# Seminars

# Atmosphere Ocean Science Friday Seminar

#### Two talks from our current students

**Speaker:**
Nick DeFilippis and Matt Pudig, CAOS

**Location:**
Warren Weaver Hall 1314

**Date:**
Friday, October 20, 2023, 4 p.m.

**Synopsis:**

**Nick**

Observations of the oceanic internal wave energy frequency spectrum reveal a peak in the near-inertial band and a power law in the super-inertial range. Recent numerical and theoretical results suggest that wave energy injected in the near-inertial band is spread to higher frequencies through scattering by the balanced eddy field. We investigate elements of this idea through a series of numerical simulations of the nonlinear shallow water equations, initialized with a narrow band of near-inertial waves, and a balanced field characterized by steady-state geostrophic turbulence. The amplitude of the balanced flow is characterized by small Rossby number, and the amplitude of the wave flow is weak relative to the balanced flow. The balanced velocities, however, are slow compared to the wave group velocity, placing the overall flow in a small-Froude-number regime. When the balanced flow is removed, wave energy does not spread, even over very long times. As the magnitude of the balanced flow is increased, however, wave energy is spread to higher frequencies and smaller scales, following a power-law.Previous theoretical work in a similar regime of rotating shallow water flow finds that unsteady balanced flows produce frequency spreading via an ‘induced diffusion’ of wave modes to higher wavenumbers. These results are supported by numerical integrations of the ray tracing equations through synthetically-generated balanced flows. We close the gap by showing to what degree current theory, and the ray tracing approach, are able to explain the results of our nonlinear simulations.

**Matt**

Much theoretical work on geostrophic turbulence in the ocean assumes a flat bottom: a sea floor absent of slopes, mounts and valleys. Of course, the sea floor is not flat, and bottom topography can in fact impact quite profoundly the large-scale turbulence occurring above. In particular, bottom topography can affect geostrophic turbulence by modifying both the horizontal scale to which the inverse energy cascade can proceed—thus affecting the eddy scale of the fully-developed turbulence—as well as the preferred vertical structure of these eddies. In this short talk, I will focus on these two effects of bottom topography and seek to give a pedagogical tour through what I have learned over the last few months. Toward the end, I will show some results from recent work on these ideas and speculate on the directions in which I hope this work to go.