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This formula implies that the group velocity of a deep water wave is half of its phase velocity, which, in turn, goes as the square root of the wavelength. Two velocity parameters of importance for the wake pattern are: v is the relative velocity of the water and the surface object that causes the wake.
Hull speed can be calculated by the following formula: where is the length of the waterline in feet, and is the hull speed of the vessel in knots. If the length of waterline is given in metres and desired hull speed in knots, the coefficient is 2.43 kn·m −½.
The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward). The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
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. New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front.
For instance, a particle floating at the free surface of water waves, experiences a net Stokes drift velocity in the direction of wave propagation. More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel, and the average Eulerian flow velocity of the fluid at a fixed
As with all wave forms, it spreads outward from the source until its energy is overcome or lost, usually by friction or dispersion. The non-dimensional parameter of interest is the Froude number . Wave cloud pattern in the wake of the Île Amsterdam (lower left, at the "tip" of the triangular formation of clouds) in the southern Indian Ocean
The phase velocity c p (blue) and group velocity c g (red) as a function of water depth h for surface gravity waves of constant frequency, according to Airy wave theory. Quantities have been made dimensionless using the gravitational acceleration g and period T, with the deep-water wavelength given by L 0 = gT 2 /(2π) and the deep-water phase ...
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]