Numerical study of internal wave reflection from sloping boundaries

Abstract

The breaking of internal waves propagating in a stratified fluid of constant buoyancy frequency on a sloping boundary was investigated numerically. It was found that at the boundary, nonlinear non-resonant interactions between the incident and reflected waves produced higher-mode waves. These modes had frequencies greater than the local buoyancy frequency and so could not radiate from the interaction region. The energy level of trapped waves increased with time and subsequently led to overturning of the density field. At the critical frequency, when the reflected wave propagated in a direction parallel to the slope, wave overturning occurred near the wall, but the point of overturning moved off the bottom as the propagation angle changed away from that of the bottom slope as the waves became increasingly supercritical. The internal wave reflection coefficient generally increased as the effects of nonlinearity and viscosity decreased, but depended strongly on the forcing frequency and the angle of the sloping boundary.