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The generation of unstable waves and the generation of transverse upwelling : two problems in geographical fluid dynamics Lee, Clinton Arthur

Abstract

In this thesis two different problems in geophysical fluid, dynamics are studied. In Part A we consider the general problem of the generation of unstable shelf waves, a problem that relates to the generation of the meanders in the Gulf Stream. In Part B we consider the generation of transverse motions of the thermocline in long two layer bodies of water by general wind stresses. The instability of fluid systems has been studied for a long time, but the problem of how the instabilities are generated and grow has been neglected. Recently, however, in the study of the interaction of plasmas with electron streams, techniques have been developed to study the growth of instabilities. These techniques can in principle be applied to any unstable linear system that is excited by stationary forcing. In Part A we describe these techniques and extend them to cover the case of moving forcing effects. He then use the results to study the generation of unstable shelf waves. Long barotropic waves trapped on an abrupt change in bottom topography are shelf waves; the presence of lateral shear in the persistent ocean currents gives rise to unstable shelf waves. The possible presence of such waves in the Gulf Stream system could explain the generation of the meanders in the Gulf Stream. Thus we study the response of a model Gulf Stream that supports unstable shelf waves to the wind. Only curl free wind stress is considered, mainly for convenience. It is found that only on the offshore side of the stream, where the response is always larger than on the inshore side, are the unstable waves always dominant. A wind system moving slowly in the direction of the stream is the most efficient at generating the unstable waves, but its efficiency is affected quite drastically by the duration of the disturbance. A wind system moving counter to the stream is less efficient by about a factor of eight, but is practically unaffected by a change in duration. In Part B we consider a stable system. We use simple Fourier expansion to study the motions of the thermocline in an infinitely long two layer body of water generated by both long axis and cross channel winds. It is found that in a wide lake, such as Lake Michigan, cross channel winds are more efficient in generating transverse motions which in all cases are multi-modal. Here wide means wide in comparison to the Rossby radius of curvature. These results agree only qualitatively with observations made on Lake Michigan. In fact reasonable wind stresses only give responses about one-tenth of those observed. In a narrow lake it is found that the response to a long axis wind is larger than that to a cross channel wind, both giving a uni-modal response. Observations of wind and thermocline depth taken at Babine Lake in northern B.C. agree quite well with the theory.

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