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Towards the Kelvin wake and beyond
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Image of Fig. 1.
Fig. 1.

The dispersion relation of Eq. (1) is used to plot the phase and group velocities as a function of frequency for water with a depth of h = 1 m. The frequency intervals where Eqs. (2) and (3) (approximately) hold with , −1, and 1/3 are indicated.

Image of Fig. 2.
Fig. 2.

The wake behind a duck is an example of short (compared to water depth) gravity waves. The wake (half-)angle is indicated.

Image of Fig. 3.
Fig. 3.

An interference pattern that results from two capillary wave fronts.

Image of Fig. 4.
Fig. 4.

Propagation of partial wave with frequency and corresponding phase velocity forming propagation angle with the direction of motion; the propagation angle obeys . The wave is represented by the line perpendicular to where the phase

Image of Fig. 5.
Fig. 5.

The coordinate along the wake is proportional to the time it takes the partial waves to travel from point A to point B. The coordinate expresses the section across the wake.

Image of Fig. 6.
Fig. 6.

Calculated wakes for behind a moving disturbance with velocity v (top) and 2 v (bottom).

Image of Fig. 7.
Fig. 7.

Capillary wake in front of a moving disturbance for (top) and an actual photograph of the ripples in front of an obstacle in flowing water (bottom). The qualitative agreement is quite good.

Image of Fig. 8.
Fig. 8.

The wake behind a moving disturbance in a non-dispersive medium ( ).

Image of Fig. 9.
Fig. 9.

The wake in a slightly dispersive medium with .

Image of Fig. 10.
Fig. 10.

The wake in a slightly dispersive medium with .

Image of Fig. 11.
Fig. 11.

Schematic depiction of partial waves and corresponding propagation angles in a dispersive medium at time t. The first wave (at for , long dashed line) is slower then the wave with phase velocity and propagation angle (solid line), while the second (at for , short dashed line) and third (at for , dotted line) waves are faster.

Image of Fig. 12.
Fig. 12.

The wake in shallow water with the depth of 1 cm shows a changing propagation angle with an accelerated disturbance.

Image of Fig. 13.
Fig. 13.

Wakes for different values of , gradually decreasing from (top) down to (bottom).

Image of Fig. 14.
Fig. 14.

Group wake from a selected partial wave at . The group arrives at , the phase at W.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Towards the Kelvin wake and beyond