A stochastic model of cascades in 2D turbulence

TL;DR

This paper introduces a stochastic spectral model for 2D turbulence that accurately reproduces the dual cascade phenomena, emphasizing the importance of non-local interactions in spectral space.

Contribution

A novel stochastic model that is local in spectral space and successfully captures the dual cascade in 2D turbulence, challenging the necessity of non-local interactions.

Findings

Model reproduces correct scaling for both cascades

Local spectral interactions suffice for dual cascade

Challenges the role of non-locality in turbulence modeling

Abstract

The dual cascade of energy and enstrophy in 2D turbulence cannot easily be understood in terms of an analog to the Richardson-Kolmogorov scenario describing the energy cascade in 3D turbulence. The coherent up- and downscale fluxes points to non-locality of interactions in spectral space, and thus the specific spatial structure of the flow could be important. Shell models, which lack spacial structure and have only local interactions in spectral space, indeed fail in reproducing the correct scaling for the inverse cascade of energy. In order to exclude the possibility that non-locality of interactions in spectral space is crucial for the dual cascade, we introduce a stochastic spectral model of the cascades which is local in spectral space and which shows the correct scaling for both the direct enstrophy - and the inverse energy cascade.