Breaking of internal waves parametrically excited by ageostrophic anticyclonic instability

TL;DR

This study numerically investigates how internal waves excited by ageostrophic anticyclonic instability break and generate turbulence, revealing two distinct breaking scenarios based on the instability growth rate.

Contribution

It introduces a novel numerical approach focusing on small-scale waves and turbulence by excluding large-scale vortex structures, and identifies two wave-breaking regimes conditioned on instability growth.

Findings

Fast-growing waves break quickly, leading to strong turbulence.

Slow-growing waves undergo wave-wave interactions, forming a Garrett-Munk-like spectrum.

Energy dissipation rates vary with wave amplitude and instability growth rate.

Abstract

A gradient-wind balanced flow with an elliptic streamline parametrically excites internal inertia-gravity waves through ageostrophic anticyclonic instability (AAI). This study numerically investigates the breaking of internal waves and the following turbulence generation resulting from the AAI. In our simulation, we periodically distort the calculation domain following the streamlines of an elliptic vortex and integrate the equations of motion using a Fourier spectral method. This technique enables us to exclude the overall structure of the large-scale vortex from the computation and concentrate on resolving the small-scale waves and turbulence. From a series of experiments, we identify two different scenarios of wave breaking conditioned on the magnitude of the instability growth rate scaled by the buoyancy frequency, $\lambda/N$. First, when $\lambda/N\gtrsim0.008$, the primary wave amplitude excited by AAI quickly goes far beyond the overturning threshold and directly breaks. The resulting state is thus strongly nonlinear turbulence. Second, if $\lambda/N\lesssim0.008$, weak wave-wave interactions begin to redistribute energy across frequency space before the primary wave reaches a breaking limit. Then, after a sufficiently long time, the system approaches a Garrett-Munk-like stationary spectrum, in which wave breaking occurs at finer vertical scales. Throughout the experimental conditions, the growth and decay time scales of the primary wave energy are well correlated. However, since the primary wave amplitude reaches a prescribed limit in one scenario but not in the other, the energy dissipation rates exhibit two types of scaling properties. This scaling classification has similarities and differences with D'Asaro and Lien's (2000) wave-turbulence transition model.