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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
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Reversible Navier-Stokes equation on logarithmic lattices
Guillaume Costa1, Amaury Barral1, Bérengère Dubrulle1
1Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France.
Physical Review. E
|July 19, 2023
Summary
This study explores reversible Navier-Stokes (RNS) equations using high-resolution simulations. We found a second-order phase transition, confirming mean-field theory and supporting the Gallavotti conjecture for turbulence models.
Area of Science:
- Fluid Dynamics
- Statistical Mechanics
- Computational Physics
Background:
- The reversible Navier-Stokes (RNS) equations modify dissipative NS equations by maintaining constant energy or enstrophy via dynamic viscosity.
- Previous spectral direct numerical simulations explored RNS, but with limitations in parameter regimes.
Purpose of the Study:
- Investigate a linear, forced RNS system using a log lattice in Fourier space for enhanced resolution.
- Explore parameter regimes beyond the reach of prior simulations.
- Examine phase transitions and validate the Gallavotti conjecture for RNS models.
Main Methods:
- Projected RNS equations onto a log lattice for spectral simulations.
- Performed numerical simulations at extremely high resolutions.
- Analyzed phase transitions using nondimensionalized forcing and enstrophy as parameters.
- Compared RNS and NS statistics to test Gallavotti conjecture adaptations.
Main Results:
- Confirmed a second-order phase transition, well-described by mean-field Landau theory.
- Observed an imperfect transition at lower resolutions, deviating from mean-field predictions.
- Found qualitative agreement with the 1D reversible Leith model of turbulence.
- Deduced conditions for statistical equivalence between RNS and NS models.
Conclusions:
- High-resolution log-lattice simulations reveal phase transitions in RNS systems.
- Results support the Gallavotti conjecture, showing ensemble equivalence for mean quantities in nonequilibrium systems.
- The study highlights the impact of resolution on transition characteristics.
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