Helicity dynamics in stratified turbulence in the absence of forcing

TL;DR

This study investigates how helicity influences the decay and energy distribution in stratified turbulence, revealing that helicity persists longer and significantly alters flow dynamics under stratification.

Contribution

It demonstrates the slow decay of helicity in stratified ABC flows and its impact on energy decay rates and spectral properties, highlighting the role of large-scale structures.

Findings

Helicity decays slower in stratified ABC flows compared to unstratified cases.

Helical flows exhibit slower energy decay than non-helical flows under stratification.

Helicity affects large-scale spectral behavior, especially at scales larger than the buoyancy scale.

Abstract

A numerical study of decaying stably-stratified flows is performed. Relatively high stratification and moderate Reynolds numbers are considered, and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations). The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a non-helical Taylor-Green (TG) flow, a fully helical Beltrami (ABC) flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative "cyclostrophic" balance can be invoked to explain this behavior. When helicity survives in the system it strongly affects the temporal energy decay and the energy distribution among Fourier modes. We discover in fact that the decay rate of energy for stratified helical flows is much slower than for stratified non-helical flows and can be considered with a phenomenological model in a way similar to what is done for unstratified rotating flows. We also show that helicity, when strong, has a measurable effect on the Fourier spectra, in particular at scales larger than the buoyancy scale for which it displays a rather flat scaling associated with vertical shear.