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

Romain Hascoët (1, 2) , Nicolas Raillard (3) , Nicolas Jacques (1, 2)

1 IRDL - Institut de Recherche Dupuy de Lôme
2 ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne
3 IFREMER - Institut Français de Recherche pour l'Exploitation de la Mer

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.

Mots clés: water wave; Gaussian; level crossing; Doppler effect; forward speed; slamming

Domaines: Mécanique des fluides [physics.class-ph]

Romain Hascoët, Nicolas Raillard, Nicolas Jacques. Effect of forward speed on the level-crossing distribution of kinematic variables in multidirectional ocean waves. 2021. ⟨hal-03263362⟩