page_title: Wind wave
section_title: Formation
hierarchical_section_title: Wind wave / Formation
caption_attribution_description: English: The Miles-Phillips wave formation mechanism
context_page_description: In fluid dynamics, wind waves, or wind-generated waves, are water surface waves that occur on the free surface of bodies of water. They result from the wind blowing over an area of fluid surface. Waves in the oceans can travel thousands of miles before reaching land. Wind waves on Earth range in size from small ripples, to waves over 100 ft high, being limited by wind speed, duration, affected area and water depth.
  When directly generated and affected by local waters, 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, wind waves are called swells and can travel thousands of miles. A noteworthy example of this are waves generated south of Tasmania during heavy winds that will travel to southern California producing desirable surfing conditions. More generally, a swell consists of wind-generated waves that are not significantly 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.
context_section_description: 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
  The uninterrupted distance of open water over which the wind blows without significant change in direction (called the fetch)
  Width of area affected by fetch (at right angle to the distance)
  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 waves are:
  Wave height (vertical distance from trough to crest)
  Wave length (distance from crest to crest in the direction of propagation)
  Wave period (time interval between arrival of consecutive crests at a stationary point)
  Wave propagation direction
  A fully developed sea has the maximum wave size theoretically possible for a wind of a 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 (usually chosen somewhere in the range from 20 minutes to twelve hours), or in a specific wave or storm system. The significant wave height is also the value a "trained observer" (e.g. from a ship's crew) 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 assumed 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 which is initiated by turbulent wind shear flows based on the inviscid Orr-Sommerfeld equation in 1957. He found the energy transfer from wind to 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 (Beaufort state 0), 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 centimetres are generated by the pressure fluctuations. (The Phillips mechanism)
  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. (
caption: Wave formation
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