Ship waves and Kelvin

Ship wakes are fascinating. They can be observed by the human eye and appear to have a V shape when the ship is advancing at constant speed along a straight trajectory. Under idealized conditions, Kelvin found that the angle between the two branches of the V is ${\sim }39^\circ $ . However, in a number of cases, this angle appears to be smaller. This phenomenon has been studied by various authors, and several explanations have been suggested. The most elegant one, which is based on the amplitude of the ship waves rather than their phase, has recently been revisited by Darmon, Benzaquen & Raphaël (J. Fluid Mech., vol. 738, 2014, R3).