + Aa·cos(wa + pa)]·cos(w·t + p)


Given that for any x and y
cos(x)·cos(y) = ½·cos( x + y ) + ½·cos( x–y ) ,

it is clear that a compound term involving the product of two cosine terms each with their own frequency is the same as three simple cosine terms that are to be added at the original frequency and also at frequencies which are the sum and difference of the two frequencies of the product term. (Three, not two terms, since the whole expression is (1 + cos(x))·cos(y) .) Consider further that the tidal force on a location depends also on whether the moon (or the sun) is above or below the plane of the equator, and that these attributes have their own periods also incommensurable with a day and a month, and it is clear that many combinations result. With a careful choice of the basic astronomical frequencies, the Doodson Number annotates the particular additions and differences to form the frequency of each simple cosine term.

Remember that astronomical tides do not include weather effects. Also, changes to local conditions (sandbank movement, dredging harbour mouths, etc.) away from those prevailing at the measurement time affect the tide's actual timing and magnitude. Organisations quoting a "highest astronomical tide" for some location may exaggerate the figure as a safety factor against analytical uncertainties, distance from the nearest measurement point, changes since the last observation time, ground subsidence, etc., to avert liability should an engineering work be overtopped. Special care is needed when assessing the size of a "weather surge" by subtracting the astronomical tide from the observed tide.

Careful Fourier data analysis
Data analysis
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making...

 over a nineteen-year period (the National Tidal Datum Epoch in the U.S.) uses frequencies called the tidal harmonic constituents. Nineteen years is preferred because the Earth, moon and sun's relative positions repeat almost exactly in the Metonic cycle
Metonic cycle
In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...

 of 19 years, which is long enough to include the 18.613 year lunar nodal tidal constituent. This analysis can be done using only the knowledge of the forcing period, but without detailed understanding of the mathematical derivation, which means that useful tidal tables have been constructed for centuries. The resulting amplitudes and phases can then be used to predict the expected tides. These are usually dominated by the constituents near 12 hours (the semi-diurnal constituents), but there are major constituents near 24 hours (diurnal) as well. Longer term constituents are 14 day or fortnightly, monthly, and semiannual. Semi-diurnal tides dominated coastline, but some areas such as the South China Sea
South China Sea
The South China Sea is a marginal sea that is part of the Pacific Ocean, encompassing an area from the Singapore and Malacca Straits to the Strait of Taiwan of around...

 and the Gulf of Mexico
Gulf of Mexico
The Gulf of Mexico is a partially landlocked ocean basin largely surrounded by the North American continent and the island of Cuba. It is bounded on the northeast, north and northwest by the Gulf Coast of the United States, on the southwest and south by Mexico, and on the southeast by Cuba. In...

 are primarily diurnal. In the semi-diurnal areas, the primary constituents M2 (lunar) and S2 (solar) periods differ slightly, so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period).

In the M2 plot above, each cotidal line differs by one hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich. The lines rotate around the amphidromic point
Amphidromic point
An amphidromic point is a point within a tidal system where the tidal range is almost zero. The tidal range is zero at the amphidromic point and increases with distance from this point...

s counterclockwise in the northern hemisphere so that from Baja California Peninsula
Baja California Peninsula
The Baja California peninsula , is a peninsula in northwestern Mexico. Its land mass separates the Pacific Ocean from the Gulf of California. The Peninsula extends from Mexicali, Baja California in the north to Cabo San Lucas, Baja California Sur in the south.The total area of the Baja California...

 to Alaska
Alaska
Alaska is the largest state in the United States by area. It is situated in the northwest extremity of the North American continent, with Canada to the east, the Arctic Ocean to the north, and the Pacific Ocean to the west and south, with Russia further west across the Bering Strait...

 and from France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 to Ireland
Ireland
Ireland is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth...

 the M2 tide propagates northward. In the southern hemisphere this direction is clockwise. On the other hand M2 tide propagates counterclockwise around New Zealand, but this is because the islands act as a dam and permit the tides to have different heights on the islands' opposite sides. (The tides do propagate northward on the east side and southward on the west coast, as predicted by theory.)

