Ocean Wave I

[Siri]

Influid 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 30 m (100 ft) high, being limited by wind speed, duration, fetch, and water depth.[1]

Although waves are usually considered in the water seas of Earth, the hydrocarbon seas of Titan may also have wind-driven waves.[3][4][5] Waves in bodies of water may also be generated by other causes, both at the surface and underwater (such as watercraft, animals, waterfalls, landslides, earthquakes, bubbles, and impact events).

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.[7]

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:[8]

The largest ever recorded wind waves are not rogue waves, but standard waves in extreme sea states. For example, 29.1 m (95 ft) high waves were recorded on the RRS Discovery in a sea with 18.5 m (61 ft) significant wave height, so the highest wave was only 1.6 times the significant wave height.[13]The biggest recorded by a buoy (as of 2011) was 32.3 m (106 ft) high during the 2007 typhoon Krosa near Taiwan.[14]

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 760 km/h (470 mph). Wind waves (deep-water waves) have a period up to about 20 seconds.

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.

where C is speed (in meters per second), g is the acceleration due to gravity, and d is the depth of the water (in meters). 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.

Some waves undergo a phenomenon called "breaking".[23] A breaking wave is one whose base can no longer support its top, causing it to collapse. A wave breaks when it runs into shallow water, or when two wave systems oppose and combine forces. When the slope, or steepness ratio, of a wave, is too great, breaking is inevitable.

In shallow water, the base of the wave is decelerated by drag on the seabed. As a result, the upper parts will propagate at a higher velocity than the base and the leading face of the crest will become steeper and the trailing face flatter. This may be exaggerated to the extent that the leading face forms a barrel profile, with the crest falling forward and down as it extends over the air ahead of the wave.

When the shoreline is near vertical, waves do not break but are reflected. Most of the energy is retained in the wave as it returns to seaward. Interference patterns are caused by superposition of the incident and reflected waves, and the superposition may cause localized instability when peaks cross, and these peaks may break due to instability. (see also clapotic waves)

Wind waves are mechanical waves that propagate along the interface between water and air; the restoring force is provided by gravity, and so they are often referred to as surface gravity waves. As the wind blows, pressure and friction perturb the equilibrium of the water surface and transfer energy from the air to the water, forming waves. The initial formation of waves by the wind is described in the theory of Phillips from 1957, and the subsequent growth of the small waves has been modeled by Miles, also in 1957.[25][26]

In reality, for finite values of the wave amplitude (height), the particle paths do not form closed orbits; rather, after the passage of each crest, particles are displaced slightly from their previous positions, a phenomenon known as Stokes drift.[30][31]

When several wave trains are present, as is always the case in nature, the waves form groups. In deep water, the groups travel at a group velocity which is half of the phase speed.[33] Following a single wave in a group one can see the wave appearing at the back of the group, growing, and finally disappearing at the front of the group.

As the water depth d \displaystyle d decreases towards the coast, this will have an effect: wave height changes due to wave shoaling and refraction. As the wave height increases, the wave may become unstable when the crest of the wave moves faster than the trough. This causes surf, a breaking of the waves.

The movement of wind waves can be captured by wave energy devices. The energy density (per unit area) of regular sinusoidal waves depends on the water density ρ \displaystyle \rho , gravity acceleration g \displaystyle g and the wave height H \displaystyle H (which, for regular waves, is equal to twice the amplitude, a \displaystyle a ):

Surfers are very interested in the wave forecasts. There are many websites that provide predictions of the surf quality for the upcoming days and weeks. Wind wave models are driven by more general weather models that predict the winds and pressures over the oceans, seas, and lakes.

Wind wave models are also an important part of examining the impact of shore protection and beach nourishment proposals. For many beach areas there is only patchy information about the wave climate, therefore estimating the effect of wind waves is important for managing littoral environments.

A wind-generated wave can be predicted based on two parameters: wind speed at 10 m above sea level and wind duration, which must blow over long periods of time to be considered fully developed. The significant wave height and peak frequency can then be predicted for a certain fetch length.[34]

A third generation wave model is presented that integrates the basic transport equation describing the evolution of a two-dimensional ocean wave spectrum without additional ad hoe assumptions regarding the spectral shape. The three source functions describing the wind input, nonlinear transfer, and white-capping dissipation are prescribed explicitly. An additional bottom dissipation source function and refraction terms are included in the finite-depth version of the model. The model was calibrated against fetch-limited wave growth data. Only two tuning parameters am introduced in the white-capping dissipation source function. The model runs on a spherical latitude-longitude grid for an arbitrary region of the ocean. Hindcast results am shown for six North Atlantic-North Sea storms, three Gulf of Mexico hurricanes, and a global run for the SEASAT period. The agreement with measurements is encouraging.

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