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

TL;DR

This paper introduces a reversible Navier-Stokes model constrained by constant Enstrophy, demonstrating through numerical experiments that it accurately reproduces turbulence statistics and supports Gallavotti's conjecture about equivalent descriptions of stationary states.

Contribution

The authors propose a new reversible model for Navier-Stokes turbulence that maintains constant Enstrophy, providing evidence for Gallavotti's conjecture and offering a simpler, effective alternative for turbulence simulation.

Findings

Reversible model reproduces turbulence statistics accurately.

Model remains mathematically simpler with bounded Enstrophy.

Supports Gallavotti's equivalence conjecture for stationary states.

Abstract

Following the Gallavotti's conjecture, Stationary states of Navier-Stokes fluids are proposed to be described equivalently by alternative equations besides the NS equation itself. We propose a model system symmetric under time-reversal based on the Navier-Stokes equations constrained to keep the Enstrophy constant. It is demonstrated through high-resolved numerical experiments that the reversible model evolves to a stationary state which reproduces quite accurately all statistical observables relevant for the physics of turbulence extracted by direct numerical simulations at different Reynolds numbers. The possibility of using reversible models to mimic turbulence dynamics is of practical importance for coarse-grained version of Navier-Stokes equations, as used in Large-eddy simulations. Furthermore, the reversible model appears mathematically simpler, since enstrophy is bounded to be constant for every Reynolds. Finally, the theoretically interest in the context of statistical mechanics is briefly discussed.