The exception is at Cook Strait
Cook Strait
Cook Strait is the strait between the North and South Islands of New Zealand. It connects the Tasman Sea on the west with the South Pacific Ocean on the east....

 where the tidal currents periodically link high to low water. This is because cotidal lines 180° around the amphidromes are in opposite phase, for example high water across from low water at each end of Cook Strait. Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so the M2 patterns cannot be used for other tide components.

Example calculation





Figure 9 shows the common pattern of two tidal peaks a day as the earth rotates under the moon; because the moon is also moving in its orbit around the earth and in the same sense as the Earth's rotation, a point on the earth must rotate slightly further to catch up so that the cycle time is not twelve but 12.4206 hours—a bit over twenty-five minutes extra. The two peaks are not equal: the twin tidal bulges beneath the moon and on the opposite side of the Earth align with the moon. Bridgeport is north of the equator, so when the moon is north of the equator also and shining upon Bridgeport, Bridgeport is closer to its maximum tide than approximately twelve hours later when Bridgeport is on the opposite side of the Earth from the moon and the high tide bulge at Bridgeport's longitude has its maximum south of the equator. Thus the two high tides a day alternate in maximum heights: lower high (just under three feet), higher high (just over three feet), and again. Likewise for the low tides.

Figure 10 shows the spring tide/neap tide cycle in tidal amplitudes as the moon orbits the Earth from being in line (sun–Earth–moon, or sun–moon–Earth) when the two main influences combine to give the spring tides, to when the two forces are opposing each other as when the angle moon–Earth–sun is close to ninety degrees, producing the neap tides. As the moon moves around its orbit it changes from north of the equator to south of the equator. The alternation in high tide heights becomes smaller, until they are the same (at the lunar equinox, the moon is above the equator), then redevelops but with the other polarity, waxing to a maximum difference and then waning again.

Figure 11 shows just over a year's worth of tidal height calculations. The sun also cycles from north to south of the equator, while the Earth–sun and Earth–moon distances change on their own cycles. None of the various cycle periods are commensurate.

Current


The tides' influence on current flow is much more difficult to analyse, and data is much more difficult to collect. A tidal height is a simple number which applies to a wide region simultaneously. A flow has both a magnitude and a direction, both of which can vary substantially with depth and over short distances due to local bathymetry. Also, although a water channel's center is the most useful measuring site, mariners object when current-measuring equipment obstructs waterways. A flow proceeding up a curved channel is the same flow, even though its direction varies continuously along the channel. Surprisingly, flood and ebb flows are often not in opposite directions. Flow direction is determined by the upstream channel's shape, not the downstream channel's shape. Likewise, eddies may form in only one flow direction.

Nevertheless, current analysis is similar to tidal analysis: in the simple case, at a given location the flood flow is in mostly one direction, and the ebb flow in another direction. Flood velocities are given positive sign, and ebb velocities negative sign. Analysis proceeds as though these are tide heights.

In more complex situations, the main ebb and flood flows do not dominate. Instead, the flow direction and magnitude trace an ellipse over a tidal cycle (on a polar plot) instead of along the ebb and flood lines. In this case, analysis might proceed along pairs of directions, with the primary and secondary directions at right angles. An alternative is to treat the tidal flows as complex numbers, as each value has both a magnitude and a direction.

Tide flow information is most commonly seen on nautical chart
Nautical chart
A nautical chart is a graphic representation of a maritime area and adjacent coastal regions. Depending on the scale of the chart, it may show depths of water and heights of land , natural features of the seabed, details of the coastline, navigational hazards, locations of natural and man-made aids...

s, presented as a table of flow speeds and bearings at hourly intervals, with separate tables for spring and neap tides. The timing is relative to high water at some harbour where the tidal behaviour is similar in pattern, though it may be far away.

As with tide height predictions, tide flow predictions based only on astronomical factors do not incorporate weather conditions, which can completely change the outcome.

