# Wave Motions in a Rotating and/or Stratified Fluid

## Abstract

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.

## Keywords

Solitary Wave Internal Wave Rossby Wave Wave Motion Stratify Fluid## Preview

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## References

- [1]Hopfinger, E.J., General concepts and examples of rotating fluids, this volume (1992)Google Scholar
- [2]Roberts, J.,
*Internal Gravity Waves in the Ocean*, Marcel Dekker, New York, 1975.Google Scholar - [3]Gill, A.,
*Atmosphere Ocean Dynamics*, Academic Press, New York, 1982.Google Scholar - [4]Long, R. R., “Some aspects of the flow of stratified fluids, I. A theoretical investigation”,
*Tellus*,**5**, 42, 1953.ADSCrossRefMathSciNetGoogle Scholar - [5]Davis, R. E., “Two-dimensional flow of a stratified fluid over an obstacle”,
*J. Fluid Mech.*,**36**, 127–143, 1969.ADSCrossRefMATHGoogle Scholar - [6]Gossard, E. E. and Hooke, W.,
*Waves in the Atmosphere*, Elsevier, Amsterdam, 1979.Google Scholar - [7]Matsuno, T., “Quasi-geostrophic motions in the equatorial area”,
*J. Met. Soc. Japan*,**44**, 25–42, 1966.Google Scholar - [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]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]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]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]Redekopp, L. G., “Nonlinear waves in geophysics: Long internal waves”,
*Lectures in Appl Math.*,**20**, 59–78, 1983.MathSciNetGoogle Scholar - [13]Benjamin, T. B., “Internal waves of finite amplitude and permanent form”,
*J. Fluid Mech.*,**25**, 241–270, 1966.ADSCrossRefMATHMathSciNetGoogle Scholar - [14]Maxworthy, T., “Experiments on solitary internal Kelvin waves”,
*J. Fluid Mech.*,**129**, 365–383, 1983.ADSCrossRefGoogle Scholar - [15]Joseph, R. I., “Solitary waves in a finite depth fluid”,
*J. Phy. A: Math (Gen.)*,**10**, L255, 1977.Google Scholar - [16]Weidman, P. D. and Maxworthy, T., “Experiments on strong interactions between solitary waves”,
*J. Fluid Mech.*,**85**, 417, 1978.ADSCrossRefGoogle Scholar - [17]Whitham, G. B.,
*Linear and Non-Linear Waves*, Wiley, New York, 1974.Google Scholar - [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]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]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]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]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