Inertial effects in an oceanic circulation model |
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| Authors: | Andrew F Bennett |
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| Institution: | 1. Pierce Hall, Harvard University , Massachusetts, Cambridge, 02138, U.S.A.;2. G. F. D. Laboratory, Monash University , Clayton, Victoria, 3168, Australia |
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| Abstract: | AbstractThe flow in a mechanically driven thin barotropic rotating fluid system is analysed. The linear theory of Baker and Robinson (1969) is modified and extended into the non-linear regime.An internal parameter, the “local Rossby number”, is indicative of the onset of nonlinear effects. If this parameter is 0(1) then inertial effects are as important as Coriolis accelerations in the interior of the transport-turning western boundary layer and both of its Ekman layers. The inertial effects in the Ekman layers, ignored in previous explorations of non-linear wind driven oceanic circulation, are retained here and calculated using an approximation of the Oseen type. The circulation problem is reduced to a system of scalar equations in only two independent variables; the system is valid for non-small local Rossby number provided only that the approximate total vorticity is positive.To complete the solution for small Rossby number a boundary condition for the inertially induced transport is needed. It is found by examining the dynamics controlling this additional transport from the western boundary layer as the transport recirculates through the rest of the ocean basin. The strong constraint of total recirculation within the western boundary layer (zero net inertial transport) is derived.The calculated primary inertial effects are in agreement with the observations of the laboratory model of Baker and Robinson (1969).The analysis indicates the extent to which three-dimensional non-linear circulation can be reduced to a two dimensional problem. |
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