# Diffusion of inertia-gravity waves by geostrophic turbulence

## TL;DR

This paper derives a diffusion equation describing how inertia-gravity waves scatter and spread in wavenumber space due to geostrophic turbulence, supported by numerical simulations and relevant to atmospheric and oceanic spectra.

## Contribution

It introduces a new diffusion model for inertia-gravity wave scattering by geostrophic turbulence and validates it with numerical simulations.

## Key findings

- Wave energy diffuses on the constant-frequency cone in wavenumber space.
- The model predicts a $k^{-2}$ energy spectrum in forced turbulence scenarios.
- Results align with observed atmospheric and oceanic spectral features.

## Abstract

The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the corresponding diffusion equation and relate its diffusivity to the wave characteristics and the energy spectrum of the turbulent flow. We check the predictions of this equation against numerical simulations of the three-dimensional Boussinesq equations in initial-value and forced scenarios with horizontally isotropic wave and flow fields. In the forced case, wavenumber diffusion results in a $k^{-2}$ wave energy spectrum consistent with as-yet-unexplained features of observed atmospheric and oceanic spectra.