Analysis of the barotropic model of the subtropical gyre in the ocean for finite Reynolds numbers. Part II.

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ID: 303145
1995
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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 e (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 e = 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 R C and R L of the Reynolds number R. For R > R C the time-dependent solution of the problem does not stabilize as time proceeds (R C = 0.38). For R > R L the structure of the solution is changed drastically : the motion becomes substantially more chaotic both in the interior and in the boundary layer (R L = 1.6). It will be shown in Sheremet et al. (1996, hereafter will be called SIK) that for R > R C the steady solution still exists but it appears to be unstable, while for R > R L the steady boundary-layer-type solution of the problem ceases to exist. The main feature of the time-averaged solutions for R > R L is a rapid increase of a recirculation gyre in the northwest corner of the basin.
Reference Key
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Authors Vitalii A. Sheremet, Vladimir M. Kamenkovich, A. R. Pastushkov
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Journal journal of marine research
Year 1995
DOI
10.1357/0022240953212945
URL
https://doi.org/10.1357/0022240953212945
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