The tidal flow through Cook Strait
Cook Strait
Cook Strait is the strait between the North and South Islands of New Zealand. It connects the Tasman Sea on the west with the South Pacific Ocean on the east....

 between the two main islands of New Zealand is particularly interesting, as the tides on each side of the strait are almost exactly out of phase, so that one side's high water is simultaneous with the other's low water. Strong currents result, with almost zero tidal height change in the strait's center. Yet, although the tidal surge normally flows in one direction for six hours and in the reverse direction for six hours, a particular surge might last eight or ten hours with the reverse surge enfeebled. In especially boisterous weather conditions, the reverse surge might be entirely overcome so that the flow continues in the same direction through three or more surge periods.

A further complication for Cook Strait's flow pattern is that the tide at the north side (e.g. at Nelson
Nelson, New Zealand
Nelson is a city on the eastern shores of Tasman Bay, and is the economic and cultural centre of the Nelson-Tasman region. Established in 1841, it is the second oldest settled city in New Zealand and the oldest in the South Island....

) follows the common bi-weekly spring–neap tide cycle (as found along the west side of the country), but the south side's tidal pattern has only one cycle per month, as on the east side: Wellington, and Napier
Napier, New Zealand
Napier is a New Zealand city with a seaport, located in Hawke's Bay on the eastern coast of the North Island. The population of Napier is about About 18 kilometres south of Napier is the inland city of Hastings. These two neighboring cities are often called "The Twin Cities" or "The Bay Cities"...

.

Figure 12 shows separately the high water and low water height and time, through November 2007; these are not measured values but instead are calculated from tidal parameters derived from years-old measurements. Cook Strait's nautical chart offers tidal current information. For instance the January 1979 edition for 41°13·9’S 174°29·6’E (north west of Cape Terawhiti
Cape Terawhiti
Cape Terawhiti is the southwesternmost point of the North Island of New Zealand.The cape is located 16 kilometres to the west of Wellington, the capital city of New Zealand...

) refers timings to Westport
Westport, New Zealand
-Economy:Economic activity is based around fishing, coal mining and dairy farming. Historically, gold mining was a major industry, and coal mining was much more extensive than today . However, the region still is home to New Zealand's largest opencast mining operation in Stockton...

 while the January 2004 issue refers to Wellington. Near Cape Terawhiti in the middle of Cook Strait the tidal height variation is almost nil while the tidal current reaches its maximum, especially near the notorious Karori Rip. Aside from weather effects, the actual currents through Cook Strait are influenced by the tidal height differences between the two ends of the strait and as can be seen, only one of the two spring tides at the north end (Nelson) has a counterpart spring tide at the south end (Wellington), so the resulting behaviour follows neither reference harbour.

Power generation



Tidal energy can be extracted by two means: inserting a water turbine
Turbine
A turbine is a rotary engine that extracts energy from a fluid flow and converts it into useful work.The simplest turbines have one moving part, a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades, or the blades react to the flow, so that they move and...

 into a tidal current, or building ponds that release/admit water through a turbine. In the first case, the energy amount is entirely determined by the timing and tidal current magnitude. However, the best currents may be unavailable because the turbines would obstruct ships. In the second, the impoundment dams are expensive to construct, natural water cycles are completely disrupted, ship navigation is disrupted. However, with multiple ponds, power can be generated at chosen times. So far, there are few installed systems for tidal power generation (most famously, La Rance
Rance tidal power plant
The Rance Tidal Power Station is the world's first tidal power station and also the world's second biggest tidal power station. The facility is located on the estuary of the Rance River, in Brittany, France. Opened on the 26th November 1966, it is currently operated by Électricité de France, and is...

 by Saint Malo, France) which faces many difficulties. Aside from environmental issues, simply withstanding corrosion and biological fouling pose engineering challenges.

Tidal power proponents point out that, unlike wind power systems, generation levels can be reliably predicted, save for weather effects. While some generation is possible for most of the tidal cycle, in practice turbines lose efficiency at lower operating rates. Since the power available from a flow is proportional to the cube of the flow speed, the times during which high power generation is possible are brief.

