In
fluid dynamicsIn physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
,
wind waves or, more precisely,
wind-generated waves are
surface waveIn physics, a surface wave is a mechanical wave that propagates along the interface between differing media, usually two fluids with different densities. A surface wave can also be an electromagnetic wave guided by a refractive index gradient...
s that occur on the
free surfaceIn physics, a free surface is the surface of a fluid that is subject to constant perpendicular normal stress and zero parallel shear stress,such as the boundary between two homogenous fluids,for example liquid water and the air in the Earth's atmosphere...
of
oceanAn ocean is a major body of saline water, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas.More than half of this area is over 3,000...
s,
seaA sea generally refers to a large body of salt water, but the term is used in other contexts as well. Most commonly, it means a large expanse of saline water connected with an ocean, and is commonly used as a synonym for ocean...
s,
lakeA lake is a body of relatively still fresh or salt water of considerable size, localized in a basin, that is surrounded by land. Lakes are inland and not part of the ocean and therefore are distinct from lagoons, and are larger and deeper than ponds. Lakes can be contrasted with rivers or streams,...
s,
riverA river is a natural watercourse, usually freshwater, flowing towards an ocean, a lake, a sea, or another river. In a few cases, a river simply flows into the ground or dries up completely before reaching another body of water. Small rivers may also be called by several other names, including...
s, and
canalCanals are man-made channels for water. There are two types of canal:#Waterways: navigable transportation canals used for carrying ships and boats shipping goods and conveying people, further subdivided into two kinds:...
s or even on small
puddleA puddle is a small accumulation of liquid, usually water, on a surface. It can form either by pooling in a depression on the surface, or by surface tension upon a flat surface...
s and
pondA pond is a body of standing water, either natural or man-made, that is usually smaller than a lake. A wide variety of man-made bodies of water are classified as ponds, including water gardens, water features and koi ponds; all designed for aesthetic ornamentation as landscape or architectural...
s. They usually result from the
windWind is the flow of gases on a large scale. On Earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's atmosphere into space...
blowing over a vast enough stretch of fluid surface. Waves in the oceans can travel thousands of miles before reaching land. Wind waves range in size from small
ripplesA capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics are dominated by the effects of surface tension.Capillary waves are common in nature and the home, and are often referred to as ripples...
to huge waves over 30 meters high. When directly being generated and affected by the local winds, a wind wave system is called a
wind sea. After the wind ceases to blow, wind waves are called
swellA swell, in the context of an ocean, sea or lake, is a series surface gravity waves that is not generated by the local wind. Swell waves often have a long wavelength but this varies with the size of the water body, e.g. rarely more than 150 m in the Mediterranean, and from event to event, with...
. Or, more generally, a swell consists of wind generated waves that are not—or hardly—affected by the local wind at that time. They have been generated elsewhere, or some time ago. Wind waves in the ocean are called
ocean surface waves.
TsunamiA tsunami is a series of water waves caused by the displacement of a large volume of a body of water, typically an ocean or a large lake...
s are a specific type of wave not caused by wind but by geological effects. In deep water, tsunamis are not visible because they are small in height and very long in
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
. They may grow to devastating proportions at the coast due to reduced water depth.
Wave formation
The great majority of large breakers one observes on a beach result from distant winds. Five factors influence the formation of wind waves:
- Wind speed
Wind speed, or wind velocity, is a fundamental atmospheric rate.Wind speed affects weather forecasting, aircraft and maritime operations, construction projects, growth and metabolism rate of many plant species, and countless other implications....
- Distance of open water that the wind has blown over (called the fetch
The fetch, often called the fetch length, is the length of water over which a given wind has blown. It is used in geography and meteorology and is usually associated with coastal erosion. It plays a large part in longshore drift as well....
)
- Width of area affected by fetch
- Time duration the wind has blown over a given area
- Water depth
All of these factors work together to determine the size of wind waves. The greater each of the variables, the larger the waves. Waves are characterized by:
- Wave height
In fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighbouring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering....
(from trough to crestA crest is the point on a wave with the maximum value or upward displacement within a cycle. A trough is the opposite of a crest, so the minimum or lowest point in a cycle.-Interference:...
)
- Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
(from crest to crest)
- Wave period (time interval between arrival of consecutive crests at a stationary point)
- Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
direction
Waves in a given area typically have a range of heights. For weather reporting and for scientific analysis of wind wave statistics, their characteristic height over a period of time is usually expressed as
significant wave heightIn physical oceanography, the significant wave height is defined traditionally as the mean wave height of the highest third of the waves , but now usually defined as four times the standard deviation of the surface elevation...
