Wind wave

In fluid dynamics, a wind wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result of the wind blowing over the water's surface. The contact distance in the direction of the wind is known as the fetch. Waves in the oceans can travel thousands of kilometers before reaching land. Wind waves on Earth range in size from small ripples to waves over high, being limited by wind speed, duration, fetch, and water depth.
When directly generated and affected by local wind, a wind wave system is called a wind sea. Wind waves will travel in a great circle route after being generated – curving slightly left in the southern hemisphere and slightly right in the northern hemisphere. After moving out of the area of fetch and no longer being affected by the local wind, wind waves are called swells and can travel thousands of kilometers. A noteworthy example of this is waves generated south of Tasmania during heavy winds that will travel across the Pacific to southern California, producing desirable surfing conditions. Wind waves in the ocean are also called ocean surface waves and are mainly gravity waves, where gravity is the main equilibrium force.
Wind waves have a certain amount of randomness: subsequent waves differ in height, duration, and shape with limited predictability. They can be described as a stochastic process, in combination with the physics governing their generation, growth, propagation, and decay – as well as governing the interdependence between flow quantities such as the water surface movements, flow velocities, and water pressure. The key statistics of wind waves in evolving sea states can be predicted with wind wave models.
Although waves are usually considered in the water seas of Earth, the hydrocarbon seas of Titan may also have wind-driven waves. Waves in bodies of water may also be generated by other causes, both at the surface and underwater.

Formation

The great majority of large breakers seen at a beach result from distant winds. Five factors influence the formation of the flow structures in wind waves:

Wind speed or strength relative to wave speed – the wind must be moving faster than the wave crest for energy transfer to the wave.
The uninterrupted distance of open water over which the wind blows without significant change in direction
Width of the area affected by fetch
Wind duration – the time for which the wind has blown over the water.
Water depth

All of these factors work together to determine the size of the water waves and the structure of the flow within them.
The main dimensions associated with wave propagation are:

A fully developed sea has the maximum wave size theoretically possible for a wind of specific strength, duration, and fetch. Further exposure to that specific wind could only cause a dissipation of energy due to the breaking of wave tops and formation of "whitecaps". 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 height. This figure represents an average height of the highest one-third of the waves in a given time period, or in a specific wave or storm system. The significant wave height is also the value a "trained observer" would estimate from visual observation of a sea state. Given the variability of wave height, the largest individual waves are likely to be somewhat less than twice the reported significant wave height for a particular day or storm.
Wave formation on an initially flat water surface by wind is started by a random distribution of normal pressure of turbulent wind flow over the water. This pressure fluctuation produces normal and tangential stresses in the surface water, which generates waves. It is usually assumed for the purpose of theoretical analysis that:

The water is originally at rest.
The water is not viscous.
The water is irrotational.
There is a random distribution of normal pressure to the water surface from the turbulent wind.
Correlations between air and water motions are neglected.

The second mechanism involves wind shear forces on the water surface. John W. Miles suggested a surface wave generation mechanism that is initiated by turbulent wind shear flows based on the inviscid Orr–Sommerfeld equation in 1957. He found the energy transfer from the wind to the water surface is proportional to the curvature of the velocity profile of the wind at the point where the mean wind speed is equal to the wave speed. Since the wind speed profile is logarithmic to the water surface, the curvature has a negative sign at this point. This relation shows the wind flow transferring its kinetic energy to the water surface at their interface.
Assumptions:

two-dimensional parallel shear flow
incompressible, inviscid water and wind
irrotational water
slope of the displacement of the water surface is small

Generally, these wave formation mechanisms occur together on the water surface and eventually produce fully developed waves.
For example, if we assume a flat sea surface, and a sudden wind flow blows steadily across the sea surface, the physical wave generation process follows the sequence:

Turbulent wind forms random pressure fluctuations at the sea surface. Ripples with wavelengths in the order of a few centimeters are generated by the pressure fluctuations.
The winds keep acting on the initially rippled sea surface causing the waves to become larger. As the waves grow, the pressure differences get larger causing the growth rate to increase. Finally, the shear instability expedites the wave growth exponentially.
The interactions between the waves on the surface generate longer waves and the interaction will transfer wave energy from the shorter waves generated by the Miles mechanism to the waves which have slightly lower frequencies than the frequency at the peak wave magnitudes, then finally the waves will be faster than the crosswind speed.
Types

Three different types of wind waves develop over time:

Capillary waves, or ripples, dominated by surface tension effects.
Gravity waves, dominated by gravitational and inertial forces.
* Seas, raised locally by the wind.
Swells, which have traveled away from where they were raised by the wind, and have to a greater or lesser extent dispersed.