Navigation


Tidal flows are important for navigation, and significant errors in position occur if they are not accommodated. Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant draft
Draft (hull)
The draft of a ship's hull is the vertical distance between the waterline and the bottom of the hull , with the thickness of the hull included; in the case of not being included the draft outline would be obtained...

 from entering at low tide.

Until the advent of automated navigation, competence in calculating tidal effects was important to naval officers. The certificate of examination for lieutenants in the Royal Navy
Royal Navy
The Royal Navy is the naval warfare service branch of the British Armed Forces. Founded in the 16th century, it is the oldest service branch and is known as the Senior Service...

 once declared that the prospective officer was able to "shift his tides".

Tidal flow timings and velocities appear in tide charts or a tidal stream atlas. Tide charts come in sets. Each chart covers a single hour between one high water and another (they ignore the leftover 24 minutes) and show the average tidal flow for that hour. An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots) for spring and neap tides. If a tide chart is not available, most nautical charts have "tidal diamond
Tidal diamond
Tidal diamonds are symbols on British admiralty charts that indicate the direction and speed of tidal streams.The symbols consist of a letter of the Roman alphabet in a rhombus, printed in purple ink...

s" which relate specific points on the chart to a table giving tidal flow direction and speed.

The standard procedure to counteract tidal effects on navigation is to (1) calculate a "dead reckoning
Dead reckoning
In navigation, dead reckoning is the process of calculating one's current position by using a previously determined position, or fix, and advancing that position based upon known or estimated speeds over elapsed time, and course...

" position (or DR) from travel distance and direction, (2) mark the chart (with a vertical cross like a plus sign) and (3) draw a line from the DR in the tide's direction. The distance the tide moves the boat along this line is computed by the tidal speed, and this gives an "estimated position" or EP (traditionally marked with a dot in a triangle).

Nautical chart
Nautical chart
A nautical chart is a graphic representation of a maritime area and adjacent coastal regions. Depending on the scale of the chart, it may show depths of water and heights of land , natural features of the seabed, details of the coastline, navigational hazards, locations of natural and man-made aids...

s display the water's "charted depth" at specific locations with "sounding
Echo sounding
Echo sounding is the technique of using sound pulses directed from the surface or from a submarine vertically down to measure the distance to the bottom by means of sound waves. This information is then typically used for navigation purposes or in order to obtain depths for charting purposes...

s" and the use of bathymetric contour line
Contour line
A contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...

s to depict the submerged surface's shape. These depths are relative to a "chart datum
Chart datum
A chart datum is the level of water that charted depths displayed on a nautical chart are measured from. A chart datum is generally a tidal datum; that is, a datum derived from some phase of the tide...

", which is typically the water level at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during the tidal cycle. "Drying heights" may also be shown on the chart, which are the heights of the exposed seabed
Seabed
The seabed is the bottom of the ocean.- Ocean structure :Most of the oceans have a common structure, created by common physical phenomena, mainly from tectonic movement, and sediment from various sources...

 at the lowest astronomical tide.

Tide tables list each day's high and low water heights and times. To calculate the actual water depth, add the charted depth to the published tide height. Depth for other times can be derived from tidal curves published for major ports. The rule of twelfths
Rule of twelfths
The Rule of Twelfths is a rule of thumb for estimating the height of the tide at any time, given only the time and height of high and low water...

 can suffice if an accurate curve is not available. This approximation presumes that the increase in depth in the six hours between low and high water is: first hour — 1/12, second — 2/12, third — 3/12, fourth — 3/12, fifth — 2/12, sixth — 1/12.

Intertidal ecology




Intertidal ecology is the study of intertidal
Intertidal zone
The intertidal zone is the area that is above water at low tide and under water at high tide . This area can include many different types of habitats, with many types of animals like starfish, sea urchins, and some species of coral...

 ecosystem
Ecosystem
An ecosystem is a biological environment consisting of all the organisms living in a particular area, as well as all the nonliving , physical components of the environment with which the organisms interact, such as air, soil, water and sunlight....

s, where organisms live between the low and high water lines. At low water, the intertidal is exposed (or ‘emersed’) whereas at high water, the intertidal is underwater (or ‘immersed’). Intertidal ecologists therefore study the interactions between intertidal organisms and their environment, as well as among the different species
Biological interaction
Biological interactions are the effects organisms in a community have on one another. In the natural world no organism exists in absolute isolation, and thus every organism must interact with the environment and other organisms...

