Editing Wind wave (section)

==Formation==
[[File:Water wave diagram.jpg|thumb|upright=1.3|{{center|Aspects of a water wave}}]]
[[File:Sjyang waveGeneration.png|thumb|upright=1.3|{{center|Wave formation}}]]
[[File:Deep water wave.gif|thumb|{{center|Water particle motion of a deep water wave}}]]
[[File:Ocean wave phases numbered.png|thumb|The phases of an ocean surface wave: 1. Wave Crest, where the water masses of the surface layer are moving horizontally in the same direction as the propagating wavefront. 2. Falling wave. 3. Trough, where the water masses of the surface layer are moving horizontally in the opposite direction of the wavefront direction. 4. Rising wave.]]
[[File:Wea00810.jpg|thumb|upright|[[NOAA]] ship ''Delaware II'' in bad weather on [[Georges Bank]]]]

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:<ref>{{cite book |title=Wind generated ocean waves |first=I. R. |last=Young |publisher=Elsevier |year=1999 |isbn=978-0-08-043317-2 |page=83}}</ref>
# [[Wind speed]] or strength relative to wave speed&nbsp;– 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 (called the ''[[fetch (geography)|fetch]]'')
# Width of the area affected by fetch (at a right angle to the distance)
# Wind duration&nbsp;– 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:
* [[Wave height]] (vertical distance from trough to [[crest (physics)|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 direction or [[azimuth]] (predominantly driven by [[wind direction]])

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 (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.<ref>{{Cite book | publisher = Springer | isbn = 978-3-540-25316-7 | last1 = Weisse | first1 = Ralf | first2 = Hans | last2 = von Storch | title = Marine climate change: Ocean waves, storms and surges in the perspective of climate change | year = 2008 | page = 51 }}</ref>

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:<ref name="Phillips, O. M. 1957">{{cite journal |last1=Phillips |first1=O. M. |author-link=Owen Martin Phillips |title=On the generation of waves by turbulent wind |journal=Journal of Fluid Mechanics |date=2006 |volume=2 |issue=5 |pages=417 |doi=10.1017/S0022112057000233 |doi-broken-date=1 November 2024 |bibcode=1957JFM.....2..417P|s2cid=116675962 }}</ref>
# 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<ref>{{cite journal |last1=Miles |first1=John W. |author-link=John W. Miles |title=On the generation of surface waves by shear flows |journal=Journal of Fluid Mechanics |date=2006 |volume=3 |issue=2 |pages=185 |doi=10.1017/S0022112057000567 |doi-broken-date=1 November 2024 |bibcode=1957JFM.....3..185M|s2cid=119795395 }}</ref>

Generally, these wave formation mechanisms occur together on the water surface and eventually produce fully developed waves.

For example,<ref>{{Cite web |url=http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_04.htm |title=Chapter 16, ''Ocean Waves'' |access-date=2013-11-12 |archive-date=2016-05-11 |archive-url=https://web.archive.org/web/20160511210532/http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_04.htm |url-status=dead }}</ref> 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 centimeters are generated by the pressure fluctuations. (The [[Owen Martin Phillips|Phillips]] mechanism<ref name="Phillips, O. M. 1957"/>)
# 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 Miles mechanism<ref name="Phillips, O. M. 1957"/>)
# The interactions between the waves on the surface generate longer waves<ref>{{cite journal |last=Hasselmann |first=K. |display-authors=etal |year=1973 |title=Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP) |url=https://www.researchgate.net/publication/256197895 |journal=Ergnzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe A |volume=8 |issue=12 |page=95 |hdl=10013/epic.20654}}</ref> 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 (Pierson & Moskowitz<ref>{{cite journal|last1=Pierson|first1=Willard J.|last2=Moskowitz|first2=Lionel|title=A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii|journal=Journal of Geophysical Research|date=15 December 1964|volume=69|issue=24|pages=5181–5190|doi=10.1029/JZ069i024p05181|bibcode=1964JGR....69.5181P}}</ref>).

{| class="collapsible wikitable" border="1" style="font-size:92%"
! colspan=6 style="background: #ccf;" | Conditions necessary for a fully developed sea at given wind speeds, and the parameters of the resulting waves
|-
! colspan=3 style | Wind conditions
! colspan= 3 style | Wave size
|-
! Wind speed in one direction !! Fetch !! Wind duration !! Average height !! Average wavelength !! Average period and speed
|-
| {{convert|19|km/h|mph|abbr=on}}|| {{convert|19|km|mi|abbr=on}} || 2 hr || {{convert|0.27|m|ft|abbr=on}}|| {{convert|8.5|m|ft|abbr=on}} || 3.0 sec, 10.2&nbsp;km/h (9.3&nbsp;ft/sec)
|-
| {{convert|37|km/h|mph|abbr=on}}|| {{convert|139|km|mi|abbr=on}} || 10 hr || {{convert|1.5|m|ft|abbr=on}}|| {{convert|33.8|m|ft|abbr=on}} || 5.7 sec, 21.4&nbsp;km/h (19.5&nbsp;ft/sec)
|-
| {{convert|56|km/h|mph|abbr=on}}|| {{convert|518|km|mi|abbr=on}} || 23 hr || {{convert|4.1|m|ft|abbr=on}}|| {{convert|76.5|m|ft|abbr=on}} || 8.6 sec, 32.0&nbsp;km/h (29.2&nbsp;ft/sec)
|-
| {{convert|74|km/h|mph|abbr=on}}|| {{convert|1,313|km|mi|abbr=on}} || 42 hr || {{convert|8.5|m|ft|abbr=on}}|| {{convert|136|m|ft|abbr=on}} || 11.4 sec, 42.9&nbsp;km/h (39.1&nbsp;ft/sec)
|-
| {{convert|92|km/h|mph|abbr=on}}|| {{convert|2,627|km|mi|abbr=on}} || 69 hr || {{convert|14.8|m|ft|abbr=on}}|| {{convert|212.2|m|ft|abbr=on}} || 14.3 sec, 53.4&nbsp;km/h (48.7&nbsp;ft/sec)
|-
| colspan=6 | NOTE: Most of the wave speeds calculated from the wave length divided by the period are proportional to the square root of the wave length. Thus, except for the shortest wave length, the waves follow the deep water theory. The 28&nbsp;ft long wave must be either in shallow water or intermediate depth.
|}