Non-Gaussian properties of second-order wave orbital velocity

TL;DR

This paper investigates the non-Gaussian statistical properties of wave orbital velocities using a second-order stochastic model, highlighting the effects of nonlinearity, water depth, and directional spreading, validated by laboratory experiments.

Contribution

It introduces a second-order wave model to analyze orbital velocity statistics, revealing significant deviations from Gaussian behavior and the influence of physical parameters, validated by experimental data.

Findings

Sub-harmonics dominate second-order orbital velocity contributions.

Notable set-down occurs for energetic and steep wave groups.

Velocities deviate from Gaussian predictions, especially below troughs and crests.

Abstract

A stochastic second-order wave model is applied to assess the statistical properties of wave orbital velocity in random sea states below the water surface. Directional spreading effects as well as the dependency of the water depth are investigated by means of a Monte-Carlo approach. Unlike for the surface elevation, sub-harmonics dominate the second-order contribution to orbital velocity. We show that a notable set-down occurs for the most energetic and steepest groups. This engenders a negative skewness in the temporal evolution of the orbital velocity. A substantial deviation of the upper and lower tails of the probability density function from the Gaussian distribution is noticed, velocities are faster below the wave trough and slower below the wave crest when compared with linear theory predictions. Second-order nonlinearity effects strengthen with reducing the water depth, while weaken with the broadening of the wave spectrum. The results are confirmed by laboratory data. Corresponding experiments have been conducted in a large wave basin taking into account the directionality of the wave field. As shown, laboratory data are in very good agreement with the numerical prediction.