. The most important interactions may vary according to the type of intertidal community. The broadest classifications are based on substrates — rocky shore
Rocky shore
A rocky shore is an intertidal area of seacoasts where solid rock predominates. Rocky shores are biologically rich environments, and make the ideal natural laboratory for studying intertidal ecology and other biological processes...

 or soft bottom.

Intertidal organisms experience a highly variable and often hostile environment, and have adapted
Adaptation
An adaptation in biology is a trait with a current functional role in the life history of an organism that is maintained and evolved by means of natural selection. An adaptation refers to both the current state of being adapted and to the dynamic evolutionary process that leads to the adaptation....

 to cope with and even exploit these conditions. One easily visible feature is vertical zonation, in which the community divides into distinct horizontal bands of specific species at each elevation above low water. A species' ability to cope with desiccation
Desiccation
Desiccation is the state of extreme dryness, or the process of extreme drying. A desiccant is a hygroscopic substance that induces or sustains such a state in its local vicinity in a moderately sealed container.-Science:...

 determines its upper limit, while competition
Competition (biology)
Competition is an interaction between organisms or species, in which the fitness of one is lowered by the presence of another. Limited supply of at least one resource used by both is required. Competition both within and between species is an important topic in ecology, especially community ecology...

 with other species sets its lower limit.

Humans use
Exploitation of natural resources
Main article: OverexploitationSome exploitation of natural resources is an essential condition of the human existence. This refers primarily to food production and necessities...

 intertidal regions
Intertidal ecology
Intertidal ecology is the study of intertidal ecosystems, where organisms live between the low and high tide lines. At low tide, the intertidal is exposed whereas at high tide, the intertidal is underwater...

 for food and recreation. Overexploitation
Overexploitation
Overexploitation, also called overharvesting, refers to harvesting a renewable resource to the point of diminishing returns. Sustained overexploitation can lead to the destruction of the resource...

 can damage intertidals directly. Other anthropogenic actions such as introducing invasive species
Invasive species
"Invasive species", or invasive exotics, is a nomenclature term and categorization phrase used for flora and fauna, and for specific restoration-preservation processes in native habitats, with several definitions....

 and climate change
Global warming
Global warming refers to the rising average temperature of Earth's atmosphere and oceans and its projected continuation. In the last 100 years, Earth's average surface temperature increased by about with about two thirds of the increase occurring over just the last three decades...

 have large negative effects. Marine Protected Area
Marine Protected Area
Marine Protected Areas, like any protected area, are regions in which human activity has been placed under some restrictions in the interest of conserving the natural environment, it's surrounding waters and the occupant ecosystems, and any cultural or historical resources that may require...

s are one option communities can apply to protect these areas and aid scientific research.

Biological rhythms


The approximately fortnightly tidal cycle has large effects on intertidal organisms. Hence their biological rhythms tend to occur in rough multiples of this period. Many other animals such as the vertebrate
Vertebrate
Vertebrates are animals that are members of the subphylum Vertebrata . Vertebrates are the largest group of chordates, with currently about 58,000 species described. Vertebrates include the jawless fishes, bony fishes, sharks and rays, amphibians, reptiles, mammals, and birds...

s, display similar rhythms. Examples include gestation
Gestation
Gestation is the carrying of an embryo or fetus inside a female viviparous animal. Mammals during pregnancy can have one or more gestations at the same time ....

 and egg hatching. In humans, the menstrual cycle
Menstrual cycle
The menstrual cycle is the scientific term for the physiological changes that can occur in fertile women for the purpose of sexual reproduction. This article focuses on the human menstrual cycle....

 lasts roughly a lunar month
Lunar month
In lunar calendars, a lunar month is the time between two identical syzygies . There are many variations. In Middle-Eastern and European traditions, the month starts when the young crescent moon becomes first visible at evening after conjunction with the Sun one or two days before that evening...

