The structure of internal waves in the ocean is sensitive to wave frequency, latitude, stratification, background currents and local bathymetry. I am particularly interested in how sloping bathymetry influences the dynamics of internal waves, both close to coasts, where dramatic continental shelf topography guides trapped wave energy in coastal trapped waves; and in the deep ocean, where both large scale gentle slopes and abrupt topography can lead to significant deviations in the structure of internal waves away from the often used flat bottom modes.
For the purposes of obtaining analytic solutions, it’s common practice to assume that the ocean seafloor is flat. The effect of sloping bathymetry is to make the solutions dependent on the angle at which the waves propagate with respect to the bathymetric slope. We use Dedalus to solve for the vertical modes with a sloping bottom, extending the work of Straub (1994) and LaCasce (2017), and demonstrating the complexity of solutions that arise from such a simple change. And example of the solutions obtained at the Argentine Basin OOI site is shown below.
Some of this work has been published in Toole et al. (2023).