Kelvin wave pattern

The Kelvin wave pattern is the V-shaped wake a steadily moving disturbance leaves on deep water, bounded by a constant half-angle of arcsin(1/3), about 19.47 degrees, independent of speed. Lord Kelvin derived it from stationary-phase analysis of dispersive gravity waves, exploiting that deep-water group velocity is half the phase velocity. The wake contains transverse waves crossing the track and divergent waves fanning outward, meeting along the cusp lines that bound the wedge. It governs wave-making resistance and is the signature checked in towing-tank and CFD free-surface solutions. At high Froude number the apparent angle narrows below 19.47 degrees.