Instabilities and radiation of thin, baroclinic jets
Talley, Lynne D.
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Oceanic fluctuations are dependent on geographical location. Near intense currents, the eddy field is highly energetic and has broad meridional extent. It is likely that the energy arises from instabilities of the intense current. However, the meridional extent of the linearly most unstable modes of such intense jets is much narrower than the observed region of energetic fluctuations. It is proposed here that weaker instabilities, in the linear sense, which are very weakly trapped to the current, may be the dominant waves in the far field. As a preliminary problem, the (barotropic) instability of parallel shear flow on the beta plane is discussed. An infinite zonal flow with a continuous cross-stream velocity gradient is approximated with segments of uniform flow, joined together by segments of uniform potential vorticity. This simplification allows an exact dispersion relation to be found. There are two classes of linearly unstable solutions. One type is trapped to the source of energy and has large growth rates. The second type are weaker instabilities of the shear flow which excite Rossby waves in the far field: the influence of these weaker instabilities extends far beyond that of the most unstable waves. The central focus of the thesis i: the linear stability of thin, twolayer, zonal jets on the beta plane, with both horizontal and vertical shear. The method used for the parallel shear flow is extended to the two-layer flow. Each layer of the jet has uniform velocity in the center, bordered by shear zones with zero potential vorticity gradient. The velocity in each layer outside the jet is constant in latitude. Separate linearly unstable modes arise from horizontal and vertical shear. The energy source for the vertical shear modes is nearly all potential while the source for the horizontal shear modes is both kinetic and potential. The most unstable waves are tightly trapped to the jet, within two or three deformation radii for small but nonzero beta. Rossby waves and baroclinically unstable waves (in the presence of vertical shear) exist outside the jet because of a nonzero potential vorticity gradient there. Weakly growing jet instabilities can force these waves when their phase speeds and wavelengths match. In particular, westward jets and any jets with vertical shear exterior to the jet can radiate in this sense. The radiating modes influence a large region, their decay scales inversely proportional to the growth rate. Two types of radiating instability are found: (1) a subset of the main unstable modes near marginal stability and (2) modes which appear to be destabilized neutral modes. Westward jets have more vigorously unstable radiating modes. Applications of the model are made to the eddy field south of the Gulf Stream, using data from the POLYMODE settings along 55°W and farther into the gyre at MODE. The energy decay scale and the variation of vertical structure with latitude in different frequency bands can be roughly explained by the model. The lower frequency disturbances decay more slowly and become more surface intensified in the far field. These disturbances are identified with the weak, radiating instabilities of the model. The higher frequency disturbances are more trapped and retain their vertical structure as they decay, and are identified with the trapped, strongly unstable modes of the jet.
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June, 1982
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