Enstrophy dissipation in two-dimensional turbulence

TL;DR

This paper explores enstrophy dissipation in two-dimensional turbulence through an analogy with heat conduction, revealing entropy fluctuations, enstrophy current directions, and a fluctuation symmetry relating cascade probabilities.

Contribution

It introduces an entropy-based framework for understanding enstrophy dissipation, highlighting the nonlocal enstrophy network and the thermodynamic analogy in turbulence.

Findings

Enstrophy current flows from higher to lower T_k, similar to heat transfer.

The enstrophy network is highly nonlocal.

A fluctuation symmetry relates probabilities of direct and inverse cascades.

Abstract

Insight into the problem of two-dimensional turbulence can be obtained by an analogy with a heat conduction network. It allows the identification of an entropy function associated to the enstrophy dissipation and that fluctuates around a positive (mean) value. While the corresponding enstrophy network is highly nonlocal, the direction of the enstrophy current follows from the Second Law of Thermodynamics. An essential parameter is the ratio $T_k = \gamma_k /(\nu k^2)$ of the intensity of driving $\gamma_k>0$ as a function of wavenumber $k$, to the dissipation strength $\nu k^2$, where $\nu$ is the viscosity. The enstrophy current flows from higher to lower values of $T_k$, similar to a heat current from higher to lower temperature. Our probabilistic analysis of the enstrophy dissipation and the analogy with heat conduction thus complements and visualizes the more traditional spectral arguments for the direct enstrophy cascade. We also show a fluctuation symmetry in the distribution of the total entropy production which relates the probabilities of direct and inverse enstrophy cascades.