Frequency spreading of internal wave energy by balanced flows in two dimensions

TL;DR

This study uses numerical simulations to analyze how internal wave energy spreads in two-dimensional turbulent flows, finding weaker frequency spreading than earlier synthetic flow models suggested.

Contribution

It provides a realistic assessment of wave frequency diffusion in turbulent flows, narrowing the gap between two- and three-dimensional theories.

Findings

Frequency spreading is weaker in realistic turbulent flows compared to synthetic flows.

The derived timescale shows significantly less diffusion in realistic flows.

Other mechanisms likely contribute to broadband spectra in the atmosphere and ocean.

Abstract

Interactions between inertia-gravity waves and balanced flows lead to a spectral diffusion of wave action. Prior work has established that this diffusion is weak across constant frequency surfaces in three-dimensional settings, but can be significant in two dimensions with a non-stationary balanced flow. We investigate the two-dimensional setting through numerical simulations that simultaneously evolve a turbulent quasigeostrophic balanced flow and advect rotating shallow water wave packets. In contrast to earlier predictions based on the synthetic flows used by Dong et al. (J. Fluid Mech., 2020, vol. 905, R3), we find that frequency spreading from wave mean-flow interactions is weaker for realistic turbulent flows. We derive a timescale for frequency diffusion and show that frequency spreading with a realistic background flow is an order of magnitude smaller than with the synthetic flow. We narrow the discrepancy between the two- and three-dimensional induced diffusion theories, which suggests other mechanisms are responsible for the broadband frequency spectra seen in the atmosphere and ocean.