Wind-driven ocean circulation—Part 2. Numerical solutions of the non-linear problem

Abstract

Results from numerical calculations of wind-driven ocean circulation with a barotropic model with bottom friction and on the β-plane are presented for a range of parameters from slightly non-linear to highly non-linear flows. The imposed wind-stress curl is steady and everywhere negative and is symmetric with a maximum amplitude at mid-latitudes. The oceanic response is strongly asymmetric with a westward intensification for nearly linear flows ( Stommel's 1948 result), and a northward concentration for non-linear flows. All of the cases showed a steady oceanic response to a steady wind. The effect of the non-linear processes is to decrease the transport below the Sverdrup transport for mildly non-linear flows. Strongly non-linear flows in which the western boundary current flows up to the northern boundary, across the ocean and southward along the eastern boundary have transports larger than the Sverdrup transport. It is shown that non-linear effects cause the western boundary current to flow northward into regions where there is no wind-stress. Thus when flows are non-linear it appears that one must consider entire oceanic basins rather than basins delimited by the sign of the wind-stress curl. The balance of forces in the different regions of the ocean are presented and the feasibility of constructing analytic models is discussed. Details such as the countercurrent on the off-shore side of the western boundary current are reflected in the associated pressure fields which are also graphed.