New additional boundary conditions for integrating a class of homogeneous models of wind-driven ocean circulation

A classical non-linear quasi-geostrophic model of wind-driven ocean circulation is integrated by using new additional boundary conditions conceived to: a) preserve, as far as possible, the typical structure of the Sverdrup flow in the southern and eastern regions of an idealised sub-tropical gyre and b) eliminate any additional boundary conditions in the northern and western regions of the fluid domain. Numerical simulations produce current and transport values close to those found in the literature whereas instability occurs at relatively low values of non-linearity, consistently with the well-known Sverdrup-like behaviour of large-scale transport in the world-wide ocean. A strict correlation emerges between the stability and the persistence of the Sverdrup-like behaviour of the so obtained solutions.