Energy Exchanges between Density Fronts and Near-Inertial Waves Reflecting off the Ocean Surface

Abstract

nertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave?wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.