New Linear Mechanisms of Acoustic Wave Generation in Smooth Shear Flows (Nonmodal Study)

  • George D. Chagelishvili
Part of the Lecture Notes in Physics book series (LNP, volume 586)


This lecture presents new linear mechanisms of acoustic wave generation in smooth shear flows using a non-modal study.


Shear Rate Acoustic Wave Dispersion Curve Mutual Transformation Acoustic Wave Generation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. C. Reddy, P. J. Schmid and D. S. Hennigson, SIAM J. Appl. Math. 53, 15 (1993).zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, New York 1976).zbMATHGoogle Scholar
  3. 3.
    S. C. Reddy and D. S. Henningson, J. Fluid Mech. 252, 209 (1993).zbMATHCrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Lord Kelvin (W. Thomson), Phil. Mag. 24, Ser. 5, 188 (1887).Google Scholar
  5. 5.
    L. H. Gustavsson, J.Fluid Mech. 224, 241 (1991).zbMATHCrossRefADSGoogle Scholar
  6. 6.
    K. M. Butler and B. F. Farrell, Phys. Fluids A 4, 1637 (1992).CrossRefADSGoogle Scholar
  7. 7.
    S. A. Balbus and J. H. Hawley, Astrophys. J. 400, 610 (1992).CrossRefADSGoogle Scholar
  8. 8.
    W.O. Criminale and P.G. Drazin, Studies in Applied Mathematics 83, 123 (1990).zbMATHMathSciNetGoogle Scholar
  9. 9.
    W.O. Criminale, T.L. Jackson, D.G. Lasseigne and R.D. Joslin, J.Fluid Mech., 339, 55 (1997).zbMATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    G. D. Chagelishvili, A. D. Rogava and I. N. Segal, Phys. Rev. E 50, R4283 (1994).CrossRefADSGoogle Scholar
  11. 11.
    G. D. Chagelishvili, G. R. Khujadze, J. G. Lominadze and A. D. Rogava, Phys. Fluids. 9, 1955 (1997).CrossRefADSGoogle Scholar
  12. 12.
    G. D. Chagelishvili, R. G. Chanishvili, T. S. Khristov and J. G. Lominadze, Phys. Rev. E 47, 366 (1993).CrossRefADSGoogle Scholar
  13. 13.
    G. D. Chagelishvili, R. G. Chanishvili, J. G. Lominadze and A. G. Tevzadze, Phys. Plasmas 4, 259 (1997).CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    A. D. Rogava, S. Mahajan, Phys. Rev. E, 55, 1185 (1997).CrossRefADSGoogle Scholar
  15. 15.
    J. S. Baggett, T. A. Driscoll and L. N. Trefethen, Phys. Fluids 7, 833 (1995).zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    A. G. Tevzadze, Phys.Plasmas, 5,1557, (1998).CrossRefADSGoogle Scholar
  17. 17.
    K. Moffatt,‘The interaction of turbulence with strong wind shear’, In: Atmospheric Turbulence and Radio wave Propagation, A. M. Yaglom and V. I. Tatarskii (editors), (Nauka Press, Moscow, 1967).Google Scholar
  18. 18.
    A. D. D. Craik and W. O. Criminale, Pros. R. Soc. Lond. A406, 13 (1986).zbMATHADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    P. Marcus and W. H. Press, J. Fluid Mech. 79, 525 (1977).zbMATHCrossRefADSGoogle Scholar
  20. 20.
    J. G. Lominadze, G. D. Chagelishvili and R. G. Chanishvili, Pis’ma Astron. Zh. 14, 856 (1988) [Sov. Astron. Lett. 14, 364 (1988)].ADSGoogle Scholar
  21. 21.
