Wind gradient

Wind gradient

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Encyclopedia
In common usage, wind gradient, more specifically wind speed gradient
or wind velocity gradient,
or alternatively shear wind,
is the vertical 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....

 of the mean horizontal wind
Wind
Wind 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...

 speed in the lower atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

. It is the rate of increase of wind strength with unit increase in height above ground level. In metric units, it is often measured in units of meters per second of speed, per kilometer of height (m/s/km), which reduces to the standard unit of shear rate, inverse seconds (s−1).

Simple explanation


Surface friction forces the surface wind
Wind
Wind 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...

 to slow and turn near the surface of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, blowing directly towards the low pressure, when compared to the winds in the nearly frictionless flow well above the Earth's surface. This layer, where surface friction slows the wind and changes the wind direction, is known as the planetary boundary layer. Daytime solar heating due to insolation
Insolation
Insolation is a measure of solar radiation energy received on a given surface area in a given time. It is commonly expressed as average irradiance in watts per square meter or kilowatt-hours per square meter per day...

 thickens the boundary layer as winds at the surface become increasingly mixed with winds aloft. Radiative cooling overnight decouples the winds at the surface from the winds above the boundary layer, increasing vertical wind shear near the surface, also known as wind gradient.

Background



Typically, due to aerodynamic drag, there is a wind gradient in the wind flow just a few hundred meters above the Earth's surface—the surface layer
Surface layer
The surface layer is the layer of a turbulent fluid most affected by interaction with a solid surface or the surface separating a gas and a liquid where the characteristics of the turbulence depend on distance from the interface...

 of the planetary boundary layer
Planetary boundary layer
The planetary boundary layer , also known as the atmospheric boundary layer , is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. On Earth it usually responds to changes in surface forcing in an hour or less...

. Wind speed increases with increasing height above the ground, starting from zero due to the no-slip condition
No-slip condition
In fluid dynamics, the no-slip condition for viscous fluids states that at a solid boundary, the fluid will have zero velocity relative to the boundary.The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary...

. Flow near the surface encounters obstacles that reduce the wind speed, and introduce random vertical and horizontal velocity components at right angles to the main direction of flow.
This turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...

 causes vertical mixing
Mixing (physics)
In physics, a dynamical system is said to be mixing if the phase space of the system becomes strongly intertwined, according to at least one of several mathematical definitions. For example, a measure-preserving transformation T is said to be strong mixing ifwhenever A and B are any measurable...

 between the air moving horizontally at one level, and the air at those levels immediately above and below it, which is important in dispersion of pollutants and in soil erosion.

The reduction in velocity near the surface is a function of surface roughness, so wind velocity profiles are quite different for different terrain types. Rough, irregular ground, and man-made obstructions on the ground, retard movement of the air near the surface, reducing wind velocity. Because of low surface roughness on the relatively smooth water surface, wind speeds do not increase as much with height above sea level as they do on land. Over a city or rough terrain, the wind gradient effect could cause a reduction of 40% to 50% of the geostrophic wind
Geostrophic wind
The geostrophic wind is the theoretical wind that would result from an exact balance between the Coriolis effect and the pressure gradient force. This condition is called geostrophic balance. The geostrophic wind is directed parallel to isobars . This balance seldom holds exactly in nature...

 speed aloft; while over open water or ice, the reduction may be only 20% to 30%.

For engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

 purposes, the wind gradient is modeled as a simple shear
Simple shear
In fluid mechanics, simple shear is a special case of deformation where only one component of velocity vectors has a non-zero value:\ V_x=f\ V_y=V_z=0And the gradient of velocity is constant and perpendicular to the velocity itself:...

 exhibiting a vertical velocity profile varying according to a power law
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...

 with a constant exponential coefficient based on surface type. The height above ground where surface friction has a negligible effect on wind speed is called the "gradient height" and the wind speed above this height is assumed to be a constant called the "gradient wind speed". For example, typical values for the predicted gradient height are 457 m for large cities, 366 m for suburbs, 274 m for open terrain, and 213 m for open sea.

