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In shallow water, the group velocity is equal to the shallow-water phase velocity. This is because shallow water waves are not dispersive. In deep water, the group velocity is equal to half the phase velocity: {{math|c g = 1 / 2 c p. [7] The group velocity also turns out to be the energy transport velocity.
(Note: Most of the wave speeds calculated from the wavelength divided by the period are proportional to the square root of the length. Thus, except for the shortest wavelength, the waves follow the deep water theory described in the next section. The 8.5 m long wave must be either in shallow water or between deep and shallow.)
In deep water, shock waves form even from slow-moving sources, because waves with short enough wavelengths move slower. These shock waves are at sharper angles than one would naively expect, because it is group velocity that dictates the area of constructive interference and, in deep water, the group velocity is half of the phase velocity.
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.
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.
Visualization of deep and shallow water waves by relating wavelength to depth to bed. deep water – for a water depth larger than half the wavelength, h > 1 / 2 λ, the phase speed of the waves is hardly influenced by depth (this is the case for most wind waves on the sea and ocean surface), [9]
The speed of a plane wave, , is a function of the wave's wavelength : = (). The wave's ... Frequency dispersion of surface gravity waves on deep water.
For an observer traveling with the wave, the coastal boundary (maximum amplitude) is always to the right in the northern hemisphere and to the left in the southern hemisphere (i.e. these waves move equatorward – negative phase speed – at the western side of an ocean and poleward – positive phase speed – at the eastern boundary; the ...