Analysis of the barotropic model of the subtropical gyre in the ocean for finite Reynolds numbers. Part I
Abstract:A barotropic time-dependent model of the wind-driven currents in the subtropical region of the ocean was considered taking both nonlinearity and lateral friction into account. The boundary conditions are the impermeability at all boundaries, no-slip at the coasts and slip at the fluid boundaries. It is shown that the solution of the problem is characterized by two nondimensional parameters ε (the ratio of width of the inertial boundary layer to a basin dimension) and R (Reynolds number for the boundary layer). A series of numerical experiments is discussed with fixed ε = 0.01 and varying R to analyze the joint effect of nonlinearity and lateral friction for a wide range of the coefficient of the horizontal friction.
The spin-up and quasistationary regimes in the evolution are identified. The most striking feature of the solution for finite R is the formation of a permanent intensive recirculation gyre. The periodic formation of the northward moving eddies in the boundary current is also observed during the quasistationary regime. A Fourier analysis of the energy oscillations as well as the time records of the stream function at certain points during the quasistationary regime is presented and the time-averaged solution of the problem is introduced.
The basic result of the analysis is the proof of the existence of two critical values RC and RL of the Reynolds number R. For R > RC the time-dependent solution of the problem does not stabilize as time proceeds (RC = 0.38). For R > RL the structure of the solution is changed drastically: the motion becomes substantially more chaotic both in the interior and in the boundary layer (RL = 1.6). It will be shown in Sheremet et al. (1996, hereafter will be called SIK) that for R > RC the steady solution still exists but it appears to be unstable, while for R > RL the steady boundary-layer-type solution of the problem ceases to exist. The main feature of the time-averaged solutions for R > RL is a rapid increase of a recirculation gyre in the northwest corner of the basin.
Document Type: Research Article
Publication date: November 1, 1995
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