Rossby Normal Modes in Basins with Barriers*
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The Rossby waver linear, normal modes for a barotropic fluid in a basin on the beta plane are calculated in the presence of a thin barrier, which nearly divides the basin in two. Narrow gaps allow one subbasin to communicate to the other. In the case of a meridional barrier it is shown that the modes split into two categories: either full-basin modest which have strong expression in both subbasins, or subbasin modes, which are limited to one or the other of the subbasins. The full-basin modes have natural frequencies very close to the eigenfrequencies of the basin in the absence of a barrier while the subbasin modes oscillate at the eigenfrequencies of the subbasins as if they were isolated. In the former case, the oscillation is accompanied by strong flow through the gaps in the barrier while, in the latter case, there is essentially no flow through the barrier. If the barrier is opened by adding additional gaps, some of the modes turn from subbasin modes to lull-basin modes. If the barrier is zonally oriented rather than meridionally oriented, the clear distinction between the two mode types disappears, although it is still possible to associate each of the modes with a subbasin mode restricted predominantly to one or the other of the subbasins. The analytic theory, based on a narrow-gap assumption, is checked and extended by considering a linearized numerical model for the forced response of the basin. Of particular significance is the ability of localized forcing in one subbasin to excite oscillations of the full basin in spite of narrow gaps that restrict the communication between adjacent subbasins.