Kelvin wake pattern

This part of the pattern is independent of the speed and size of the wake source over a significant range of values.

[2] The angles in this pattern are not intrinsic properties of merely water: Any isentropic and incompressible liquid with low viscosity will exhibit the same phenomenon.

Two velocity parameters of importance for the wake pattern are: As the surface object moves, it continuously generates small disturbances which are the sum of sinusoidal waves with a wide spectrum of wavelengths.

Those waves with the longest wavelengths have phase speeds above v and dissipate into the surrounding water and are not easily observed.

For slow swimmers, low Froude number, the Lighthill−Whitham geometric argument that the opening of the Kelvin chevron (wedge, V pattern) is universal goes as follows.

Equivalently, and more intuitively, fix the position of the boat and have the water flow in the opposite direction, like a piling in a river.

As indicated above, the openings of these chevrons vary with wavenumber, the angle θ between the phase shock wavefront and the path of the boat (the water) being θ = arcsin(c/v) ≡ π/2 − ψ. Evidently, ψ increases with k. However, these phase chevrons are not visible: it is their corresponding group wave manifestations which are observed.

Similarly, it lies on a semicircle now centered on R, where, manifestly, RQ=PQ/4, an effective group wavefront emitted from R, with radius vt/4 now.

The nature of two types of crests, longitudinal and transverse, is graphically illustrated by the pattern of wavefronts of a moving point source in proper frame.