, an even multiple of the tidal period. Such parallels at least hint at the common descent
Common descent
In evolutionary biology, a group of organisms share common descent if they have a common ancestor. There is strong quantitative support for the theory that all living organisms on Earth are descended from a common ancestor....

 of all animals from a marine ancestor.

Other tides


When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate internal waves with tidal frequencies. Such waves are called internal tides.

In addition to oceanic tides, large lakes can experience small tides and even planets can experience atmospheric tide
Atmospheric tide
Atmospheric tides are global-scale periodic oscillations of the atmosphere. In many ways they are analogous to ocean tides. Atmospheric tides can be excited by:*The regular day/night cycle in the insolation of the atmosphere...

s and Earth tide
Earth tide
Earth tide is the sub-meter motion of the Earth of about 12 hours or longer caused by Moon and Sun gravitation, also called body tide which is the largest contribution globally. The largest body tide contribution is from the semidiurnal constituents, but there are also significant diurnal...

s. These are continuum mechanical
Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...

 phenomena. The first two take place in fluid
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

s. The third affects the Earth's thin solid
Solid mechanics
Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions . It is part of a broader study known as continuum mechanics. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation...

 crust surrounding its semi-liquid interior (with various modifications).

Lake tides


Large lakes such as Superior
Lake Superior
Lake Superior is the largest of the five traditionally-demarcated Great Lakes of North America. It is bounded to the north by the Canadian province of Ontario and the U.S. state of Minnesota, and to the south by the U.S. states of Wisconsin and Michigan. It is the largest freshwater lake in the...

 and Erie
Lake Erie
Lake Erie is the fourth largest lake of the five Great Lakes in North America, and the tenth largest globally. It is the southernmost, shallowest, and smallest by volume of the Great Lakes and therefore also has the shortest average water residence time. It is bounded on the north by the...

 can experience tides of 1 to 4 cm, but these can be masked by meteorologically induced phenomena such as seiche
Seiche
A seiche is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbors and seas...

. The tide in Lake Michigan
Lake Michigan
Lake Michigan is one of the five Great Lakes of North America and the only one located entirely within the United States. It is the second largest of the Great Lakes by volume and the third largest by surface area, after Lake Superior and Lake Huron...

 is described as 0.5 to 1.5 in (12.7 to 38.1 mm) or 1¾ inches.

Atmospheric tides


Atmospheric tides are negligible at ground level and aviation altitudes, masked by weather
Weather
Weather is the state of the atmosphere, to the degree that it is hot or cold, wet or dry, calm or stormy, clear or cloudy. Most weather phenomena occur in the troposphere, just below the stratosphere. Weather refers, generally, to day-to-day temperature and precipitation activity, whereas climate...

's much more important effects. Atmospheric tides are both gravitational and thermal in origin and are the dominant dynamics from about 80–120 km (49.7–74.6 mi) above which the molecular density becomes too low to support fluid behavior.

Earth tides


Earth tides or terrestrial tides affect the entire Earth's mass, which acts similarly to a liquid gyroscope
Gyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...

 with a very thin crust. The Earth's crust shifts (in/out, east/west, north/south) in response to lunar and solar gravitation, ocean tides, and atmospheric loading. While negligible for most human activities, terrestrial tides' semi-diurnal amplitude can reach about 55 centimetres (21.7 in) at the equator—15 centimetres (5.9 in) due to the sun—which is important in GPS calibration and VLBI measurements. Precise astronomical angular measurements require knowledge of the Earth's rotation rate and nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

, both of which are influenced by Earth tides. The semi-diurnal M2 Earth tides are nearly in phase with the moon with a lag of about two hours.

Some particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

 experiments must adjust for terrestrial tides. For instance, at CERN
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...

 and SLAC, the very large particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s account for terrestrial tides. Among the relevant effects are circumference deformation for circular accelerators and particle beam energy. Since tidal forces generate currents in conducting fluids in the Earth's interior, they in turn affect the Earth's magnetic field
Earth's magnetic field
Earth's magnetic field is the magnetic field that extends from the Earth's inner core to where it meets the solar wind, a stream of energetic particles emanating from the Sun...