Although the power law exponent approximation is convenient, it has no theoretical basis. When the temperature profile is adiabatic, the wind speed should vary logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

ically with height, Measurements over open terrain in 1961 showed good agreement with the logarithmic fit up to 100 m or so, with near constant average wind speed up through 1000 m.

The shearing
Shearing (physics)
Shearing in continuum mechanics refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. It is induced by a shear stress in the material...

 of the wind is usually three-dimensional, that is, there is also a change in direction between the 'free' pressure-driven geostrophic wind and the wind close to the ground. This is related to the Ekman spiral
Ekman spiral
The Ekman spiral refers to a structure of currents or winds near a horizontal boundary in which the flow direction rotates as one moves away from the boundary. It derives its name from the Swedish oceanographer Vagn Walfrid Ekman...

 effect.
The cross-isobar angle of the diverted ageostrophic flow near the surface ranges from 10° over open water, to 30° over rough hilly terrain, and can increase to 40°-50° over land at night when the wind speed is very low.

After sundown the wind gradient near the surface increases, with the increasing stability.
Atmospheric stability occurring at night with radiative cooling
Radiative cooling
Radiative cooling is the process by which a body loses heat by thermal radiation.- Earth's energy budget :In the case of the earth-atmosphere system it refers to the process by which long-wave radiation is emitted to balance the absorption of short-wave energy from the sun.The exact process by...

 tends to contain turbulent eddies vertically, increasing the wind gradient. The magnitude of the wind gradient is largely influenced by the height of the convective boundary layer and this effect is even larger over the sea, where there is no diurnal variation of the height of the boundary layer as there is over land.
In the convective boundary layer, strong mixing diminishes vertical wind gradient.

Architecture


The design of buildings must account for wind loads, and these are affected by wind gradient. The respective gradient levels, usually assumed in the Building Codes, are 500 meters for cities, 400 meters for suburbs, and 300 m for flat open terrain. For engineering purposes, a power law wind speed profile may be defined as follows:


where:
= speed of the wind at height = gradient wind at gradient height = exponential coefficient

Wind turbines



Wind turbine
Wind turbine
A wind turbine is a device that converts kinetic energy from the wind into mechanical energy. If the mechanical energy is used to produce electricity, the device may be called a wind generator or wind charger. If the mechanical energy is used to drive machinery, such as for grinding grain or...

s are affected by wind gradient. Vertical wind-speed profiles result in different wind speeds at the blades nearest to the ground level compared to those at the top of blade travel, and this in turn affects the turbine operation. The wind gradient can create a large bending moment in the shaft of a two bladed turbine when the blades are vertical. The reduced wind gradient over water means shorter and less expensive wind turbine towers can be used in shallow seas. It would be preferable for wind turbines to be tested in a wind tunnel
Wind tunnel
A wind tunnel is a research tool used in aerodynamic research to study the effects of air moving past solid objects.-Theory of operation:Wind tunnels were first proposed as a means of studying vehicles in free flight...

 simulating the wind gradient that they will eventually see, but this is rarely done.

For wind turbine engineering, an exponential variation in wind speed with height can be defined relative to wind measured at a reference height of 10 meters as:


where:
= velocity of the wind at height, [m/s] = velocity of the wind at height, = 10 meters [m/s] = Hellman exponent

The Hellman exponent depends upon the coastal location and the shape of the terrain on the ground, and the stability of the air. Examples of values of the Hellman exponent are given in the table below:
location α
Unstable air above open water surface: 0.06
Neutral air above open water surface: 0.10
Neutral air above flat open coast: 0.16
Unstable air above flat open coast: 0.11
Stable air above open water surface: 0.27
Unstable air above human inhabited areas: 0.27
Neutral air above human inhabited areas: 0.34
Stable air above flat open coast: 0.40
Stable air above human inhabited areas: 0.60


Source:
"Renewable energy: technology, economics, and environment" by
Martin Kaltschmitt, Wolfgang Streicher, Andreas Wiese, (Springer, 2007, ISBN 3540709479, 9783540709473), page 55

Gliding



In gliding, wind gradient affects the takeoff and landing phases of flight of a glider
Glider (sailplane)
A glider or sailplane is a type of glider aircraft used in the sport of gliding. Some gliders, known as motor gliders are used for gliding and soaring as well, but have engines which can, in some cases, be used for take-off or for extending a flight...

