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