Geophysical turbulence and the duality of the energy flow across scales

TL;DR

This paper demonstrates through simulations that geophysical turbulence exhibits simultaneous large-scale inverse energy cascade and small-scale dissipation, resolving a long-standing contradiction in understanding oceanic and atmospheric flows.

Contribution

It provides the first direct numerical evidence that both inverse cascade and small-scale dissipation can occur concurrently in rotating stratified turbulence.

Findings

Large-scale coherence and small-scale mixing develop simultaneously.

Energy flux remains constant across scales, confirming theoretical predictions.

The dual behavior resolves the apparent contradiction in geophysical turbulence dynamics.

Abstract

The ocean and the atmosphere, and hence the climate, are governed at large scale by interactions between pressure gradient, Coriolis and buoyancy forces. This leads to a quasi-geostrophic balance in which, in a two-dimensional-like fashion, the energy injected by solar radiation, winds or tides goes to large scales in what is known as an inverse cascade. Yet, except for Ekman friction, energy dissipation and turbulent mixing occur at small scale implying the formation of such scales associated with breaking of geostrophic dynamics through wave-eddy interactions \cite{ledwell_00, vanneste_13} or frontogenesis \cite{hoskins_72, mcwilliams_10}, in opposition to the inverse cascade. Can it be both at the same time? We exemplify here this dual behavior of energy with the help of three-dimensional direct numerical simulations of rotating stratified Boussinesq turbulence. We show that efficient small-scale mixing and large-scale coherence develop simultaneously in such geophysical and astrophysical flows, both with constant flux as required by theoretical arguments, thereby clearly resolving the aforementioned contradiction.