Internal waves forcing mean flows

At the simplest level, two sets of independent eigenmodes are sufficient to describe oceanic fluid motion: fast inertia-gravity waves, and slow, balanced motions. In the ocean's interior, the former are the cousins of the surface waves, swells, and tides that most people are familiar with. The latter on the other hand are the cousins of the weather systems and jet streams of the atmosphere and look like vortices or ribbon-like jets.

When the dynamics are linear, and away from any forcing or dissipation, both sets of eigenmodes live happy independent lives. Waves keep oscillating, while balanced modes keep jetting and whirling, conserving their so-called potential vorticity (a quantity whose conservation law, one deduces from the conservation laws for angular momentum, mass, and entropy in a rotating, stratified flow). But when the dynamics are non-linear, exchanges between fast and slow modes arise. While the fundamental process is well-known in other areas of physics and fluid dynamics (look up "acoustic streaming"), how it might play out in the oceans, and its consequences there, are still barely understood.

While most of my studies on this topic have been curiosity-driven, oceanography as a community is getting to a point where such processes can be both measured, and believed to be important.

My first exposure to this phenomenon came serendipitously, as a parasite phenomenon in the lab. While studying nonlinear wave-wave interactions on the Coriolis turntable in Grenoble (FR), I came across a systematic bending of my otherwise-perfectly-crafted wave beams. The slow, balanced flow that would develop over time was the culprit. You can see a video of it below, with a camera sitting on the side of the setup, looking at a vertical slice of the flow (false contrast).


My first post-doctoral experience at the Courant Institute of Mathematical Sciences addressed this question from an analytical point of view. We were able to compute the non-linear forcing of the balanced modes, by a dissipating internal tide, using the Generalize Lagrangian Formalism. Our particular theoretical setup explains how to generate balanced flows on top of seamounts. It could potentially close the angular momentum budget of the vortices, ubiquitously hovering above seamounts. See animations below.

 References (see Publications page for pdfs or pre-prints):

  • Grisouard, Nicolas, Matthieu Leclair, Louis Gostiaux, and Chantal Staquet. 2013. “Large Scale Energy Transfer from an Internal Gravity Wave Reflecting on a Simple Slope.” Procedia IUTAM 8 (January). Moscow: Elsevier: 119–28. doi:10.1016/j.piutam.2013.04.016.

  • Grisouard, Nicolas, and Oliver Bühler. 2012. “Forcing of Oceanic Mean Flows by Dissipating Internal Tides.” Journal of Fluid Mechanics 708 (August): 250–78. doi:10.1017/jfm.2012.303.