A Parameter Space Study of Internal Wave Dynamics in Continental Slope Canyons

When internal waves interact with topography, they have the potential to deposit their energy to local diapycnal mixing. The majority of such mixing has been shown to occur at the continental slope, for which a variety of parameterizations have been developed. Since submarine canyons comprise approximately ten percent of global continental slopes, they pose a significant means for dissipating internal wave energy, yet such parameterizations are currently missing from OGCMs. As a first step in the development of these parameterizations, we conduct a parameter space study of tidally-generated, M2-frequency, internal waves interacting with idealized V-shaped canyon topographies. Specifically, we employ a two-pronged approach: a suite of numerical simulations using the MITgcm, as well as a theoretical ray-tracing algorithm in which we vary the mouth width and sidewall angle (i.e. flat bottom or critical slope) of the canyon. Using the ray tracing algorithm in conjunction with dissipation and Richardson number diagnostics from the numerical simulations, we observe multiple wave reflections for intermediate canyon widths, with increased vertical wavenumber, and thus decreased Richardson number. Relative to the cliff/supercritical slope case, we find that V-shaped flat bottom canyons always dissipate more energy and are an effective geometry for wave trapping and subsequent energy loss. We also show that critical slope canyons always dissipate less energy than a plain critical slope, and achieve a large amount of that energy loss through a shallow boundary layer. As a next step, we seek to expand this parameter-space study to realistic topographies, such as Monterey and Atlantis Canyons, in order to validate our wave reflection and dissipation theory.