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

TL;DR

This paper analyzes how a constant forward speed affects the frequency and distribution of wave surface crossings in a stationary Gaussian wave field, with implications for marine structure safety.

Contribution

It introduces an analytical approach to quantify the Doppler shift effects on up-crossing events in multidirectional ocean waves.

Findings

Forward speed influences up-crossing frequency through Doppler shift.

Wave direction distribution affects crossing statistics.

Method applicable to marine structure impact assessments.

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.