Role of wave velocity for encountered wave statistics

Encountering waves overtaking a ship sailing on the ocean may cause instability. Therefore it is of great importance to study the properties of such waves, for example slope, wavelength and amplitude. When making statistics on the properties of overtaking waves, only the waves that are faster than the ship will affect the resulting distribution. Thus the velocity of the individual waves plays an important role and in this paper we describe how it comes into play when computing distibutions for certain wave characteristics. The distributions are evaluated for a Gaussian sea having a Pierson-Moskowitz spectrum.