Wind stress
Encyclopedia
In physical oceanography
and fluid dynamics
, the wind stress is the shear stress
exerted by the wind
on the surface
of large bodies of water – such as ocean
s, sea
s, estuaries
and lake
s. It is the force
component parallel
to the surface, per unit area
, as applied by the wind on the water surface. The wind stress is affected by the wind speed
, the shape of the wind waves and the atmospheric stratification. It is one of the components of the air–sea interaction, with others being the atmospheric pressure
on the water surface, as well as the exchange of heat
and mass
between the water and the atmosphere.
This is a downward transfer of momentum from the air to the water that ultimately generates a drift current underneath.
The water surface also deforms under the action of wind and becomes wavy for increasing wind speeds, which modifies the grip that the wind has on the surface itself.
The mechanics of the interaction between wind and water becomes thus increasingly complex.
The Beaufort scale
, for example, shows the correspondence between wind speed and sea states.
The magnitude of this shear force per unit contact area (
, shear stress
) is estimated through wind-shear or wind-drag formulas.
These formulas parametrize the shear stress as a function of the wind speed at a certain height above the surface (
) in the form
where
is the density of the air; 
is a dimensionless quantity wind-drag coefficient and is a repository function for all remaining dependencies.
The height at which the wind speed is referred to in wind-drag formulas is usually 10 meters above the water surface.
The expression of
contains, in first place, the correction to dependency on the second power of 
for different ranges of 
.
The functional form of
is determined by an empirical formula that is determined from experiments in the laboratory and/or in the field.
Different formulas have been established by various authors for different wind-speed ranges and taking into account the mechanics of the wind to varying degrees of detail.
Physical oceanography
Physical oceanography is the study of physical conditions and physical processes within the ocean, especially the motions and physical properties of ocean waters.Physical oceanography is one of several sub-domains into which oceanography is divided...
and fluid dynamics
Fluid dynamics
In 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...
, the wind stress is the shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
exerted by the 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...
on the surface
Free surface
In 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 large bodies of water – such as ocean
Ocean
An 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, sea
Sea
A 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, estuaries
Estuary
An estuary is a partly enclosed coastal body of water with one or more rivers or streams flowing into it, and with a free connection to the open sea....
and lake
Lake
A 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. It is the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
component parallel
Parallel (geometry)
Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not...
to the surface, per unit area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
, as applied by the wind on the water surface. The wind stress is affected by the wind speed
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....
, the shape of the wind waves and the atmospheric stratification. It is one of the components of the air–sea interaction, with others being the atmospheric pressure
Atmospheric pressure
Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...
on the water surface, as well as the exchange of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
and mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
between the water and the atmosphere.
Dynamics
The air blowing parallel to a water body imparts motion to the surface water by shear action.This is a downward transfer of momentum from the air to the water that ultimately generates a drift current underneath.
The water surface also deforms under the action of wind and becomes wavy for increasing wind speeds, which modifies the grip that the wind has on the surface itself.
The mechanics of the interaction between wind and water becomes thus increasingly complex.
The Beaufort scale
Beaufort scale
The Beaufort Scale is an empirical measure that relates wind speed to observed conditions at sea or on land. Its full name is the Beaufort Wind Force Scale.-History:...
, for example, shows the correspondence between wind speed and sea states.
The magnitude of this shear force per unit contact area (
, shear stressShear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
) is estimated through wind-shear or wind-drag formulas.
These formulas parametrize the shear stress as a function of the wind speed at a certain height above the surface (
) in the formwhere
is the density of the air; is a dimensionless quantity wind-drag coefficient and is a repository function for all remaining dependencies.The height at which the wind speed is referred to in wind-drag formulas is usually 10 meters above the water surface.
The expression of
contains, in first place, the correction to dependency on the second power of for different ranges of .The functional form of
is determined by an empirical formula that is determined from experiments in the laboratory and/or in the field.Different formulas have been established by various authors for different wind-speed ranges and taking into account the mechanics of the wind to varying degrees of detail.