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Bobylev's instability

Uribe1, Velasco, Garcia-Colin

  • 1Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa 09340, Mexico Distrito Federal, Mexico.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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The Burnett equations, used to describe gases, are unstable beyond a critical wave number. This study extends prior analysis, suggesting these equations have limits based on the Knudsen number for gas dynamics.

Area of Science:

  • Fluid dynamics
  • Non-equilibrium thermodynamics
  • Kinetic theory

Background:

  • The Burnett equations are a higher-order approximation to the Boltzmann equation for rarefied gases.
  • Previous linear stability analysis by Bobylev (1982) indicated instability in the Burnett equations for Maxwellian molecules.
  • Understanding the validity of the Burnett equations is crucial for accurately modeling gas behavior in various flow regimes.

Purpose of the Study:

  • To extend Bobylev's linear stability analysis of the Burnett equations to arbitrary interaction potentials.
  • To investigate the conditions under which the Burnett equations remain valid.
  • To reinterpret the stability analysis in terms of a Knudsen number bound.

Main Methods:

  • Linear stability analysis of the Burnett equations.

Related Experiment Videos

  • Extension of the analysis to general interaction potentials beyond Maxwellian molecules.
  • Examination of normal modes and their growth rates.

    • Main Results:

    • The Burnett equations exhibit linear instability beyond a critical reduced wave number for any interaction potential.
    • The analysis provides a reinterpretation of Bobylev's findings.
    • A bound for the Knudsen number is suggested, above which the Burnett equations are not applicable.

    Conclusions:

    • The Burnett equations are linearly unstable for a broad range of interaction potentials.
    • The stability analysis provides a criterion for the validity of the Burnett equations based on the Knudsen number.
    • These findings have implications for the use of the Burnett equations in rarefied gas dynamics.