Authors : Giorgos Margazoglu, Luca Biferale, Massimo Cencini, Giovanni Gallavotti, Valerio Lucarini

Title:: Non-equilibrium Ensembles for the 3D Navier-Stokes Equations

Abstract: At the molecular level fluid motions are, by first principles, described by time reversible laws. On the other hand, the coarse grained macroscopic evolution is suitably described by the Navier Stokes equations, which are inherently irreversible, due to the dissipation term. Here, a reversible version of 3D Navier Stokes is studied, by introducing a fluctuating viscosity constructed in such a way that enstrophy is conserved, along the lines of the paradigm of microcanonical versus canonical treatment in equilibrium statistical mechanics. Through systematic simulations we provide evidences of the conditions that must be satisfied in order to have a statistical equivalence between the two non-equilibrium ensembles. Moreover, we numerically study the empirical distribution of the fluctuating viscosity by changing the Reynolds number and the number of modes used in the discretization of the evolution equation.

Keywords: Irreversible fluid equations, Reversible fluid equations, Equivalence Irreversible-Reversible

Giovanni Gallavotti
INFN-Roma1 and Universit\`a "La Sapienza” Roma, Italy