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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.
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.
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.
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.
In deep water, the orbit's diameter is reduced to 4% of its free-surface value at a depth of half a wavelength. In a similar fashion, there is also a pressure oscillation underneath the free surface, with wave-induced pressure oscillations reducing with depth below the free surface – in the same way as for the orbital motion of fluid parcels.
By measuring the level of water remaining in the vessel, the time can be measured with uniform graduation. This is an example of outflow clepsydra. Since the water outflow rate is higher when the water level is higher (due to more pressure), the fluid's volume should be more than a simple cylinder when the water level is high.
The red square moves with the phase velocity, and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square traverses the figure in the time it takes the green dot to traverse half. The dispersion relation for deep water waves is often written as
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).