A stochastic model of cascades in two-dimensional turbulence

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 upscale and downscale fluxes point to non-locality of interactions in spectral space, and thus the specific spatial structure of the flow could be important. Shell models, which lack spatial 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.