Fluctuations in 2D reversibly-damped turbulence

Abstract

Gallavotti proposed an equivalence principle in hydrodynamics, which states that forced-damped fluids can be equally well represented by means of the Navier-Stokes equations and by means of time reversible dynamical systems called GNS. In the GNS systems, the usual viscosity is replaced by a state-dependent dissipation term which fixes one global quantity. The principle states that the mean values of properly chosen observables are the same for both representations of the fluid. In the same paper, the chaotic hypothesis of Gallavotti and Cohen is applied to hydrodynamics, leading to the conjecture that entropy fluctuations in the GNS system verify a relation first observed in nonequilibrium molecular dynamics. We tested these ideas in the case of two-dimensional fluids. We examined the fluctuations of global quadratic quantities in the statistically stationary state of a) the Navier-Stokes equations; b) the GNS equations. Our results are consistent with the validity of the fluctuation relation, and of the equivalence principle, indicating possible extensions thereof. Moreover, in these results the difference between the Gallavotti-Cohen fluctuation theorem and the Evans-Searles identity is evident.

latex-2e, 14 pages, 6 figures, submitted to Nonlinearity. Revised version following the referees' comments: text polished, a few algebraic mistakes corrected, figures improved, reference to the Evans-Searles identity added

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Cited by in corpus (19)

• Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
• On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium
• The Steady State Fluctuation Relation for the Dissipation Function
• The Gallavotti-Cohen Fluctuation Theorem for a non-chaotic model
• Entropy, irreversibility and cascades in the inertial range of isotropic turbulence
• Heat and Fluctuations from Order to Chaos
• Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence
• Generalized fluctuation relation and effective temperatures in a driven fluid
• Phase transition in time-reversible Navier-Stokes equations
• Equivalence of nonequilibrium ensembles in turbulence models
• Non equilibrium in statistical and fluid mechanics. Ensembles and their equivalence. Entropy driven intermittency
• Anomalies, absence of local equilibrium and universality in 1-d particles systems
• Fluctuations of entropy production in turbulent thermal convection
• Coherent structures at the origin of time irreversibility in wall turbulence
• Constrained Reversible system for Navier-Stokes Turbulence: evidence for Gallavotti's equivalence conjecture
• Fluctuations of energy injection rate in a shear flow
• Equivalence of nonequilibrium ensembles: Two-dimensional turbulence with a dual cascade
• Poles, Shocks and Tygers: The Time-reversible Burgers equation
• Lyapunov spectra and nonequilibrium ensembles equivalence in 2D fluid mechanics