Enstrophy dissipation in two-dimensional turbulence

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 with 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 equivalent to gamma(k)/(nu k(2)) of the intensity of driving gamma(k)>0 as a function of wave number 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.