. This figure represents an
averageIn 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....
height of the highest one-third of the waves in a given time period (usually chosen somewhere in the range from 20 minutes to twelve hours), or in a specific wave or storm system. Given the variability of wave height, the largest individual waves are likely to be about twice the reported significant wave height for a particular day or storm.
Types of wind waves
Three different types of wind waves develop over time:
- Capillary wave
A capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics are dominated by the effects of surface tension.Capillary waves are common in nature and the home, and are often referred to as ripples...
s, or ripples
- Seas
- Swells
A swell, in the context of an ocean, sea or lake, is a series surface gravity waves that is not generated by the local wind. Swell waves often have a long wavelength but this varies with the size of the water body, e.g. rarely more than 150 m in the Mediterranean, and from event to event, with...
Ripples appear on smooth water when the wind blows, but will die quickly if the wind stops. The restoring force that allows them to propagate is
surface tensionSurface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
. Seas are the larger-scale, often irregular motions that form under sustained winds. They tend to last much longer, even after the wind has died, and the restoring force that allows them to persist is gravity. As seas propagate away from their area of origin, they naturally separate according to their direction and wavelength. The regular wave motions formed in this way are known as swells.
Individual "rogue waves" (also called "freak waves", "monster waves", "killer waves", and "king waves") much higher than the other waves in the
sea stateIn oceanography, a sea state is the general condition of the free surface on a large body of water—with respect to wind waves and swell—at a certain location and moment. A sea state is characterized by statistics, including the wave height, period, and power spectrum. The sea state varies with...
can occur. In the case of the
Draupner waveThe Draupner wave or New Year's wave was the first rogue wave to be detected by a measuring instrument, occurring at the Draupner platform in the North Sea off the coast of Norway on January 1, 1995...
, its 25 m (82 ft) height was 2.2 times the
significant wave heightIn physical oceanography, the significant wave height is defined traditionally as the mean wave height of the highest third of the waves , but now usually defined as four times the standard deviation of the surface elevation...
. Such waves are distinct from
tideTides 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....
s, caused by the
MoonThe 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
SunThe 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...
's
gravitational pullThe 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...
,
tsunamiA tsunami is a series of water waves caused by the displacement of a large volume of a body of water, typically an ocean or a large lake...
s that are caused by underwater
earthquakeAn earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. The seismicity, seismism or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time...
s or
landslideA landslide or landslip is a geological phenomenon which includes a wide range of ground movement, such as rockfalls, deep failure of slopes and shallow debris flows, which can occur in offshore, coastal and onshore environments...
s, and waves generated by
underwater explosionAn underwater explosion, also known as an UNDEX, is an explosion beneath the surface of water. The type of explosion may be chemical or nuclear...
s or the fall of
meteoriteA meteorite is a natural object originating in outer space that survives impact with the Earth's surface. Meteorites can be big or small. Most meteorites derive from small astronomical objects called meteoroids, but they are also sometimes produced by impacts of asteroids...
s—all having far longer
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s than wind waves.
Yet, the largest ever recorded wind waves are common—not rogue—waves in extreme sea states. For example: 29.1 m (95.5 ft) high waves have been recorded on the
RRS DiscoveryRRS Discovery is a British Royal Research Ship operated by NERC.RRS Discovery was built in Aberdeen in 1962 and named after Robert Falcon Scott's 1901 ship, RRS Discovery. Until 2006, she was the largest general purpose oceanographic research vessel in use in the United Kingdom...
in a sea with 18.5 m (60.7 ft) significant wave height, so the highest wave is only 1.6 times the significant wave height.
Wave shoaling and refraction
As waves travel from deep to shallow water, their shape alters (wave height increases, speed decreases, and length decreases as wave orbits become asymmetrical). This process is called shoaling.
Wave refraction is the process by which wave crests realign themselves as a result of decreasing water depths. Varying depths along a wave crest cause the crest to travel at different speeds, with those parts of the wave in deeper water moving faster than those in shallow water. This process continues until the crests become parallel to the depth contours and/or the wave breaks. Orthogonals (lines normal to wave crests between which a fixed amount of energy is contained) converge on headlands and diverge in bays. Therefore, wave energy is concentrated on headlands but is dissipated in bays, with resulting increase in wave height at headlands and decrease in bays.
