Properties of Waves with Small Amplitudes in Continuous Media

  • M. I. Rabinovich
  • D. I. Trubetskov
Part of the Mathematics and Its Applications (Soviet Series) book series (MASS, volume 50)


In this chapter we discuss the dispersion characteristics of waves in various real media. We shall restrict ourselves to media in which physical phenomena permit a hydrodynamic description. This clearly includes fluids and gases, but it also includes plasmas and plasma-like media (such as charged particle beams), during the analysis of which kinetic effects can either be ignored or allowed for phenomenologically. We shall examine waves known from general physics courses, such as sound waves, and more specific ones, such as waves in the atmosphere and the oceans associated with the rotation of the Earth, internal waves in a stratified ocean, and ion-sound waves in anisothermal plasmas.


Gravity Wave Internal Wave Rossby Wave Dispersion Equation Liquid Helium 
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  1. 1.
    L.D. Landau and E.M. Lifshits, Fluid Mechanics [in Russian], Nauka, Moscow (1986), Ch. 1.Google Scholar
  2. 2.
    L.I. Sedov, Mechanics of Continuous Media [in Russian], Nauka, Moscow (1970), Vol.1, Ch.4, Sec.1.Google Scholar
  3. 3.
    L.M. Brekhovskikh, V.V. Goncharov, K.A. Naugol’nykh, and S.A. Rybak, “Ocean waves,” Izv. Vuzov: Radiofiz., 19, 842–852 (1976).Google Scholar
  4. 4.
    A.S. Monin and M.N. Koshlyakov, “Synoptic vortices or Rossby waves in the ocean” in: A.V. Gaponov (ed), Nonlinear Waves [in Russian], Nauka, Moscow (1979), pp.281–287.Google Scholar
  5. 5.
    M.J. Lighthill, Waves in Fluids [Russian translation], Mir, Moscow (1981).Google Scholar
  6. 6.
    D.B. Sivukhin, General Course of Physics, Vol. II, Thermodynamics and Heat Physics [in Russian], Nauka, Moscow (1980), Sec.40.Google Scholar
  7. 7.
    M. A. Lavrent’ev and B.V. Shabat, Problems of Hydrodynamics and Their Mathematical Models [in Russian], Nauka, Moscow (1973).Google Scholar
  8. 8.
    S. Flugge, Practical Quantum Mechanics [Russian translation], Mir, Moscow (1974), Vols.1–2, pp.292–300.Google Scholar
  9. 9.
    I.M. Khalatnikov, Theory of Superfluidity [in Russian], Nauka, Moscow (1971).Google Scholar
  10. 10.
    S.J. Putterman, Superfluid Hydromechanics (Amsterdam, 1974) [Russian translation], Mir, Moscow (1978).Google Scholar
  11. 11.
    E.M. Lifshits and L.P. Pitaevskii, Statistical Physics [in Russian], Nauka, Moscow (1978), Pt.2, Ch.3.Google Scholar
  12. 12.
    L.A. Artsimovich, “Selected works: atomic physics and plasma physics” in: Lectures on Plasma Physics [in Russian], Nauka, Moscow (1978), pp.164–245.Google Scholar
  13. 13.
    B.B. Kadomtsev, Group Phenomena in Plasmas [in Russian], Nauka, Moscow (1976), Ch.2.Google Scholar
  14. 14.
    N.A. Krall and A.W. Trivelpiece, Principles of Plasmaa Physics (Springer Verlag, 1971) [Russian translation], Mir, Moscow (1975), Ch.4.Google Scholar
  15. 15.
    K.E. Lonngren, H.C.S. Hsuan, L.D. Landt, et al., “Properties of plasma waves defined by dispersion realtions,” IEEE Trans, on Plasma Sci., Ps-2, 93–108 (1974).Google Scholar
  16. 16.
    L.A. Artsimovich and P.Z. Sagdeev, Plasma Physics for Physicists [in Russian], Atomizdat, Moscow (1979), Sec.10.Google Scholar
  17. 17.
    W.H. Louisell, Coupled Mode and Parametric Electronics [Russian translation], Izd. Ino. Lit., Moscow (1963), Chs.2–3.Google Scholar
  18. 18.
    M.C. Steele and B. Vural, Wave Interactions in Solid State Plasmas [in Russian], Atomizdat, Moscow (1973).Google Scholar
  19. 19.
    Yu.K. Pozhela, Plasma and Current Instabilities in Semiconductors [in Russian], Nauka, Moscow (1977).Google Scholar
  20. 20.
    V.V. Vladimirov, A.F. Volkov, and E.Z. Melikhov, Plasma Semiconductors [in Russian], Atomizdat, Moscow (1979).Google Scholar
  21. 21.
    O.M. Phillips, The Dynamics of the Upper Ocean [Russian translation], Mir, Moscow (1969).Google Scholar
  22. 22.
    P.H. LeBlond and L.Mysak, Waves in Oceans (Elsevier, 1978) [Russian translation], Mir, Moscow (1981).Google Scholar
  23. 23.
    L.M. Brekhovskikh, Waves in Stratified Media [in Russian], Nauka, Moscow (1973).Google Scholar
  24. 24.
    Z.L. Miropol’skii, Dynamics of Internal Gravity Waves in the Ocean [in Russian], Gidrometeoizdat, Leningrad (1981).Google Scholar
  25. 25.
    E.L. Andronikashvili, Notes on Liquid Helium [in Russian], Ganatelba, Tibilisi (1980).Google Scholar
  26. 26.
    L.M. Brekhovskikh and L.M. Chyncharov, Introduction to the Mechanics of Continuous Media [in Russian], Nauka, Moscow (1982), Pt.2.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • M. I. Rabinovich
    • 1
  • D. I. Trubetskov
    • 2
  1. 1.Institute of Applied PhysicsAcademy of Sciences of the USSRGorkyUSSR
  2. 2.Saratov State UniversityUSSR

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