EMERGENCE OF FOFONOFF STATES IN INVISCID AND VISCOUS OCEAN CIRCULATION MODELS

Numerical experiments are performed to directly test the emergence of the Fofonoff solution in an inviscid closed barotropic domain, and to explore its significance to the weakly dissipative system. The Fofonof f solution, characterized by a linear relationship between absolute vo rticity and streamfunction, is generally realized as the time mean sta te of inviscid simulations over a fairly broad parameter range of vary ing (beta-plane) Rossby number and resolution, in different geometrica l domains, and with and without topography. The relevance of the Fofon off solution to the viscous, decaying system is examined by numerical experiments with two different forms of viscosity, namely, biharmonic and harmonic, as well as with various boundary conditions. It is found that the boundary condition is generally more important than the orde r of the viscosity in determining the time mean fields. All of the fri ctional forms and boundary conditions prevented the complete realizati on of the Fofonoff state to a greater or lesser extent. Of the various boundary conditions used, the super-slip condition is most conducive to realizing a Fofonoff state. In this case, at high enough resolution the timescale of energy variability is much longer than a dynamical t imescale, and the Fofonoff flow may be considered a 'minimum enstrophy ' state. At high Reynolds number and high Rossby number an almost line ar q - psi relationship can be achieved. For lower Rossby numbers, abs olute vorticity tends to become homogenized, preventing the Fofonoff s olution from arising. In the case of a free slip condition, it is stil l harder to reach a quasi-equilibrium. The time mean fields, after spi n-up, generally show a two-gyre structure with homogenization in the a bsolute vorticity fields. In the no slip case, neither a quasi-equilib rium nor any well formed time mean field can be reached. As a slight g eneralization of the flow on beta-plane, the inviscid topographic expe riments also ultimately yield a linear relationship between absolute v orticity and stream-function.