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Following the Gallavotti's conjecture, Stationary states of Navier-Stokesfluids are proposed to be described equivalently by alternative equationsbesides the NS equation itself. We propose a model system symmetric undertime-reversal based on the Navier-Stokes equations constrained to keep theEnstrophy constant. It is demonstrated through high-resolved numericalexperiments that the reversible model evolves to a stationary state whichreproduces quite accurately all statistical observables relevant for thephysics of turbulence extracted by direct numerical simulations at differentReynolds numbers. The possibility of using reversible models to mimicturbulence dynamics is of practical importance for coarse-grained version ofNavier-Stokes equations, as used in Large-eddy simulations. Furthermore, thereversible model appears mathematically simpler, since enstrophy is bounded tobe constant for every Reynolds. Finally, the theoretically interest in thecontext of statistical mechanics is briefly discussed.

Constrained Reversible system for Navier-Stokes Turbulence: evidence for Gallavotti's equivalence conjecture