Journal of Applied Mechanics and Technical Physics

, Volume 39, Issue 5, pp 729–737 | Cite as

Linear theory of the propagation of internal wave beams in an arbitrarily stratified liquid

  • Yu. V. Kistovich
  • Yu. D. Chashechkin


Beams of harmonic internal waves in a liquid with smoothly changing stratification are calculated in the Boussinesq approximation taking into account the effects of diffusion and viscosity. A procedure of local reduction of the beam in a medium with an arbitrary smooth stratification to the case of an exponentially stratified liquid is constructed. The coefficient of energy losses in the case of beam reflection on the critical level is calculated. Parameters of internal boundary flows with split scales of velocity and density that are formed by a wave beam on discontinuities of the buoyancy frequency and its higher derivatives are determined.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. M. Brekhovskikh and V. V. Goncharov,Introduction to Continuum Mechanics [in Russian], Nauka, Moscow (1982).Google Scholar
  2. 2.
    S. A. Gabov and A. G. Sveshnikov,Problems of Dynamics of Stratified Fluid [in Russian], Nauka, Moscow (1986).Google Scholar
  3. 3.
    J. Lighthill,Waves in Fluids, Cambridge Univ. Press, Cambridge (1978).MATHGoogle Scholar
  4. 4.
    J. S. Turner,Buoyancy Effects in Fluids, Cambridge Univ. Press (1973).Google Scholar
  5. 5.
    N. H. Thomas and T. N. Stevenson, “A similarity solution for viscous internal waves,”J. Fluid Mech.,54, Part 3, 495–506 (1972).MATHCrossRefADSGoogle Scholar
  6. 6.
    Yu. V. Kistovich and Yu. D. Chashechkin, “Reflection of internal-wave trains in a viscous fluid from a flat rigid boundary,”Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana,30, No. 6, 752–758 (1994).Google Scholar
  7. 7.
    Yu. V. Kistovich and Yu. D. Chashechkin, “Reflection of internal gravity wave trains from a plane rigid surface,”Dokl. Ross. Akad. Nauk,337, No. 3, 401–404 (1994).Google Scholar
  8. 8.
    Yu. V. Kistovich and Yu. D. Chashechkin, “Reflection of internal gravity wave beams from a plane rigid surface,”Prikl. Mat. Mekh.,59, No. 4, 607–613 (1995).MATHMathSciNetGoogle Scholar
  9. 9.
    Yu. V. Kistovich and Yu. D. Chashechkin, “Geometry and energetics of internal wave beams,”Dokl. Ross. Akad. Nauk,344, No. 5, 684–686 (1995).MathSciNetGoogle Scholar
  10. 10.
    S. V. Nesterov, “Eigenfrequencies of internal waves in a fluid with an arbitrary Brunt-Väisälä frequency,”Dokl. Akad. Nauk SSSR,271, No. 3, 570–573 (1983).MATHMathSciNetGoogle Scholar
  11. 11.
    N. K. Fedorov,Thin Thermohaline Structure of Ocean Waters [in Russian], Gidrometeoizdat, Leningrad (1976).Google Scholar
  12. 12.
    S. A. Makarov, V. I. Neklyudov, and Yu. D. Chashechkin, “Spatial structure of beams of two-dimensional monochromatic internal waves in an exponentially stratified fluid,”Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana,26, No. 7, 744–754 (1990).ADSGoogle Scholar
  13. 13.
    V. M. Kamenkovich and A. S. Monin (eds.),Oceanology. Physics of Ocean, Vol. 1:Hydrophysics of Ocean [in Russian], Nauka, Moscow (1978).Google Scholar
  14. 14.
    M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, John Wiley and Sons, New York (1972).Google Scholar
  15. 15.
    Yu. V. Kistovich and Yu. D. Chashechkin, “Structure of unsteady boundary flow on an inclined plane in a continuously stratified medium,”Prikl. Mat. Mekh.,57, No. 4, 50–56 (1993).MATHMathSciNetGoogle Scholar
  16. 16.
    A. D. McEwan, “Interactions between internal gravity waves and their traumatic effect on a continuous stratification,”Bound.-Lay. Meteorol.,5, 159–175 (1973).CrossRefADSGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • Yu. V. Kistovich
  • Yu. D. Chashechkin

There are no affiliations available

Personalised recommendations