Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows

TL;DR

This study uses high-resolution simulations and a coarse-graining approach to analyze energy and potential enstrophy cascades in rotating stratified Boussinesq flows, providing empirical evidence of a potential enstrophy cascade.

Contribution

It introduces a method to resolve the simultaneous evolution of energy and potential enstrophy in space and scale, demonstrating their constant fluxes across scales in different flow regimes.

Findings

Constant fluxes of energy and potential enstrophy observed across scales.

First empirical evidence supporting a cascade of potential enstrophy.

Flows differ from classical two-dimensional turbulence with persistent forward cascades.

Abstract

We employ a coarse-graining approach to analyze nonlinear cascades in Boussinesq flows using high-resolution simulation data. We derive budgets which resolve the evolution of energy and potential enstrophy simultaneously in space and in scale. We then use numerical simulations of Boussinesq flows, with forcing in the large-scales, and fixed rotation and stable stratification along the vertical axis, to study the inter-scale flux of energy and potential enstrophy in three different regimes of stratification and rotation: (i) strong rotation and moderate stratification, (ii) moderate rotation and strong stratification, and (iii) equally strong stratification and rotation. In all three cases, we observe constant fluxes of both global invariants, the mean energy and mean potential enstrophy, from large to small scales. The existence of constant potential enstrophy flux ranges provides the first direct empirical evidence in support of the notion of a cascade of potential enstrophy. The persistent forward cascade of the two invariants reflects a marked departure of these flows from two-dimensional turbulence.