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A fully-implicit model of the global ocean circulation. (English) Zbl 1032.76557
Summary: With the recent developments in the solution methods for large-dimensional nonlinear algebraic systems, fully-implicit ocean circulation models are now becoming feasible. In this paper, the formulation of such a three-dimensional global ocean model is presented. With this implicit model, the sensitivity of steady states to parameters can be investigated efficiently using continuation methods. In addition, the implicit formulation allows for much larger time steps than can be used with explicit models. To demonstrate current capabilities of the implicit global ocean model, we use a relatively low-resolution (4$$^\circ$$ horizontally and 12 levels vertically) version. For this configuration, we present: (i) an explicit calculation of the bifurcation diagram associated with hysteresis behavior of the ocean circulation and (ii) the scaling behavior of the Atlantic meridional overturning versus the magnitude of the vertical mixing coefficient of heat and salt.

##### MSC:
 76E20 Stability and instability of geophysical and astrophysical flows 65P30 Numerical bifurcation problems 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
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