When breaking occurs before the refraction process is complete,
Longshore driftLongshore drift consists of the transportation of sediments along a coast at an angle to the shoreline, which is dependent on prevailing wind direction, swash and backwash. This process occurs in the littoral zone, and in or within close proximity to the surf zone...
may occur, often causing a redistribution of sediment from headlands to bays.
Wave breaking
Some waves undergo a
phenomenonA phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'...
called "breaking". A
breaking waveIn fluid dynamics, a breaking wave is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur that causes large amounts of wave energy to be transformed into turbulent kinetic energy...
is one whose base can no longer support its top, causing it to collapse. A wave breaks when it runs into
shallow waterShallow water may refer to:* Shallow water blackout* Waves and shallow water** Shallow water equations** Boussinesq equations * Shallow Water, Kansas...
, or when two wave systems oppose and combine forces. When the slope, or steepness ratio, of a wave is too great, breaking is inevitable.
Individual waves in deep water break when the wave steepness—the
ratioIn mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
of the
wave heightIn fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighbouring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering....
H to the
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
λ—exceeds about 0.17, so for
H > 0.17
λ. In shallow water, with the water depth small compared to the wavelength, the individual waves break when their wave height
H is larger than 0.8 times the water depth
h, that is
H > 0.8
h. Waves can also break if the wind grows strong enough to blow the crest off the base of the wave.
Three main types of breaking waves are identified by surfers or surf lifesavers. Their varying characteristics make them more or less suitable for surfing, and present different dangers.
- Spilling, or rolling: these are the safest waves on which to surf. They can be found in most areas with relatively flat shorelines. They are the most common type of shorebreak
- Plunging, or dumping: these break suddenly and can "dump" swimmers—pushing them to the bottom with great force. These are the preferred waves for experienced surfers. Strong offshore winds and long wave periods can cause dumpers. They are often found where there is a sudden rise in the sea floor, such as a reef or sandbar.
- Surging: these may never actually break as they approach the water's edge, as the water below them is very deep. They tend to form on steep shorelines. These waves can knock swimmers over and drag them back into deeper water.
Science of waves
Wind waves are mechanical
waveIn physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
s that propagate along the interface between
waterWater is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...
and air; the restoring force is provided by gravity, and so they are often referred to as
surface gravity wavesIn fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media which has the restoring force of gravity or buoyancy....
. As the
windWind is the flow of gases on a large scale. On Earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's atmosphere into space...
blows, pressure and friction forces perturb the equilibrium of the water surface. These forces transfer energy from the air to the water, forming waves. The initial formation of waves by the wind is described in the theory of Phillips from 1957, and the subsequent growth of the small waves has been modeled by
MilesJohn Wilder Miles was a research professor emeritus of applied mechanics and geophysics at Scripps Institution of Oceanography, University of California, San Diego...
, also in 1957.
In the case of monochromatic linear plane waves in deep water, particles near the surface move in circular paths, making wind waves a combination of
longitudinalLongitudinal waves, as known as "l-waves", are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. Mechanical longitudinal waves have been also...
(back and forth) and
transverseA transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer...
(up and down) wave motions. When waves propagate in
shallow waterShallow water may refer to:* Shallow water blackout* Waves and shallow water** Shallow water equations** Boussinesq equations * Shallow Water, Kansas...
, (where the depth is less than half the wavelength) the particle trajectories are compressed into
ellipseIn geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
s.
As the wave amplitude (height) increases, the particle paths no longer form closed orbits; rather, after the passage of each crest, particles are displaced slightly from their previous positions, a phenomenon known as
Stokes driftFor a pure wave motion in fluid dynamics, the Stokes drift velocity is the average velocity when following a specific fluid parcel as it travels with the fluid flow...
.
For intermediate and shallow water, the
Boussinesq equationsIn fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation...
are applicable, combining
frequency dispersionIn fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, and forced by gravity and surface tension...
and nonlinear effects. And in very shallow water, the
shallow water equationsThe shallow water equations are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid .The equations are derived from depth-integrating the Navier–Stokes...
can be used.
As the depth below the free surface increases, the radius of the circular motion decreases. At a depth equal to half the
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
λ, the orbital movement has decayed to less than 5% of its value at the surface. The phase speed of the surface wave (also called the
celerityCelerity may refer to:* Speed, quickness* Celerity BBS, a computer bulletin board system popular in the 1990s* Celerity Computing Inc., defunct San Diego, California vendor of Unix-based "supermini" computers...
