Doppler-shift approximations of encountered wave statistics

In this paper the joint density of waveheight and half-wavelength is considered for waves observed at a fixed time point and encountering waves that are overtaking a ship from behind. The densities for these two cases are related by a Doppler shift, expressed in terms of the relative velocity of the waves and the ship. Based on this observation, an approximation of the encountered density is proposed. This approximation is then investigated for a Gaussian sea having a Pierson-Moskowitz spectrum.