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Phase transition in time-reversible Navier-Stokes equations.

Vishwanath Shukla1,2,3, Bérengère Dubrulle4, Sergey Nazarenko3

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This study explores a modified Navier-Stokes system, revealing a phase transition in turbulence statistics. The findings suggest a connection to established turbulence models and Gallavotti's conjecture.

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Area of Science:

  • Fluid Dynamics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Standard Navier-Stokes equations describe fluid motion but lack time-reversibility.
  • Turbulence exhibits complex statistical features, including energy dissipation and scale interactions.
  • Fluctuating thermostats offer a way to modify systems while preserving time-reversibility.

Purpose of the Study:

  • To investigate the statistical properties of a 3D time-reversible Navier-Stokes system with a fluctuating thermostat.
  • To analyze the transition between different statistical regimes controlled by a parameter R_r.
  • To explore the connection between this system and phase transitions in statistical mechanics.

Main Methods:

  • Numerical simulations of the 3D time-reversible Navier-Stokes (RNS) system.
  • Analysis of statistical features using a dimensionless control parameter R_r.
  • Comparison with diffusion models of turbulence (Leith model) and Landau theory.

Main Results:

  • A sharp transition is observed between 'warm' (small R_r) and hydrodynamic-like (large R_r) statistics.
  • The transition is characterized as a continuous second-order phase transition with R_r as a control parameter.
  • Low-order statistics in the critical regime resemble those of standard Navier-Stokes simulations.

Conclusions:

  • The RNS system exhibits phase transition behavior analogous to thermodynamic systems.
  • Gallavotti's ensemble equivalence conjecture may apply to 3D turbulent statistics.
  • The study provides a framework for further numerical investigations of turbulence.