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A Simple Model of Hydrodynamic Instability

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Microscopic Simulations of Complex Flows

Part of the book series: NATO ASI Series ((NSSB,volume 236))

Abstract

For the theoretical physicist, molecular dynamics (MD) is a sort of ideal laboratory for testing a theory, the validity of some approximation scheme, etc… A nice aspect of this procedure is its generality: By setting up a microscopic model, with given interaction rules, and by specifying the nature of the boundary conditions and external forces, an MD experiment can be performed which, without corresponding closely to a real world system, captures nevertheless some essential aspects of the phenomenon of interest. For instance, hard sphere or hard disk fluids have been used since the early development of MD1. Another example is the so called “Lorentz gas”, where the trajectory of a single molecule around randomly distributed scatterers is studied through MD2.

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References

  1. B. J. Alder and T. E. Wainwright, J. Chem. Phys., 27, 1208 (1957)

    Article  ADS  Google Scholar 

  2. W. W. Wood and F. Lado, J. Comp. Phys., 7, 528 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  3. C. Bruin, Physica, 72, 261 (1974);

    Article  ADS  Google Scholar 

  4. B. L. Hohan, Phys. Rev. A37, 2562 (1988)

    ADS  Google Scholar 

  5. W. G. Hoover, Phys. Rev. Lett. 42, 1531 (1979)

    Article  ADS  Google Scholar 

  6. D. C. Rapaport, E. Clementi, Phys. Rev. Lett. 57, 695 (1987)

    Article  ADS  Google Scholar 

  7. L. Hannon, G. Lie and E. Clementi, J. Sc. Comp.1, 145 (1986)

    Article  MATH  Google Scholar 

  8. D. C. Rapaport, Phys. Rev. A 36, 3288 (1987)

    Article  ADS  Google Scholar 

  9. E. Meiburg, Phys.Fluids, 29, 3107 (1986)

    Article  ADS  Google Scholar 

  10. M. Mareschal, E. Kestemont, Nature, 323, 427 (1987)

    Article  ADS  Google Scholar 

  11. M. Mareschal, E. Kestemont, J. Stat. Phys. 48, 1187 (1987)

    Article  ADS  Google Scholar 

  12. D. C. Rapaport, Phys. Rev. Lett. 60, 2480 (1988)

    Article  ADS  Google Scholar 

  13. M. Mareschal, M. Malek Mansour, A. Puhl, E. Kestemont, Phys. Rev. Lett. 61, 2550 (1988)

    Article  ADS  Google Scholar 

  14. A. Puhl, M. Malek Mansour and M. Mareschal, Phys. Rev. A 40, 1999(1989)

    Article  ADS  Google Scholar 

  15. A nearly up to date account of the field is given in “Molecular Dynamics Simulation of Statistical Mechanical Systems”, G. Ciccotti and W. G. Hoover, Eds., North Holland (1986)

    Google Scholar 

  16. G. Ahlers, C. Meyer and D. Cannel, J. Stat. Phys. 54, 1121 (1989)

    Article  ADS  Google Scholar 

  17. H. Van Beijeren and E. D. G. Cohen, Phys. Rev. Lett. 60, 1208 (1988)

    Article  ADS  Google Scholar 

  18. H. Van Beijeren and E. D. G. Cohen, J. Stat. Phys. 53, 77 (1988)

    Article  ADS  Google Scholar 

  19. V. M. Zaitsev and M. I. Shliomis, Sov. Phys. JETP, 32, 866 (1971)

    ADS  Google Scholar 

  20. H. Lekkerkeker and J. P. Boon, Phys. Rev. A10, 1355 (1974)

    ADS  Google Scholar 

  21. R. Graham, Phys. Rev. A10, 1762 (1974)

    ADS  Google Scholar 

  22. R. Graham and H. Pleiner, Phys. Fluids, 18, 130 (1975)

    Article  ADS  MATH  Google Scholar 

  23. J. Swift and P. C. Hohenberg, Phys. Rev. A15, 319 (1977)

    ADS  Google Scholar 

  24. T. R. Kirkpatrick and E. D. G. Cohen, J. Stat. Phys. 33, 639 (1983)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. A systematic derivation of the results of ref. 10 is given in: R. Schmitz and E. G. D. Cohen, J. Stat. Phys., 38, 285 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  26. R. Schmitz and E. G. D. Cohen, J. Stat. Phys., 40, 431 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  27. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford (1961)

    MATH  Google Scholar 

  28. E. Knobloch and J. Guckenheimer, Phys. Rev. A27, 408 (1983)

    MathSciNet  ADS  Google Scholar 

  29. F. H. Busse and A. C. Or, ZAMP 37, 608 (1986)

    Article  ADS  MATH  Google Scholar 

  30. A molecular dynamic study of the compressible Bénard problem is reported in ref. 6.

    Google Scholar 

  31. See for instance W. E. Alley and B. J. Alder, Phys. Rev. A27, 3158 (1983)

    ADS  Google Scholar 

  32. W. E. Alley, B. J. Alder and S. Yip, Phys. Rev. A27, 3174 (1983)

    ADS  Google Scholar 

  33. L. D. Landau, E. M. Lifshitz, Fluid Mechanics, Pergamon Press, London (1958)

    Google Scholar 

  34. T. R. Kirkpatrick and E. D. G. Cohen, Phys. Rev. A 26, 995 (1982)

    Google Scholar 

  35. M. Malek Mansour, J. W. Turner and A. Garcia, J. Stat. Phys. 48, 1157(1987)

    Article  ADS  Google Scholar 

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© 1990 Plenum Press, New York

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Mansour, M.M. (1990). A Simple Model of Hydrodynamic Instability. In: Mareschal, M. (eds) Microscopic Simulations of Complex Flows. NATO ASI Series, vol 236. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1339-7_13

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  • DOI: https://doi.org/10.1007/978-1-4684-1339-7_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-1341-0

  • Online ISBN: 978-1-4684-1339-7

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