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The influence of forward speed on stochastic free-surface crossing, in aGaussian wave field, is investigated. The case of a material point moving witha constant forward speed is considered; the wave field is assumed stationary intime, and homogeneous in space. The focus is on up-crossing events, which aredefined as the material point crossing the free surface, into the water domain.The effect of the Doppler shift (induced by the forward speed) on theup-crossing frequency, and the related conditional joint distribution of wavekinematic variables is analytically investigated. Some general trends areillustrated through different examples, where three kinds of wave directiondistribution are considered: unidirectional, short-crested anisotropic, andisotropic. The way the developed approach may be used in the context ofslamming on marine structures is briefly discussed.

Effect of forward speed on the level-crossing distribution of kinematic variables in multidirectional ocean waves