Internal Waves Generated by Tidal Flows over a Triangular Ridge with Critical Slopes

Abstract

Direct numerical simulations are performed to investigate the generation of internal waves by tide-topography interaction in a lab-scale model. The bottom topography is a triangular ridge with two critical slopes. With increasing tidal forcing, subhar-monic instabilities are identified, which cause internal wave beams to become unstable and turbulent. Kinetic energy densities in the upward going beams from the ridge top are stronger than those from the ridge bottom, whereas the reverse is true for the energy flux. This disparity between energy and energy flux is due to the existence of strong pressure disturbances near the ridge bottom. On each side of the critical ridge, there exists an amphidromic point, from which internal wave beams are emitted in opposite directions. The calculated energy conversion rate scales linearly with the square of the forcing amplitude and agrees within 13% of theoretical prediction, even when turbulence occurs. The fraction of radiated baroclinic energy becomes saturated in the range of low excursion parameter considered, which agrees with the behavior in large-scale systems wherein mixing parameterizations must be used. The present work enriches the studies on the generation of internal waves over a critical triangular ridge.