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 tension. Sea waves are larger-scale, often irregular motions that form under sustained winds. These waves tend to last much longer, even after the wind has died, and the restoring force that allows them to propagate is gravity. As waves propagate away from their area of origin, they naturally separate into groups of common direction and wavelength. The sets of waves formed in this manner are known as swells. The Pacific Ocean is from Indonesia to the coast of Colombia and, based on an average wavelength of, would have ~258,824 swells over that width.
It is sometimes alleged that out of a set of waves, the seventh wave in a set is always the largest; while this isn't the case, the waves in the middle of a given set tend to be larger than those before and after them.
Individual "rogue waves" much higher than the other waves in the sea state can occur. In the case of the Draupner wave, its height was 2.2 times the significant wave height. Such waves are distinct from tides, caused by the Moon and Sun's gravitational pull, tsunamis that are caused by underwater earthquakes or landslides, and waves generated by underwater explosions or the fall of meteorites—all having far longer wavelengths than wind waves.
The largest ever recorded wind waves are not rogue waves, but standard waves in extreme sea states. For example, high waves were recorded aboard the RRS Discovery, in a sea with significant wave height, so the highest wave was only 1.6 times the significant wave height.
The biggest recorded by a buoy was high during the 2007 typhoon Krosa near Taiwan.

Spectrum

Ocean waves can be classified based on: the disturbing force that creates them; the extent to which the disturbing force continues to influence them after formation; the extent to which the restoring force weakens or flattens them; and their wavelength or period. Seismic sea waves have a period of about 20 minutes, and speeds of. Wind waves have a period up to about 20 seconds.

Wave type	Typical wavelength	Disturbing force	Restoring force
Capillary wave	< 2 cm	Wind	Surface tension
Wind wave		Wind over ocean	Gravity
Seiche	Large, variable; a function of basin size	Change in atmospheric pressure, storm surge	Gravity
Seismic sea wave		Faulting of sea floor, volcanic eruption, landslide	Gravity
Tide	Half the circumference of Earth	Gravitational attraction, rotation of Earth	Gravity

The speed of all ocean waves is controlled by gravity, wavelength, and water depth. Most characteristics of ocean waves depend on the relationship between their wavelength and water depth. Wavelength determines the size of the orbits of water molecules within a wave, but water depth determines the shape of the orbits. The paths of water molecules in a wind wave are circular only when the wave is traveling in deep water. A wave cannot "feel" the bottom when it moves through water deeper than half its wavelength because too little wave energy is contained in the water movement below that depth. Waves moving through water deeper than half their wavelength are known as deep-water waves. On the other hand, the orbits of water molecules in waves moving through shallow water are flattened by the proximity of the sea bottom surface. Waves in water shallower than 1/20 their original wavelength are known as shallow-water waves. Transitional waves travel through water deeper than 1/20 their original wavelength but shallower than half their original wavelength.
In general, the longer the wavelength, the faster the wave energy will move through the water. The relationship between the wavelength, period and velocity of any wave is:
where C is speed, L is the wavelength, and T is the period. Thus the speed of the wave derives from the functional dependence of the wavelength on the period.
The speed of a deep-water wave may also be approximated by:
where g is the acceleration due to gravity, per second squared. Because g and π are constants, the equation can be reduced to:
when C is measured in meters per second and L in meters. In both formulas the wave speed is proportional to the square root of the wavelength.
The speed of shallow-water waves is described by a different equation that may be written as:
where C is speed, g is the acceleration due to gravity, and d is the depth of the water. The period of a wave remains unchanged regardless of the depth of water through which it is moving. As deep-water waves enter the shallows and feel the bottom, however, their speed is reduced, and their crests "bunch up", so their wavelength shortens.

Wind wave

Formation

Types

Spectrum