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This study explores a reversible Navier-Stokes model, investigating statistical equivalence between ensembles and fluctuating viscosity. Results show negative viscosity probabilities rapidly decrease with higher Reynolds numbers in resolved hydrodynamics.

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Area of Science:

  • Fluid dynamics
  • Statistical mechanics
  • Computational physics

Background:

  • Molecular fluid motion follows time-reversible laws.
  • Macroscopic fluid evolution is described by irreversible Navier-Stokes equations due to dissipation.
  • This work introduces a reversible Navier-Stokes variant inspired by statistical mechanics ensembles.

Purpose of the Study:

  • Investigate statistical equivalence between microcanonical and canonical ensembles in a reversible Navier-Stokes model.
  • Analyze the distribution of fluctuating viscosity across varying Reynolds numbers and discretization modes.
  • Establish regularity conditions for reversible fluid dynamics equations.

Main Methods:

  • Developed a reversible three-dimensional Navier-Stokes model with fluctuating viscosity.
  • Implemented systematic numerical simulations to explore system behavior.
  • Analyzed the impact of Reynolds number and mode discretization on viscosity distribution.

Main Results:

  • Identified conditions for statistical equivalence between nonequilibrium ensembles.
  • Observed that the probability of negative fluctuating viscosity diminishes rapidly as the effective Reynolds number increases.
  • The probability of negative viscosity becomes negligible in the fully resolved hydrodynamical regime.

Conclusions:

  • The reversible Navier-Stokes model provides insights into fluid dynamics at different scales.
  • Fluctuating viscosity behavior is strongly dependent on the Reynolds number.
  • The findings contribute to understanding regularity and statistical properties of reversible fluid equations.