Large-scale anisotropy in stably stratified rotating flows

TL;DR

This study uses high-resolution simulations to explore anisotropic energy transfer in rotating and stratified turbulence, revealing inverse cascades and horizontal spectra consistent with Kolmogorov scaling.

Contribution

It demonstrates the development of anisotropic energy transfer and horizontal spectra in stratified turbulence, extending understanding beyond previous studies by including high Reynolds numbers and scale separation.

Findings

Inverse energy cascades occur in rotating turbulence regardless of stratification.

Purely stratified flows develop anisotropic transfer with near-zero isotropic flux.

Horizontal energy spectra follow a rac{5}{3} power law, indicating a direct cascade in stratified turbulence.

Abstract

We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to $1024^3$ grid points and Reynolds numbers of $\approx 1000$. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with $\sim k_\perp^{-5/3}$, including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.