Wave-current interaction on a free surface

TL;DR

This paper derives new closed equations for free-surface fluid flow that incorporate wave-current interactions, allowing for circulation and vorticity dynamics, thus advancing the understanding of nonlinear wave phenomena.

Contribution

It introduces a novel set of free-surface motion equations that are not limited to potential flow, enabling true wave-current interaction modeling.

Findings

Derived closed free-surface equations including wave-current interactions

Demonstrated wave activity can induce circulation and vorticity

Opened new avenues for nonlinear wave analysis

Abstract

The classic evolution equations for potential flow on the free surface of a fluid flow are not closed because the pressure and the vertical velocity dynamics are not specified on the free surface. Moreover, their wave dynamics does not cause circulation of the fluid velocity on the free surface. The equations for free-surface motion we derive here are closed and they are not restricted to potential flow. Hence, true wave-current interaction dynamics can occur. In particular, the Kelvin-Noether theorem demonstrates that wave activity can induce fluid circulation and vorticity dynamics on the free surface. The wave-current interaction equations introduced here open new vistas for both the deterministic and stochastic analysis of nonlinear waves on free surfaces.