A balanced and absolutely stable numerical thermodynamic model for closed and open oceanic basins

Abstract

By setting special boundary conditions the well-posed problem is formulated for the Adem thermodynamic model in an open oceanic basin when there is an anomalous heat flow across the lateral boundaries. Uniqueness and stability of the model solutions are shown. Estimates of the rate of dissipation of the temperature anomalies in the presence of diffusion and the absence of forcing are provided. The model operator is positive definite, positive semidefmite or skew-symmetric depending on the boundary conditions type and the diffusion. The splitting method is applied to construct an implicit 2nd order fmite-difference scheme that is economical, balanced, and unconditionally stable. Each of the split problems is one-dimensional and can easily be solved by factorization. The numerical algorithm can readily be generalized to three dimensions.