Nonlinear inertia-gravity wave-mode interactions in three dimensional rotating stratified flows

TL;DR

This study examines the dynamics of inertia-gravity wave modes in 3D rotating stratified fluids, highlighting the importance of vortical interactions for energy distribution and spectral scaling, with implications for geophysical simulations.

Contribution

It introduces the GGG model focusing solely on wave interactions and compares it to the full system to assess the role of vortical modes in energy transfer.

Findings

Vortical modes are crucial for wave energy equilibration.

Wave-wave interactions influence spectral scaling at moderate parameters.

Resolving wave interactions is challenging in realistic geophysical simulations.

Abstract

We investigate the dynamics of inertia-gravity wave modes in 3D rotating stratified fluids. We start by deriving a reduced PDE, the GGG model, consisting of only wave-mode interactions. In principle, comparing this model to the full rotating Boussinesq system allows us to gauge the importance of wave-vortical-wave vs. wave-wave-wave interactions in determining the transfer and distribution of wave-mode energy. As in many atmosphere-ocean phenomena we work in a skewed aspect ratio domain (H/L) with Fr = Ro < 1 such that Bu = 1. Our focus is on the equilibration of wave-mode energy and its spectral scaling under the influence of random large-scale forcing. As anticipated, when forcing is applied to all modes, with Fr=Ro ~ 0.05 and H/L=1/5, the wave-mode energy equilibrates and its spectrum scales as a power-law. For the same parameters, when forcing is restricted to only wave modes, the energy fails to equilibrate in both the full system as well as the GGG subsystem at resolutions we can achieve. This cleary demonstrates the importance of the vortical mode in determining the wave-mode energy distribution. Proceeding to the second set of simulations, i.e. for the larger Fr=Ro ~ 0.1 in a less skewed aspect ratio domain with H/L=1/3, we observe that the energy of the GGG subsystem equilibrates. Further, the full system with forcing restricted to wave modes also equilbrates and both yield identical energy spectra. Thus it is clear that the wave-wave-wave interactions play a role in the overall dynamics at moderate Ro, Fr and aspect ratios. Apart from theoretical concerns, these results highlight the difficulty in properly resolving wave-mode interactions when simulating realistic geophysical phenomena.