Wave Motions in a Rotating and/or Stratified Fluid

  • T. Maxworthy
Part of the International Centre for Mechanical Sciences book series (CISM, volume 329)


When considering wave motions in natural systems one immediately realizes that a number of important external effects need to be taken into account. In particular these motions take place in a fluid that is compressible, stratified and rotating on a spherical surface. Thus any general theory is necessarily complex and any simplifying concepts lost in the overwhelming mass of mathematical details. It therefore behooves us to make rational assumptions concerning the relative magnitudes of these effects and then study their consequences in isolation. Firstly we ignore the effects of the sphericity of the system and assume the motion takes place on a plane surface rotating at constant angular frequency. The details of this assumption are treated later but essentially restrict both the lateral or horizontal and the vertical extent of the motion. As a first approximation we ignore, also, the compressibility of the fluid, essentially requiring that the “scale-height” of the system be much larger than the vertical extent of the fluid. This is a very good approximation in the ocean but obviously much weaker in the atmosphere, where in fact we should, finally, consider the effects of compressibility in order to be completely realistic.


Solitary Wave Internal Wave Rossby Wave Wave Motion Stratify Fluid 
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.


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  1. [1]
    Hopfinger, E.J., General concepts and examples of rotating fluids, this volume (1992)Google Scholar
  2. [2]
    Roberts, J., Internal Gravity Waves in the Ocean, Marcel Dekker, New York, 1975.Google Scholar
  3. [3]
    Gill, A., Atmosphere Ocean Dynamics, Academic Press, New York, 1982.Google Scholar
  4. [4]
    Long, R. R., “Some aspects of the flow of stratified fluids, I. A theoretical investigation”, Tellus, 5, 42, 1953.ADSCrossRefMathSciNetGoogle Scholar
  5. [5]
    Davis, R. E., “Two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech., 36, 127–143, 1969.ADSCrossRefMATHGoogle Scholar
  6. [6]
    Gossard, E. E. and Hooke, W., Waves in the Atmosphere, Elsevier, Amsterdam, 1979.Google Scholar
  7. [7]
    Matsuno, T., “Quasi-geostrophic motions in the equatorial area”, J. Met. Soc. Japan, 44, 25–42, 1966.Google Scholar
  8. [8]
    Heikes, K. and Max worthy, T., “Observations of inertial waves in a homogeneous, rotating fluid”, J. Fluid Mech., 125, 319–345, 1982.ADSCrossRefGoogle Scholar
  9. [9]
    Hide, R., Ibbotson, A. and Lighthill, M. J., “On slow transverse flow past obstacles in a rapidly rotating fluid”, J. Fluid Mech., 67, 397–412, 1968.Google Scholar
  10. [10]
    Stewartson, K. and Cheng, H. K., “On the structure of inertial waves produced by an obstacle in a deep, rotating container”, J. Fluid Mech., 91, 415–432, 1979.ADSCrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    Richards, K. J., Smeed, D. A. and Hopfinger, E. J., “Boundary layer separation of rotating flows past surface-mounted obstacles”, J. Fluid Mech., in press, 1991.Google Scholar
  12. [12]
    Redekopp, L. G., “Nonlinear waves in geophysics: Long internal waves”, Lectures in Appl Math., 20, 59–78, 1983.MathSciNetGoogle Scholar
  13. [13]
    Benjamin, T. B., “Internal waves of finite amplitude and permanent form”, J. Fluid Mech., 25, 241–270, 1966.ADSCrossRefMATHMathSciNetGoogle Scholar
  14. [14]
    Maxworthy, T., “Experiments on solitary internal Kelvin waves”, J. Fluid Mech., 129, 365–383, 1983.ADSCrossRefGoogle Scholar
  15. [15]
    Joseph, R. I., “Solitary waves in a finite depth fluid”, J. Phy. A: Math (Gen.), 10, L255, 1977.Google Scholar
  16. [16]
    Weidman, P. D. and Maxworthy, T., “Experiments on strong interactions between solitary waves”, J. Fluid Mech., 85, 417, 1978.ADSCrossRefGoogle Scholar
  17. [17]
    Whitham, G. B., Linear and Non-Linear Waves, Wiley, New York, 1974.Google Scholar
  18. [18]
    Fu, L.-L., and Holt, B., “Seasat views oceans and sea-ice with synthetic-aperture radar”, Jet Propulsion Laboratory Publication81–120, Pasadena, 1982.Google Scholar
  19. [19]
    Maxworthy, T., “A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge”, JGR, 84, C.1, 338–346, 1979.ADSCrossRefGoogle Scholar
  20. [20]
    Maxworthy, T., “A mechanism for the generation of internal solitary waves by tidal flow over submarine topography”, Ocean Modelling, 14, University of Cambridge, 1978 (Unpublished manuscript).Google Scholar
  21. [21]
    Maxworthy, T., Chabert d’Hieres, G. and Didelle, H., “The generation and propagation of internal gravity waves in a rotating fluid”, JGR, 89, C4, 6383–6396, 1984.ADSCrossRefGoogle Scholar
  22. [22]
    Lee, C. Y. and Beardsley, R. C, “The generation of long, nonlinear internal waves in a weakly stratified shear-flow”, JGR, 79, 453–462, 1974.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1992

Authors and Affiliations

  • T. Maxworthy
    • 1
  1. 1.University of Southern CaliforniaLos AngelesUSA

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