The Transmission of Rossby Waves through Basin Barriers*
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The response of a basin with a topographic barrier to spatially localized and time periodic forcing is considered. The barrier, which almost completely divides the full basin into two adjacent subbasins, is offered as a model of either a planetary island in the wind-driven circulation or a portion of the midocean ridge in the abyssal circulation. The barrier completely blocks the flow between the two adjacent subbasins except for the possibility of flow through two small gaps at the termini of the barrier. The barrier has nonzero thickness, and scale-dependent Lateral friction acts in the gap channels to impede the flow from one subbasin to the next. Bottom friction also acts uniformly on the flow in the basin. The degree to which localized forcing is able to excite large-scale motions in the adjacent subbasin is shown to be connected to the structure of the forcing and its frequency. In the absence of forcing and friction a set of full basin normal modes exist. The degree to which the forcing is able to resonate with such modes determines the degree to which energy can be transmitted from one subbasin to the other. Friction in the gaps reduces both the amplitude of that transmission and smooths the peaks of the response curve of the motion as a function of frequency in both subbasins. However, even for substantial friction, a considerable amount of large-scale variability can be excited in the adjacent basin. The quantitative dependence of the response on the degree of friction, the length of the channels representing the gaps, and the meridional structure of the forcing are discussed. In cases where the western boundary of the basin is nonreflecting, so that no full basin normal modes are possible, substantial energy transmission is still demonstrated. Whether resonance occurs or not, the necessity for energy transmission is closely related to the existence of the integral circulation constraint around the island barrier and the possibility of resonance acts mainly to set the level of the response.