Internal Wave Scattering in Continental Slope Canyons

Abstract

This thesis investigates internal wave scattering in continental slope canyons using a ray tracing algorithm derived from linear internal wave theory and a fully nonlinear numerical model (MITgcm). We seek to understand how topographic parameters modulate the percentage of internal wave energy lost to wave breaking, dissipation and mixing within the canyon.

We first construct and utilize the ray tracing algorithm for idealized canyons. For the first time, we use ray tracing to quantify the likelihood of instability leading to wave breaking. We find that both increases in the ray (energy) density and vertical wavenumber can lead to instability within canyons. The spatial extent for potential instability is at a maximum for canyons that are relatively tall, narrow, and long compared to the wavelength.

Results from the ray tracing algorithm are compared with MITgcm results for continental slope canyons which occupy half the water column. Canyons with vertical sidewalls can dissipate all the incoming internal wave energy, while canyons with near-critical to supercritical sidewalls can only dissipate approximately 50% of the incoming wave's energy. For both cases, dissipation extends outside the canyon. Compared to a uniform vertical continental slope, canyons with vertical sidewalls can dissipate eight times as much energy, while canyons with near-critical to supercritical sidewalls can dissipate, at most, the same as a uniform near-critical continental slope. Canyons can thus be efficient internal wave dissipators compared to the surrounding continental slope. We additionally test the robustness of the ray tracing algorithm.

We finally consider three realistic continental slope canyons: Veatch, La Jolla and Eel Canyons. We find that the canyon-integrated energy loss in Veatch and Eel Canyons agrees with the idealized canyon results, despite introducing realistic topography and stratification. The dynamics leading to dissipation differ from the idealized canyons, as mixing is confined near the topography in a turbulent boundary layer rather than in large-scale overturns. Including rotation changes the energy loss' topographic dependence, as rotation alters both the canyon-integrated dissipation and the spatial distribution of dissipation. Based on our results, we estimate that continental slope canyons can dissipate approximately 2-24% of the global internal tide's energy budget.