Using Viscosity Instead of Drag

It should be emphasized that neither the Stommel nor the Munk models are accurate descriptors of the real ocean, but taken together the similarities of their solutions are a powerful argument for the relative insensitivity of the qualitative form of the solution to the detailed form of the friction. The models do in fact produce reasonably realistic patterns of large-scale flow in the major basins of the world.

The figure below shows the solution (streamfunction, in Sverdrups) to the Stommel-Munk problem numerically calculated for the North Atlantic, using the observed wind field. The model has realistic geometry, but is flat-bottomed. The calculation reproduces the observed large-scale patterns, but the Gulf Stream and its extension are too diffuse, and its separation from the coast is a little too far north.

WindCalculatedStommelMunkSolution

1Vallis, G.K. (2017) Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. 2nd edn. Cambridge: Cambridge University Press.