Navier-Stokes Equations Do Not Describe the Smallest Scales of Turbulence in Gases
Abstract
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.
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1854611
- Alternate Identifier(s):
- OSTI ID: 1888554
- Report Number(s):
- SAND2022-3088J
Journal ID: ISSN 0031-9007; PRLTAO; 114501
- Grant/Contract Number:
- NA0003525
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 128 Journal Issue: 11; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; kinetic theory; turbulence
Citation Formats
McMullen, Ryan M., Krygier, Michael C., Torczynski, John R., and Gallis, Michael A. Navier-Stokes Equations Do Not Describe the Smallest Scales of Turbulence in Gases. United States: N. p., 2022.
Web. doi:10.1103/PhysRevLett.128.114501.
McMullen, Ryan M., Krygier, Michael C., Torczynski, John R., & Gallis, Michael A. Navier-Stokes Equations Do Not Describe the Smallest Scales of Turbulence in Gases. United States. https://doi.org/10.1103/PhysRevLett.128.114501
McMullen, Ryan M., Krygier, Michael C., Torczynski, John R., and Gallis, Michael A. Mon .
"Navier-Stokes Equations Do Not Describe the Smallest Scales of Turbulence in Gases". United States. https://doi.org/10.1103/PhysRevLett.128.114501.
@article{osti_1854611,
title = {Navier-Stokes Equations Do Not Describe the Smallest Scales of Turbulence in Gases},
author = {McMullen, Ryan M. and Krygier, Michael C. and Torczynski, John R. and Gallis, Michael A.},
abstractNote = {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.},
doi = {10.1103/PhysRevLett.128.114501},
journal = {Physical Review Letters},
number = 11,
volume = 128,
place = {United States},
year = {Mon Mar 14 00:00:00 EDT 2022},
month = {Mon Mar 14 00:00:00 EDT 2022}
}
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https://doi.org/10.1103/PhysRevLett.128.114501
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