The Vortical Structure of Parasitic Capillary Waves

Abstract

A two-dimensional numerical simulation of the parasitic capillary waves that form on a 5 cm gravity-capillary wave is performed. A robust numerical algorithm is developed to simulate flows with complex boundary conditions and topologies. The free-surface boundary layer is resolved at the full-scale Reynolds, Froude, and Weber numbers. Seventeen million grid points are used to resolve the flow to within 6 × 10–4 cm. The numerical method is used to investigate the formation of parasitic capillary waves on the front face of a gravity-capillary wave. The parasitic capillary waves shed vorticity that induces surface currents that exceed twenty-five percent of the phase velocity of the gravity-capillary wave when the steepness of the parasitic capillary waves is approximately 0.8 and the total wave steepness is 1.1. A mean surface current develops in the direction of the wave’s propagation and is concentrated on the front face of the gravity-capillary wave. This current enhances mixing, and remnants of this surface current are probably present in post-breaking waves. Regions of high vorticity occur on the back sides of the troughs of the parasitic capillary waves. The vorticity separates from the free surface in regions where the wave-induced velocities exceed the vorticity-induced velocities. The rate of energy dissipation of the gravity-capillary wave with parasitic capillaries riding on top is twenty-two times greater than that of the gravity-capillary wave alone.