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Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by shallow-water phase velocity √ gh as a function of relative depth h / λ. Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity √ gh valid in shallow water.
The dispersion relation for deep water waves is often written as =, where g is the acceleration due to gravity. Deep water, in this respect, is commonly denoted as the case where the water depth is larger than half the wavelength. [4] In this case the phase velocity is
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]
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.
Stokes drift under periodic waves in deep water, for a period T = 5 s and a mean water depth of 25 m. Left: instantaneous horizontal flow velocities. Right: average flow velocities. Black solid line: average Eulerian velocity; red dashed line: average Lagrangian velocity, as derived from the Generalized Lagrangian Mean (GLM).
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]
Because water is much more dense than air, the displacement of water by air from a surface gravity wave feels nearly the full force of gravity (′). The displacement of the thermocline of a lake, which separates warmer surface from cooler deep water, feels the buoyancy force expressed through the reduced gravity. For example, the density ...