Wave Motions in a Rotating and/or Stratified Fluid
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.
KeywordsSolitary Wave Internal Wave Rossby Wave Wave Motion Stratify Fluid
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