.
Wind gradient can have a noticeable effect on ground launches. If the wind gradient is significant or sudden,
or both, and the pilot maintains the same pitch attitude, the indicated airspeed will increase, possibly exceeding
the maximum ground launch tow speed. The pilot must adjust the airspeed to deal with the effect of the
gradient.

When landing, wind gradient is also a hazard, particularly when the winds are strong. As the glider descends through the wind gradient on final approach to landing, airspeed decreases while sink rate increases, and there is insufficient time to accelerate prior to ground contact. The pilot must anticipate the wind gradient and use a higher approach speed to compensate for it.

Wind gradient is also a hazard for aircraft making steep turns near the ground. It is a particular problem for gliders which have a relatively long wingspan
Wingspan
The wingspan of an airplane or a bird, is the distance from one wingtip to the other wingtip. For example, the Boeing 777 has a wingspan of about ; and a Wandering Albatross caught in 1965 had a wingspan of , the official record for a living bird.The term wingspan, more technically extent, is...

, which exposes them to a greater wind speed difference for a given bank angle. The different airspeed experienced by each wing tip can result in an aerodynamic stall on one wing, causing a loss of control accident. The rolling moment generated by the different airflow over each wing can exceed the aileron
Aileron
Ailerons are hinged flight control surfaces attached to the trailing edge of the wing of a fixed-wing aircraft. The ailerons are used to control the aircraft in roll, which results in a change in heading due to the tilting of the lift vector...

 control authority, causing the glider to continue rolling into a steeper bank angle.

Sailing


In sailing
Sailing
Sailing is the propulsion of a vehicle and the control of its movement with large foils called sails. By changing the rigging, rudder, and sometimes the keel or centre board, a sailor manages the force of the wind on the sails in order to move the boat relative to its surrounding medium and...

, wind gradient affects sailboats by presenting a different wind speed to the sail
Sail
A sail is any type of surface intended to move a vessel, vehicle or rotor by being placed in a wind—in essence a propulsion wing. Sails are used in sailing.-History of sails:...

 at different heights along the mast
Mast (sailing)
The mast of a sailing vessel is a tall, vertical, or near vertical, spar, or arrangement of spars, which supports the sails. Large ships have several masts, with the size and configuration depending on the style of ship...

. The direction also varies with height, but sailors refer to this as "wind shear."

The mast head instruments indication of apparent wind speed and direction is different from what the sailor sees and feels near the surface. Sailmaker
Sailmaker
A sailmaker makes and repairs sails for sailboats, kites, hang gliders, wind art, architectural sails, or other structures using sails. A sailmaker typically works on shore in a sail loft. The sail loft has other sailmakers. Large ocean-going sailing ships often had sailmakers in the crew. The...

s may introduce sail twist
Sail twist
Sail twist is a phenomenon in sailing where the head of the sail is at a different angle of incidence from the foot of the sail in order to change the lift distribution with height. Twist is measured by comparing the angle of a straight line between the leading edge and trailing edge with that of...

 in the design of the sail, where the head of the sail is set at a different angle of attack from the foot of the sail in order to change the lift distribution with height. The effect of wind gradient can be factored into the selection of twist in the sail design, but this can be difficult to predict since the wind gradient may vary widely in different weather conditions. Sailors
Sailors
Sailors is the plural form of Sailor, or mariner.Sailors may also refer to:*Sailors , a 1964 Swedish film*Ken Sailors , American basketball playerSports teams*Erie Sailors, baseball teams in Pennsylvania, USA...

 may also adjust the trim of the sail to account for wind gradient, for example using a boom vang
Boom vang
A boom vang or kicking strap is a line or piston system on a sailboat used to exert downward force on the boom and thus control the shape of the sail. An older term is "martingale"....

.

