2D turbulence in physical scales of the Navier-Stokes equations

TL;DR

This paper analyzes 2D turbulence through local analysis of the Navier-Stokes equations, deriving conditions for energy and enstrophy cascades using physical scales without assuming homogeneity.

Contribution

It provides new bounds on energy and enstrophy fluxes in 2D turbulence based on physical scales, without homogeneity assumptions.

Findings

Derived conditions for enstrophy and energy cascades.

Established locality of fluxes under certain conditions.

Utilized actual physical scales in R^2 without homogeneity.

Abstract

Local analysis of the two dimensional Navier-Stokes equations is used to obtain estimates on the energy and enstrophy fluxes involving Taylor and Kraichnan length scales and the size of the domain. In the framework of zero driving force and non-increasing global energy, these bounds produce sufficient conditions for existence of the direct enstrophy and inverse energy cascades. Several manifestations of locality of the fluxes under these conditions are obtained. All the scales involved are actual physical scales in R^2 and no homogeneity assumptions are made.