Effect of forward speed on the level-crossing distribution of kinematic variables in multidirectional ocean waves. (1st September 2021) - Hascoët, Romain; Raillard, Nicolas; Jacques, Nicolas
Abstract: 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. Highlights: Forward speed of a ship induces a Doppler shift on the wave encounter frequency. Doppler shift significantly affects stochastic free-surface crossing. The crossing frequency and crossing kinematics are affected by Doppler shift. The effect of forward speed on free-surface crossing is analytically investigated. The Doppler shift is of practical importance for slamming on ship.