The effect of induced flow on the water wave skewness

TL;DR

This paper investigates how nonlinear wave-induced perturbations, especially the second harmonic, influence wave skewness and pressure fluctuations at different depths, revealing complex effects on wave shape and statistics.

Contribution

It introduces a second-order theory analysis of wave skewness, highlighting the impact of induced flow on wave shape and pressure statistics at various depths.

Findings

Bottom pressure skewness varies with depth and wave group configuration.

Surface displacement skewness is less affected by induced flow.

Second harmonic perturbations can invert phase and alter wave shape.

Abstract

Nonlinear wave-induced perturbations are discussed within the framework of the second-order theory. Due to the slow attenuation of the long perturbations with depth, they modulate motions beneath surface waves down to the bottom and can strongly affect the wave statistics. The disturbance which corresponds to the second harmonic, at a sufficient depth inverses the phase, thereby qualitatively changes the shape of individual waves. The skewness coefficients of the surface displacement and the bottom pressure fluctuations are considered. It is shown that the bottom pressure skewness may have different signs and magnitudes depending on the water depth and the configuration of nonlinear wave groups which compose the wave field. The effect on the surface displacement skewness is much weaker. Mechanisms leading to strong deviation of the skewness coefficient from the nonlinear Stokes wave theory are discussed.