Beneath the ocean’s surface lies a field of internal waves that transports energy and contributes to mixing. Despite widely varying winds, tides, and topography, many observations share a remarkably similar spectral shape, captured by the empirical Garrett–Munk model. Why should such a complicated system admit such a simple description?

This talk explores that question through a two-dimensional model of rotating, stratified flow. We introduce the wave-turbulence picture of resonant interactions and energy cascades, then show how conservation laws and scaling reduce the search for a turbulent spectrum. A singularity associated with slow waves leads to a crucial role for rotation. Combining analytic arguments with numerical evidence in the weak-rotation regime yields a spectral shape consistent with Garrett–Munk. The talk is intended for a broad mathematical audience; no background in oceanography or wave turbulence is assumed.

Joint work with Michal Shavit and Oliver Bühler.