    G. D. Chagelishvili, R. G. Chanishvili, J. G. Lominadze and I. N. Segal, ‘Turbulization of Free Shear Flows—3D Perturbations’, In: Proceedings of the fourth International Conference on Plasma Physics and Controlled Nuclear Fusion, Toki, Japan 17-20 November 1992 (ESA SP-351, 1993), p.23.Google Scholar
  22. 22.
    G. D. Chagelishvili, A. D. Rogava and D. G. Tsiklauri, Phys. Rev. E 53, 6028 (1996).CrossRefADSGoogle Scholar
  23. 23.
    G. D. Chagelishvili and O. G. Chkhetiani, JETP Lett. 62, 301 (1995).Google Scholar
  24. 24.
    T. Gebhardt and S. Grossmann, Phys. Rev. E 50, 3705 (1994).CrossRefADSGoogle Scholar
  25. 25.
    G.D. Chagelishvili, A.G. Tevzadze, G. Bodo, S.S. Moiseev, Phys. Rev. Lett., 79,3178, (1997).CrossRefADSGoogle Scholar
  26. 26.
    G.D. Chagelishvili, A. G. Tevzadze, G. Bodo, P. Rossi, G.T. Gogoberidze, ‘Vortex-wave conversion in high shear flows’, In: Advances in Turbulence. VIII, Barcelona, Spain, June 27-30,2000, ed. by C. Dopazo, (CIMNE, 2000), pp. 737–740.Google Scholar
  27. 27.
    K. Magnus, Schwingungen (B. G. Teubner, Stuttgart)(1976).zbMATHGoogle Scholar
  28. 28.
    Ya. B. Zel’dovich and A. D. Mishkis Elementi Prikladnoi Matematiki Nauka, Moscow, (1972).Google Scholar
  29. 29.
    G. D. Chagelishvili, R. G. Chanishvili and J. G. Lominadze, JETP Lett. 63, N6 (1996).Google Scholar
  30. 30.
    E. G. Broadbent and D. Moore, Philos. Trans. R. Soc. London, Ser. A 290, 353 (1979).CrossRefADSGoogle Scholar
  31. 31.
    C. M. Ho and P. Huerre, Annu. Rev. Fluid Mech. 16, 365 (1984).CrossRefADSGoogle Scholar
  32. 32.
    F. Lound and C. Rojas, Physica D 37, 508(1989).CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    S. C. Crow, Fluid Mech. 37, 529 (1969).zbMATHCrossRefADSGoogle Scholar
  34. 34.
    J. E. Williams and M. S. Howe, J. Fluid Mech. 58, 461 (1973).zbMATHCrossRefADSMathSciNetGoogle Scholar
  35. 35.
    A. D. Pierce, J. Acoust. Soc. Am. 49 906 (1971).CrossRefADSGoogle Scholar
  36. 36.
    L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics, 2nd ed. (Wiley, New York, 1962).zbMATHGoogle Scholar
  37. 37.
    M. J. Lighthill, Proc. R. Soc. London Ser. A 211, 564 (1952).zbMATHADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    M. J. Lighthill, Proc. R. Soc. London Ser. A 222, 1 (1954).zbMATHADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    A.J. Lichtenberg, A.M. Lieberman, Regular and Chaotic Dynamics, (Springer-Verlag, New York) (1982).Google Scholar
  40. 40.
    F.C. Hoppensteadt, Analysis and Simulations of Chaotic Systems, (Springer-Verlag, New York) (1993).Google Scholar
  41. 41.
    R.C. Davidson, Methods in Nonlinear Plasma Physics, (Academic Press, New York) (1972).Google Scholar
  42. 42.
    S.S. Moiseev, V.R. Smilianski, Magn.Gidrodin. 2, 23 (1965).Google Scholar
  43. 43.
    A.H. Kritz, D. Mintzer, Phys. Rev. 117, 382 (1960).CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • George D. Chagelishvili
    • 1
    • 2
  1. 1.Centre for Plasma AstrophysicsAbastumani Astrophysical ObservatoryTbilisiGeorgia
  2. 2.Space Research InstituteMoscowRussia

Personalised recommendations