Reversible Viscosity and Navier–Stokes Fluids

  title={Reversible Viscosity and Navier–Stokes Fluids},
  author={Giovanni Gallavotti},
  journal={Stochastic Dynamics Out of Equilibrium},
  • G. Gallavotti
  • Published 12 June 2017
  • Physics
  • Stochastic Dynamics Out of Equilibrium
Exploring the possibility of describing a fluid flow via a time-reversible equation and its relevance for the fluctuations statistics in stationary turbulent (or laminar) incompressible Navier-Stokes flows. 

Equivalent Ensembles, Turbulence and Fluctuation Theorem

Stationary states of Navier-Stokes fluids have been proposed to be described equivalently by several alternative equations, besides the NS equation itself. In particular equivalence between the NS

Reversibility, Irreversibility, Friction and nonequilibrium ensembles in N-S equations

: Viscosity, as a physical property of fluids, re-flects an average effect over a chaotic microscopic motion described by Hamiltonian equations. It is proposed, as an example, that stationary states of

Viscosity, Reversibillity, Chaotic Hypothesis, Fluctuation Theorem and Lyapunov Pairing

  • G. Gallavotti
  • Mathematics, Physics
    Journal of Statistical Physics
  • 2021
Incompressible fluid equations are studied with UV cut-off and in periodic boundary conditions. Properties of the resulting ODEs holding uniformly in the cut-off are considered and, in particular,

Ensembles, turbulence and fluctuation theorem

  • G. Gallavotti
  • Physics
    The European physical journal. E, Soft matter
  • 2020
The paradigmatic example of irreversible evolution, the 2D Navier-Stokes incompressible flow is considered, to show how universal properties of fluctuations in systems evolving irreversibily could be predicted in a general context.

Navier-Stokes and equivalence conjectures

: General considerations on the Equivalence conjectures and a review of few mathematical results.

Equivalence of nonequilibrium ensembles in turbulence models.

The equivalence of reversible and irreversible ensembles for the case of a multiscale shell model of turbulence is tested and it is verified that the equivalence is obeyed for the mean values of macroscopic observables, up to an error that vanishes as the system becomes more and more chaotic.



An example of absence of turbulence for any Reynolds number

We consider a viscous incompressible fluid moving in a two-dimensional flat torus. We show a particular external forcef0 for which there is a globally attractive stationary state for any Reynolds

Constrained Euler system for Navier-Stokes turbulence.

It is demonstrated computationally that the Euler equations with integral constraints to describe high-Reynolds-number Navier-Stokes turbulence evolves to a quasiequilibrium state which reproduces accurately both low- and high-order statistical measures of turbulence observed in laboratory experiments and direct numerical simulations.

New Methods in Nonequilibrium Gases and Fluids

Kinematical and dynamical properties of chaotic systems are reviewed and a few applications are described.

Statistical Mechanics of Nonequilibrium Liquids

1. Introduction 2. Linear irreversible thermodynamics 3. The microscopic connection 4. The Green-Kubo relations 5. Linear response theory 6. Computer simulation algorithms 7. Nonlinear response

On the nature of turbulence

A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.

Sequences of infinite bifurcations and turbulence in a five-mode truncation of the Navier-Stokes equations

Two infinite sequences of orbits leading to turbulence in a five-mode truncation of the Navier-Stokes equations for a 2-dimensional incompressible fluid on a torus are studied in detail. Their

Fixed point limit behavior ofN-mode truncated Navier-Stokes equations asN increases

The fixed point behavior ofN-mode truncations of the Navier-Stokes equations on a two-dimensional torus is investigated asN increases. FromN=44 on the behavior does not undergo any qualitative

Dynamical Ensembles in Nonequilibrium Statistical Mechanics.

This presents the first test of the Ruelle principle on a many particle system far from equilibrium, and a specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid.

Equivalence of Non-equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model

We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive $$N$$N-degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector