Interplay of waves and eddies in rotating stratified turbulence and the link with kinetic-potential energy partition

TL;DR

This study uses high-resolution simulations to analyze how waves and eddies interact in rotating stratified turbulence, revealing a scale-independent energy partition and linking it to potential energy dynamics.

Contribution

It identifies a critical wavenumber for wave-vortex transition that is independent of Reynolds number and correlates with energy exchange stabilization, advancing understanding of stratified turbulence.

Findings

Transition wavenumber $k_R$ is Reynolds number independent.

$k_R$ is comparable to the wavenumber of kinetic-potential energy equipartition.

$k_R$ scales inversely with the Froude number.

Abstract

The interplay between waves and eddies in stably stratified rotating flows is investigated by means of world-class direct numerical simulations using up to $3072^3$ grid points. Strikingly, we find that the shift from vortex to wave dominated dynamics occurs at a wavenumber $k_R$ which does not depend on Reynolds number, suggesting that partition of energy between wave and vortical modes is not sensitive to the development of turbulence at the smaller scales. We also show that $k_R$ is comparable to the wavenumber at which exchanges between kinetic and potential modes stabilize at close to equipartition, emphasizing the role of potential energy, as conjectured in the atmosphere and the oceans. Moreover, $k_R$ varies as the inverse of the Froude number as explained by the scaling prediction proposed, consistent with recent observations and modeling of the Mesosphere-Lower Thermosphere and of the ocean.