Nonequilibrium ensembles for the three-dimensional Navier-Stokes equations.

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.