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.

研究了在高斯波场中前进速度对随机自由表面交叉的影响。考虑材料点以恒定前进速度移动的情况；假设波场在时间上是静止的，在空间上是均匀的。重点是向上穿越事件，这些事件被定义为穿过自由表面的物质点进入水域。分析研究了多普勒频移（由前进速度引起）对上交叉频率的影响，以及波运动学变量的相关条件联合分布。通过不同的例子说明了一些一般趋势，其中考虑了三种波浪方向分布：单向、短波峰各向异性和各向同性。