. Earth tides have also been linked to the triggering of earthquakes (see also earthquake prediction).

Galactic tides


Galactic tide
Galactic tide
A galactic tide is a tidal force experienced by objects subject to the gravitational field of a galaxy such as the Milky Way. Particular areas of interest concerning galactic tides include galactic collisions, the disruption of dwarf or satellite galaxies, and the Milky Way's tidal effect on the...

s are the tidal forces exerted by galaxies on stars within them and satellite galaxies orbiting them. The galactic tide's effects on the Solar System
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

's Oort cloud
Oort cloud
The Oort cloud , or the Öpik–Oort cloud , is a hypothesized spherical cloud of comets which may lie roughly 50,000 AU, or nearly a light-year, from the Sun. This places the cloud at nearly a quarter of the distance to Proxima Centauri, the nearest star to the Sun...

 are believed to cause 90 percent of long-period comets.

Misapplications


Tsunamis, the large waves that occur after earthquakes, are sometimes called tidal waves, but this name is given by their resemblance to the tide, rather than any actual link to the tide. Other phenomena unrelated to tides but using the word tide are rip tide
Rip current
A rip current, commonly referred to by the misnomer rip tide, is a strong channel of water flowing seaward from near the shore, typically through the surf line. Typical flow is at 0.5 metres per second , and can be as fast as 2.5 metres per second...

, storm tide
Storm tide
A storm tide is a tide with a high flood period caused by a storm. Storm tides can be a severe danger to the coast and the people living along the coast. The water level can rise to more than 5 meters above the normal tide....

, hurricane tide, and black
Oil spill
An oil spill is the release of a liquid petroleum hydrocarbon into the environment, especially marine areas, due to human activity, and is a form of pollution. The term is mostly used to describe marine oil spills, where oil is released into the ocean or coastal waters...

 or red tide
Red tide
Red tide is a common name for a phenomenon also known as an algal bloom , an event in which estuarine, marine, or fresh water algae accumulate rapidly in the water column and results in discoloration of the surface water. It is usually found in coastal areas...

s.

See also



  • Aquaculture
    Aquaculture
    Aquaculture, also known as aquafarming, is the farming of aquatic organisms such as fish, crustaceans, molluscs and aquatic plants. Aquaculture involves cultivating freshwater and saltwater populations under controlled conditions, and can be contrasted with commercial fishing, which is the...

  • Clairaut's theorem
    Clairaut's theorem
    Clairaut's theorem, published in 1743 by Alexis Claude Clairaut in his Théorie de la figure de la terre, tirée des principes de l'hydrostatique, synthesized physical and geodetic evidence that the Earth is an oblate rotational ellipsoid. It is a general mathematical law applying to spheroids of...

  • Coastal erosion
    Coastal erosion
    Coastal erosion is the wearing away of land and the removal of beach or dune sediments by wave action, tidal currents, wave currents, or drainage...

  • Head of tide
    Head of tide
    Head of tide is the farthest point upstream where a river is affected by tidal fluctuations. This applies to rivers which flow into tidal bodies such as oceans, bays and sloughs. Though this point may vary due to storms and seasonal or annual differences in water flows, there is generally an...

  • Hough function
    Hough function
    In applied mathematics, the Hough functions are the eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating sphere. As such, they are relevant in geophysics and meteorology where they form part of the solutions for atmospheric and ocean waves.Each Hough mode is a...

  • Internal tide
    Internal tide
    Internal tides are generated as the surface tides move stratified water up and down sloping topography, which produces a wave in the ocean interior. So internal tides are internal waves at a tidal frequency. The other major source of internal waves is the wind which produces internal waves near...

  • Lunar Laser Ranging Experiment
    Lunar laser ranging experiment
    The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Lasers on Earth are aimed at retroreflectors planted on the moon during the Apollo program, and the time for the reflected light to return is determined...

        
  • Lunar phase
    Lunar phase
    A lunar phase or phase of the moon is the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases change cyclically as the Moon orbits the Earth, according to the changing relative positions of the Earth, Moon, and Sun...