According to one source, the wind gradient is not significant for sailboats when the wind is over 6 knots (because a wind speed of 10 knots at the surface corresponds to 15 knots at 300 meters, so the change in speed is negligible over the height of a sailboat's mast). According to the same source, the wind increases steadily with height up to about 10 meters in 5 knot winds but less if there is less wind. That source states that in winds with average speeds of six knots or more, the change of speed with height is confined almost entirely to the one or two meters closest to the surface. This is consistent with another source, which shows that the change in wind speed is very small for heights over 2 meters and with a statement by the Australian Government Bureau of Meterology according to which differences can be as little as 5% in unstable air.

In kitesurfing
Kitesurfing
Kitesurfing or Kiteboarding is an adventure surface water sport that has been described as combining wakeboarding, windsurfing, surfing, paragliding, and gymnastics into one extreme sport. Kitesurfing harnesses the power of the wind to propel a rider across the water on a small surfboard or a...

, the wind gradient is even more important, because the power kite
Power kite
A power kite or traction kite is a large kite designed to provide significant pull to the user.They come in three main forms: foils, leading edge inflatables and supported leading edge. There are also rigid-framed kites and soft single skin kites. There are several different control systems used...

 is flown on 20-30m lines, and the kitesurfer can use the kite to jump off the water, bringing the kite to even greater heights above the sea surface.

Sound propagation


Wind gradient can have a pronounced effect upon sound propagation in the lower atmosphere. This effect is important in understanding sound propagation from distant sources, such as foghorn
Foghorn
A foghorn or fog signal or fog bell is a device that uses sound to warn vehicles of hazards or boats of the presence of other vehicles in foggy conditions. The term is most often used in relation to marine transport...

s, thunder
Thunder
Thunder is the sound made by lightning. Depending on the nature of the lightning and distance of the listener, thunder can range from a sharp, loud crack to a long, low rumble . The sudden increase in pressure and temperature from lightning produces rapid expansion of the air surrounding and within...

, sonic boom
Sonic boom
A sonic boom is the sound associated with the shock waves created by an object traveling through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding much like an explosion...

s, gunshot
Gunshot
A gunshot is the discharge of a firearm, producing a mechanical sound effect and a chemical gunshot residue. The term can also refer to a gunshot wound caused by such a discharge. Multiple discharges of a firearm or firearms are referred to as gunfire. The word can connotate either the sound of a...

s or other phenomena like mistpouffers
Mistpouffers
Mistpouffers are unexplained reports that sound like a cannon or a sonic boom. They have been heard in many waterfront communities around the world such as the banks of the river Ganges in India, the East Coast and inland Finger Lakes of the United States, as well as areas of the North Sea, Japan...

. It is also important in studying noise pollution
Noise pollution
Noise pollution is excessive, displeasing human, animal or machine-created environmental noise that disrupts the activity or balance of human or animal life...

, for example from roadway noise
Roadway noise
Roadway noise is the collective sound energy emanating from motor vehicles. In the USA it contributes more to environmental noise exposure than any other noise source, and is constituted chiefly of engine, tire, aerodynamic and braking elements...

 and aircraft noise
Aircraft noise
Aircraft noise is noise pollution produced by any aircraft or its components, during various phases of a flight: on the ground while parked such as auxiliary power units, while taxiing, on run-up from propeller and jet exhaust, during take off, underneath and lateral to departure and arrival paths,...

, and must be considered in the design of noise barrier
Noise barrier
A noise barrier is an exterior structure designed to protect sensitive land uses from noise pollution...

s.
When wind speed increases with altitude, wind blowing towards the listener from the source will refract sound waves downwards, resulting in increased noise levels behind the barrier. These effects were first quantified in the field of highway engineering to address variations of noise barrier efficacy in the 1960s.

When the sun warms the Earth's surface, there is a negative temperature gradient
Temperature gradient
A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degrees per unit length...

 in atmosphere. The speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....

 decreases with decreasing temperature, so this also creates a negative sound speed gradient
Sound speed gradient
In acoustics, the sound speed gradient is the rate of change of the speed of sound with distance, for example with depth in the ocean,or height in the Earth's atmosphere. A sound speed gradient leads to refraction of sound wavefronts in the direction of lower sound speed, causing the sound rays to...

