A fully implicit model of the three-dimensional thermohaline ocean circulation

In this paper, a fully implicit numerical model of the three-dimensional thermohaline ocean circulation is presented. With this numerical model it is possible to follow branches of steady states in parameter space and monitor their linear stability. Also, transient flows can be computed allowing much larger time steps than those possible with explicit schemes. By using recently developed solvers for linear systems of equations and for generalized eigenvalue problems, results for reasonable spatial resolution can be obtained. Bifurcation diagrams and transient flows are computed for typical flows in a single hemispheric basin situation, with focus on (i) the performance of the methodology and (ii) the new type of information which can be obtained on these flows.