This thesis is concerned with the two basic modes of barotropic wave motions in rotating fluid: inertia-gravity waves and Rossby waves. The emphasis of the study is on the non-linear aspects of these wave motions. The existence of finite amplitude inertia-gravity wave solutions in the shallow water equations with Coriolis terms is demonstrated. These waves have narrow sharp crests and broad flat troughs as in the case of Stokes' waves but they induce no mass flux and are stable to side-band perturbations. The excitation of inertia-gravity lee waves by mountain barriers is studied both analytically and numerically. Supercritical basic flow is shown to be a necessary but not sufficient condition for the establishment of stationary lee waves. Some new solutions for the Rossby wave equation are obtained. The stability of finite amplitude channel Rossby waves is examined. The stability of the wave is found to depend critically on the aspect ratio (the ratio of the channel width to the wave length) of the wave. Resonant interactions between Rossby waves and inertia-gravity waves are also investigated. Finite amplitude retrogressive inertia-gravity waves are found to be unstable to perturbations of resonantly interacting infinitesimal amplitude Rossby waves and forward propagating inertia-gravity waves.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:645992 |
| Date | January 1975 |
| Creators | Hock, Lim |
| Publisher | University of Reading |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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