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x is the horizontal coordinate and the wave propagation direction (meters), z is the vertical coordinate, with the positive z direction pointing out of the fluid layer (meters), λ is the wave length (meters), T is the wave period . As derived below, the horizontal component ū S (z) of the Stokes drift velocity for deep-water waves is ...
For a certain water depth, surface gravity waves – i.e. waves occurring at the air–water interface and gravity as the only force restoring it to flatness – propagate faster with increasing wavelength. On the other hand, for a given (fixed) wavelength, gravity waves in deeper water have a larger phase speed than in shallower water. [1]
Stokes waves of maximum wave height on deep water, under the action of gravity. The maximum wave steepness, for periodic and propagating deep-water waves, is H / λ = 0.1410633 ± 4 · 10 −7 , [ 29 ] so the wave height is about one-seventh ( 1 / 7 ) of the wavelength λ. [ 24 ]
Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure.
A Sverdrup wave (also known as Poincaré wave, or rotational gravity wave [1]) is a wave in the ocean, or large lakes, which is affected by gravity and Earth's rotation (see Coriolis effect). For a non-rotating fluid, shallow water waves are affected only by gravity (see Gravity wave ), where the phase velocity of shallow water gravity wave ( c ...
Stokes drift – Average velocity of a fluid parcel in a gravity wave; Undertow (water waves) – Return flow below nearshore water waves. Ursell number – Dimensionless number indicating the nonlinearity of long surface gravity waves on a fluid layer. Wave shoaling – Effect by which surface waves entering shallower water change in wave height
When a small water parcel is displaced from its equilibrium position, it will return either downwards due to gravity or upwards due to buoyancy. The water parcel will overshoot its original equilibrium position and this disturbance will set off an internal gravity wave. Munk (1981) notes, "Gravity waves in the ocean's interior are as common as ...
The air-water interface is now endowed with a surface roughness due to the capillary-gravity waves, and a second phase of wave growth takes place. A wave established on the surface either spontaneously as described above, or in laboratory conditions, interacts with the turbulent mean flow in a manner described by Miles. [ 6 ]