Advertisement

Dissipation of the Kelvin–Helmholts Waves in a Relaxing Molecular Gas

  • Yurii N. GrigoryevEmail author
  • Igor V. Ershov
Chapter
  • 328 Downloads
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 117)

Abstract

This chapter presents the results of numerical simulations of the full cycle of evolution of the Kelvin -Helmholtz instability, which adequately reproduce the local mechanism of turbulization of the free shear flow. The problem is considered both within the frameworks of the Navier-Stokes equations for a moderate level of thermal nonequilibrium and using the full system of equations of two-temperature aerodynamics for a vibrationally excited gas. Plane waves preliminary calculated by numerical solution of appropriate linearized systems of inviscid gas-dynamic equations are used as initial perturbations. The known pattern of the evolution of the “cat’s-eye” large-scale vortex structure typical for the emergence and development of inertial instability is reproduced in detail. The calculated results show the enhancement of dissipation of the kinetic energy of the structure on a background of relaxation process.

Keywords

Mach Number Vibrational Mode Vortex Structure Bulk Viscosity Initial Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Blumen, W.: Shear layer instability of an inviscid compressible fluid. J. Fluid Mech. 40, 769–781 (1970)ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Kovenya, V.M., Yanenko, N.N.: Splitting Method in Problems of Gas Dynamics. Nauka, Novosibirsk (1981) (in Russian)Google Scholar
  3. 3.
    Grigor’ev, Yu.N, Ershov, I.V., Zyryanov, K.V., Sinyaya, A.V.: Numerical simulation of the bulk viscosity effect on a sequence of nested grids. Vych. Tekhnol. 11, 36–49 (2006) (in Russian)Google Scholar
  4. 4.
    Kvasov, B.I.: Interpolation by Cubic and Bicubic Splines. Novosibirsk State University Publication, Novosibirsk (2004) (in Russian)Google Scholar
  5. 5.
    Betchov, R., Criminale, W.O.: Stability of Parallel Flows. Academic Press, New York (1967)zbMATHGoogle Scholar
  6. 6.
    Patnaik, P.C., Sherman, F.S., Corcos, G.M.: A numerical simulation of Kelvin–Helmholtz waves of finite amplitude. J. Fluid Mech. 73, 215–239 (1976)ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    Corcos, G.M., Sherman, F.S.: The mixing layer deterministic models of a turbulent flow. Part I. Introduction and two-dimensional flow. J. Fluid Mech. 139, 29–65 (1984)ADSCrossRefzbMATHGoogle Scholar
  8. 8.
    Stepanov, V.V.: Course of Differential Equations. Fizmatlit, Moscow (1959) (in Russian)Google Scholar
  9. 9.
    Grigor’ev, Yu.N, Ershov, I.V.: Relaxation-induced suppression of vortex disturbances in a molecular gas. J. Appl. Mech. Tech. Phys. 44, 471–481 (2003)Google Scholar
  10. 10.
    Grigor’ev, Yu.N, Ershov, I.V., Zyryanov, K.V.: Numerical modeling of Kelvin–Helmholtz waves in a weakly nonequilibrium molecular gas. Vych. Tekhnol. 13, 25–40 (2008) (in Russian)Google Scholar
  11. 11.
    Osipov, A.I., Uvarov, A.V.: Kinetic and gas-dynamic processes in nonequilibrium molecular physics. Usp. Fiz. Nauk 162, 1–42 (1992) (in Russian)Google Scholar
  12. 12.
    Grigor’ev, Yu.N, Ershov, I.V., Zyryanov, K.V.: Numerical modeling of inertial instability in a vibrationally nonequilibrium diatomic gas. Vych. Tekhnol. 15, 42–57 (2010) (in Russian)Google Scholar
  13. 13.
    Vinnichenko, N.A., Nikitin, N.V., Uvarov, A.V.: Karman vortex street in a vibrationally nonequilibrium gas. Fluid Dyn. 40, 762–768 (2005)ADSCrossRefzbMATHGoogle Scholar
  14. 14.
    Grigor’ev, Yu.N, Ershov, I.V., Ershova, E.E.: Influence of vibrational relaxation on the pulsation activity in flows of an excited diatomic gas. J. Appl. Mech. Tech. Phys. 45, 321–327 (2004)Google Scholar
  15. 15.
    Savill, A.M.: Drag reduction by passive devices - a review of some recent developments. In: Gyr, A. (ed.) Structure of Turbulence and Drag Reduction, pp. 429–465. Springer, Berlin (1990)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Computational TechnologiesRussian Academy of SciencesNovosibirskRussia

Personalised recommendations