On the emergence of helicity in rotating stratified turbulence

TL;DR

This study demonstrates that helicity naturally arises in rotating stratified turbulence due to the interaction of buoyancy and rotation, with the amount of helicity depending on the ratio of buoyancy to rotation frequencies and the flow's Reynolds number.

Contribution

It reveals the spontaneous emergence of helicity in rotating stratified turbulence and provides a quantitative prediction of helicity production based on flow parameters.

Findings

Helicity is generated due to buoyancy and rotation interplay.

Helicity production is predicted by a quasi-linear balance for N/f < 3.

Helicity persists at high Reynolds numbers and large N/f ratios.

Abstract

We perform numerical simulations of decaying rotating stratified turbulence and show, in the Boussinesq framework, that helicity (velocity-vorticity correlation), as observed in super-cell storms and hurricanes, is spontaneously created due to an interplay between buoyancy and rotation common to large-scale atmospheric and oceanic flows. Helicity emerges from the joint action of eddies and of inertia-gravity waves (with inertia and gravity with respective associated frequencies $f$ and $N$), and it occurs when the waves are sufficiently strong. For $N/f < 3$ the amount of helicity produced is correctly predicted by a quasi-linear balance equation. Outside this regime, and up to the highest Reynolds number obtained in this study, namely $Re\approx 10000$, helicity production is found to be persistent for $N/f$ as large as $\approx 17$, and for $ReFr^2$ and $ReRo^2 $ respectively as large as $\approx 100$ and $\approx 24000$.