Enstrophy dissipation in two-dimensional turbulence

Original · EN

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 Tₖ = γₖ /(νk²) of the intensity of driving γₖ>0 as a function of wavenumber k, to the dissipation strength νk², where ν is the viscosity. The enstrophy current flows from higher to lower values of Tₖ, 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.