. The sound wave front travels faster near the ground, so the sound is refracted
Refraction
Refraction 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...

 upward, away from listeners on the ground, creating an acoustic shadow
Acoustic Shadow
An acoustic shadow is an area through which sound waves fail to propagate, due to topographical obstructions or disruption of the waves via phenomena such as wind currents. A gobo refers to a movable acoustic isolation panel and that makes an acoustic shadow. As one website refers to it, "an...

 at some distance from the source. The radius of curvature of the sound path is inversely proportional to the velocity gradient.

A wind speed gradient of 4 (m/s)/km can produce refraction equal to a typical temperature lapse rate
Lapse rate
The lapse rate is defined as the rate of decrease with height for an atmospheric variable. The variable involved is temperature unless specified otherwise. The terminology arises from the word lapse in the sense of a decrease or decline; thus, the lapse rate is the rate of decrease with height and...

 of 7.5 °C/km. Higher values of wind gradient will refract sound downward toward the surface in the downwind direction, eliminating the acoustic shadow on the downwind side. This will increase the audibility of sounds downwind. This downwind refraction effect occurs because there is a wind gradient; the sound is not being carried along by the wind.

There will usually be both a wind gradient and a temperature gradient. In that case, the effects of both might add together or subtract depending on the situation and the location of the observer.
The wind gradient and the temperature gradient can also have complex interactions. For example, a foghorn can be audible at a place near the source, and a distant place, but not in a sound shadow between them.
In the case of transverse sound propagation, wind gradients do not sensibly modify sound propegation relative to the windless condition; the gradient effect appears to be important only in upwind and downwind configurations.

For sound propagation, the exponential variation of wind speed with height can be defined as follows:



where:
= speed of the wind at height , and is a constant = exponential coefficient based on ground surface roughness, typically between 0.08 and 0.52 = expected wind gradient at height

In the 1862 American Civil War
American Civil War
The American Civil War was a civil war fought in the United States of America. In response to the election of Abraham Lincoln as President of the United States, 11 southern slave states declared their secession from the United States and formed the Confederate States of America ; the other 25...

 Battle of Iuka
Battle of Iuka
The Battle of Iuka was fought on September 19, 1862, in Iuka, Mississippi, during the American Civil War. In the opening battle of the Iuka-Corinth Campaign, Union Maj. Gen. William S. Rosecrans stopped the advance of the army of Confederate Maj. Gen. Sterling Price.Maj. Gen. Ulysses S...

, an acoustic shadow
Acoustic Shadow
An acoustic shadow is an area through which sound waves fail to propagate, due to topographical obstructions or disruption of the waves via phenomena such as wind currents. A gobo refers to a movable acoustic isolation panel and that makes an acoustic shadow. As one website refers to it, "an...

, believed to have been enhanced by a northeast wind, kept two divisions of Union soldiers out of the battle, because they could not hear the sounds of battle only six miles downwind.

Scientists have understood the effect of wind gradient upon refraction
Refraction
Refraction 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...

 of sound since the mid 1900s; however, with the advent of the U.S. Noise Control Act
Noise Control Act
The Noise Pollution and Abatement Act of 1972 is a statute of the United States initiating a federal program of regulating noise pollution with the intent of protecting human health and minimizing annoyance of noise to the general public....

, the application of this refractive phenomena became applied widely beginning in the early 1970s, chiefly in the application to noise propagation from highway
Highway
A highway is any public road. In American English, the term is common and almost always designates major roads. In British English, the term designates any road open to the public. Any interconnected set of highways can be variously referred to as a "highway system", a "highway network", or a...

s and resultant design of transportation facilities.

Wind gradient soaring



Wind gradient soaring, also called dynamic soaring
Dynamic soaring
Dynamic soaring is a flying technique used to gain energy by repeatedly crossing the boundary between air masses of significantly different velocity...

, is a technique used by soaring birds including albatross
Albatross
Albatrosses, of the biological family Diomedeidae, are large seabirds allied to the procellariids, storm-petrels and diving-petrels in the order Procellariiformes . They range widely in the Southern Ocean and the North Pacific...

es. If the wind gradient is of sufficient magnitude, a bird can climb into the wind gradient, trading ground speed for height, while maintaining airspeed. By then turning downwind, and diving through the wind gradient, they can also gain energy.