Navier-Stokes Equations Do Not Describe the Smallest Scales of Turbulence in Gases
In turbulent flows, kinetic energy is transferred from the largest scales to progressively smaller scales, until it is ultimately converted into heat. The Navier-Stokes equations are almost universally used to study this process. Here, by comparing with molecular-gas-dynamics simulations, we show that the Navier-Stokes equations do not describe turbulent gas flows in the dissipation range because they neglect thermal fluctuations. We investigate decaying turbulence produced by the Taylor-Green vortex and find that in the dissipation range the molecular-gas-dynamics spectra grow quadratically with wave number due to thermal fluctuations, in agreement with previous predictions, while the Navier-Stokes spectra decay exponentially. Furthermore, the transition to quadratic growth occurs at a length scale much larger than the gas molecular mean free path, namely in a regime that the Navier-Stokes equations are widely believed to describe. In fact, our results suggest that the Navier-Stokes equations are not guaranteed to describe the smallest scales of gas turbulence for any positive Knudsen number.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- NA0003525
- OSTI ID:
- 1854611
- Alternate ID(s):
- OSTI ID: 1888554
- Report Number(s):
- SAND2022-3088J; PRLTAO; 114501
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Vol. 128 Journal Issue: 11; ISSN 0031-9007
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Similar Records
Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations
Smoothed particle hydrodynamics model for Landau-Lifshitz Navier-Stokes and advection-diffusion equations