Nancy Soontiens, Applied Math, University of Waterloo
Stratified Flow Over Topography: Steady Nonlinear Waves, Boundary Layer Instabilities, and Crater Topography
This thesis investigates several aspects of stratified flow over isolated topography in ocean, lake, and atmospheric settings. Three major sub-topics are addressed: steady, inviscid internal waves trapped over topography in a pycnocline stratification, topographically generated internal waves and their interaction with the viscous bottom boundary layer, and flow over large-scale crater topography in the atmosphere.
The first topic examines the conditions that lead to very large internal waves trapped over topography. The steady-state Euler equations of motion are used to derive a single partial differential equation for the isopycnal displacement in supercritical flows. It is found that over depression topography wave amplitudes can approach up to 50% of the water column depth when the background flow speed is close to a limiting value called the conjugate flow speed. The second topic aims to extend the above subject by considering unsteady, viscous flows and the generation of boundary layer instabilities. Lastly, the final topic is motivated by the connection between dust streaks on the Martian surface and crater topography. Flow over a large 100-km diameter crater is examined with numerical simulations conducted using the Weather Research and Forecasting model. It is found that a large hydraulic structure of amplitude comparable to the crater depth forms in many cases.