Nonlinear superposition of direct and inverse cascades in two-dimensional turbulence forced at large and small scales

TL;DR

This paper investigates two-dimensional turbulence driven simultaneously at large and small scales, revealing that the velocity field can be represented as a sum of two auxiliary fields each exhibiting distinct cascade behaviors, which reconcile universal flux properties.

Contribution

It introduces a nonlinear superposition approach to analyze 2D turbulence with dual-scale forcing, linking direct enstrophy and inverse energy cascades.

Findings

Velocity field decomposes into two auxiliary fields with distinct cascades.

Auxiliary fields exhibit positive correlation in the inertial range.

Universal flux properties are maintained despite dual forcing.

Abstract

We inquire about the properties of 2d Navier-Stokes turbulence simultaneously forced at small and large scales. The background motivation comes by observational results on atmospheric turbulence. We show that the velocity field is amenable to the sum of two auxiliary velocity fields forced at large and small scale and exhibiting a direct-enstrophy and an inverse-energy cascade, respectively. Remarkably, the two auxiliary fields reconcile universal properties of fluxes with positive statistical correlation in the inertial range.