Kelvin Deep-Water Wake Cusp

The wave pattern generated by a ship moving steadily across deep water forms a distinctive V-shape. By analyzing the linear gravity waves stationary relative to the moving source, we can determine the maximum angle of this envelope, known as the Kelvin wake angle.

experiment

Using the module controls, we can explore how the ray angle changes with the squared normal cosine, q.

1. Observe that changing the "Source speed" scales the wavenumber and wavelength, but the Ray angle and Cusp angle remain unchanged.
2. Select "Squared normal cosine" to "1". The wave propagates exactly in the direction of the source, and the relative group velocity is directly backward with a ray angle of 0°.
3. Select "Squared normal cosine" to "2/3". This is the critical angle where the ray angle reaches its maximum of approx 19.47°, the Kelvin cusp angle.
4. Select "Squared normal cosine" to "0". The resonance condition cannot be met for finite waves, showing "No finite resonant wave".