) is well approximated by
where
- c = phase speed;
- λ = wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
;
- d = water depth;
- g = acceleration due to gravity at the Earth's surface
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...
.
In deep water, where
, so
and the hyperbolic tangent approaches
, the speed
, in m/s, approximates
, when
is measured in metres.
This expression tells us that waves of different wavelengths travel at different speeds. The fastest waves in a storm are the ones with the longest wavelength. As a result, after a storm, the first waves to arrive on the coast are the long-wavelength swells.
When several wave trains are present, as is always the case in nature, the waves form groups. In deep water the groups travel at a
group velocityThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
which is half of the phase speed. Following a single wave in a group one can see the wave appearing at the back of the group, growing and finally disappearing at the front of the group.
As the water depth
decreases towards the
coastA 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...
, this will have an effect: wave height changes due to
wave shoalingIn fluid dynamics, wave shoaling is the effect by which surface waves entering shallower water increase in wave height . It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, decreases with the reduction of water depth...
and
refractionRefraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
. As the wave height increases, the wave may become unstable when the
crestA crest is the point on a wave with the maximum value or upward displacement within a cycle. A trough is the opposite of a crest, so the minimum or lowest point in a cycle.-Interference:...
of the wave moves faster than the trough. This causes
surf, a breaking of the waves.
The movement of wind waves can be captured by
wave energy devicesWave power is the transport of energy by ocean surface waves, and the capture of that energy to do useful work — for example, electricity generation, water desalination, or the pumping of water...
. The energy density (per unit area) of regular sinusoidal waves depends on the water
densityThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
, gravity acceleration
and the wave height
(which, for regular waves, is equal to twice the
amplitudeAmplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
,
):
The velocity of propagation of this energy is the
group velocityThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
.
Wind wave models
Surfers are very interested in the
wave forecastsIn fluid dynamics, wind wave modeling describes the effort to depict the sea state and predict the evolution of the energy of wind waves using numerical techniques...
. There are many websites that provide predictions of the surf quality for the upcoming days and weeks. Wind wave models are driven by more general
weather modelsNumerical weather prediction uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic...
that predict the winds and pressures over the oceans, seas and lakes.
Wind wave models are also an important part of examining the impact of shore protection and
beach nourishmentBeach nourishment— also referred to as beach replenishment—describes a process by which sediment lost through longshore drift or erosion is replaced from sources outside of the eroding beach...
proposals. For many beach areas there is only patchy information about the wave climate, therefore estimating the effect of wind waves is important for managing
littoralThe littoral zone is that part of a sea, lake or river that is close to the shore. In coastal environments the littoral zone extends from the high water mark, which is rarely inundated, to shoreline areas that are permanently submerged. It always includes this intertidal zone and is often used to...
environments.
See also
- Airy wave theory
In fluid dynamics, Airy wave theory gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational...
- Boussinesq approximation (water waves)
In fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation...
- Clapotis
In hydrodynamics, the clapotis is a non-breaking standing wave pattern, caused for example, by the reflection of a traveling surface wave train from a near vertical shoreline like a breakwater, seawall or steep cliff....
- index of wave articles
- Luke's variational principle
In fluid dynamics, Luke's variational principle is a Lagrangian variational description of the motion of surface waves on a fluid with a free surface, under the action of gravity. This principle is named after J.C. Luke, who published it in 1967...
- Mild-slope equation
In fluid dynamics, the mild-slope equation describes the combined effects of diffraction and refraction for water waves propagating over bathymetry and due to lateral boundaries—like breakwaters and coastlines. It is an approximate model, deriving its name from being originally developed for wave...
- Rogue wave
- Shallow water equations
The shallow water equations are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid .The equations are derived from depth-integrating the Navier–Stokes...
- Tsunami
A tsunami is a series of water waves caused by the displacement of a large volume of a body of water, typically an ocean or a large lake...
- Wave power
Wave power is the transport of energy by ocean surface waves, and the capture of that energy to do useful work — for example, electricity generation, water desalination, or the pumping of water...
- Wave radar
Wind waves can be measured by several radar remote sensing techniques. Several instruments based on a variety of different concepts and techniques are available to the user and these are all often called wave radars...
- Waves and shallow water
When waves travel into areas of shallow water, they begin to be affected by the ocean bottom. The free orbital motion of the water is disrupted, and water particles in orbital motion no longer return to their original position. As the water becomes shallower, the swell becomes higher and steeper,...
Scientific
External links