  • Lunitidal interval
    Lunitidal interval
    The lunitidal interval, measures the time lag from the moon passing overhead, to the next high or low tide. It is also called the high water interval /Tides are known to be mainly caused by the moon's gravity...

  • Marine terrace
    Marine terrace
    A marine terrace, coastal terrace, raised beach or perched coastline is a relatively flat, horizontal or gently inclined surface of marine origin, mostly an old abrasion platform which has been lifted out of the sphere of wave activity . Thus it lies above or under the current sea level, depending...


  • Mean high water spring
  • Mean low water springs
    Mean low water springs
    The mean low water spring is the lowest level to which spring tides retreat on average over a period of time .-External links:* of various tide related terms on the Proudman Oceanographic Laboratory site....

  • Orbit of the moon
  • Perigean Spring Tides
    Perigean Spring Tides
    A perigean spring tide is when the moon is closest to the Earth during the spring tide.The moon's orbit around the Earth is elliptical which causes the moon to be closer to the Earth and farther away at different times. The moon and the sun are aligned every two weeks which result in spring tides;...

            
  • Primitive equations
    Primitive equations
    The primitive equations are a set of nonlinear differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models...

  • Red tide
    Red tide
    Red tide is a common name for a phenomenon also known as an algal bloom , an event in which estuarine, marine, or fresh water algae accumulate rapidly in the water column and results in discoloration of the surface water. It is usually found in coastal areas...

  • Rip current
    Rip current
    A rip current, commonly referred to by the misnomer rip tide, is a strong channel of water flowing seaward from near the shore, typically through the surf line. Typical flow is at 0.5 metres per second , and can be as fast as 2.5 metres per second...

  • Slack water
    Slack water
    Slack water, which used to be known as 'The stand of the tide', is a short period in a body of tidal water either side of high water or low water essentially when the water is completely unstressed, and therefore with no rise or fall of the tide and no movement either way in the tidal stream, and...

  • Storm tide
    Storm tide
    A storm tide is a tide with a high flood period caused by a storm. Storm tides can be a severe danger to the coast and the people living along the coast. The water level can rise to more than 5 meters above the normal tide....

  • Tidal bore
    Tidal bore
    A tidal bore is a tidal phenomenon in which the leading edge of the incoming tide forms a wave of water that travel up a river or narrow bay against the direction of the river or bay's current...


  • Tidal island
    Tidal island
    A tidal island is a piece of land that is connected to the mainland by a natural or man-made causeway that is exposed at low tide and submerged at high tide. Because of the mystique surrounding tidal islands many of them have been sites of religious worship, such as Mont Saint Michel with its...

  • Tidal locking
    Tidal locking
    Tidal locking occurs when the gravitational gradient makes one side of an astronomical body always face another; for example, the same side of the Earth's Moon always faces the Earth. A tidally locked body takes just as long to rotate around its own axis as it does to revolve around its partner...

  • Tidal power
    Tidal power
    Tidal power, also called tidal energy, is a form of hydropower that converts the energy of tides into useful forms of power - mainly electricity....

  • Tidal prism
    Tidal prism
    A tidal prism is the volume of water in an estuary or inlet between mean high tide and mean low tide. or the volume of water leaving an estuary at ebb tide....

  • Tidal range
    Tidal range
    The tidal range is the vertical difference between the high tide and the succeeding low tide. Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and the Sun and the rotation of the Earth...

  • Tidal resonance
    Tidal resonance
    In oceanography, a tidal resonance occurs when the tide excites one of the resonant modes of the ocean.The effect is most striking when a continental shelf is about a quarter wavelength wide...

  • Tide pool
    Tide pool
    Tide pools are rocky pools by oceans that are filled with seawater. Many of these pools exist as separate entities only at low tide.Tide pools are habitats of uniquely adaptable animals that have engaged the special attention of naturalists and marine biologists, as well as philosophical...

  • Tideline
    Tideline
    A tideline refers to where two currents in the ocean converge. Driftwood, floating seaweed, foam, and other floating debris may accumulate, forming sinuous lines called tidelines...



External links




Tide predictions