Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

TL;DR

This study investigates how energy is partitioned between waves and vortices in stratified turbulence with or without rotation, revealing the dominance of slow quasi-geostrophic modes in the inverse cascade and how this behavior changes with stratification strength.

Contribution

The paper provides new insights into the energy transfer mechanisms in stratified turbulence, especially the role of slow modes and the impact of increasing stratification on the inverse cascade.

Findings

Inverse cascade dominated by slow quasi-geostrophic modes.

Energy spectra and fluxes show characteristics of inverse cascade.

Inverse cascade weakens and disappears as N/f increases in stratified turbulence.

Abstract

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behavior of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number Re=1000, with the ratio between the Brunt-V\"ais\"al\"a frequency N and the inertial frequency f varying from 1/4 to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range 0.02 < Fr < 0.32. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio N/f increases, also in the stratified case, although less and less so. However, when N/f increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing N/f can be interpreted in terms of the waves and vortices, and identify three major effects that can explain this transition based on inviscid invariants arguments.