A two-level wind and buoyancy driven thermocline model by Peter Killworth (updated)

I was discussing with my colleagues about a recent northward shift of the Gulf Stream position and debating why that happened. So, I decided to read again one of my favorite physical oceanography papers “A two-level wind and buoyancy driven thermocline model” by the late Dr. Peter D. Killworth. This paper was published in 1985 in the Journal of Physical Oceanography, while I was still in my high school. In this study, Dr. Killworth used an idealized two-level box model for the North Atlantic to delineate the wind-driven gyre circulations, buoyancy-driven circulation (i.e., an idealized representation of the Atlantic Meridional Overturning Circulation, or AMOC), and their interactions. Although this paper is not about the Gulf Stream, by inspecting one of the figures, it occurred to me why the Gulf Stream separates from the North American coast well south of the zero-wind stress curl line. Below is my rationale.

In the two-level model, intense surface cooling in the subpolar North Atlantic helps form deep, cold and dense water, and produce a barotropic cyclonic circulation. This rotating cold and dense water slowly propagates westward in the form of Rossby waves. Then, it has to expand southward since there is no buoyancy-driven counterpart anticyclonic circulation in the subtropical region preventing it. To feed the cold water production in the high latitudes, the warm and light subtropical water has to be carried to the subpolar region. However, it cannot penetrate the potential vorticity barrier of cold and dense water in the western subpolar region, and thus has to take the interior pathways toward the eastern subpolar region. So, if the cold water production in the subpolar region is strong enough, the cold and dense subpolar water must expands southward along the western boundary below the zero-wind stress curl line, which in turn enforces the Gulf Stream to separate from the coast below the zero-wind stress curl line. A good analogy is a southward shift of the atmospheric jet stream during a cold Arctic air mass expanding southward.

This notion of the AMOC maintaining the separation latitude of the Gulf Stream is well supported by previous ocean model studies that consistently show a northward migration of the Gulf Stream under a weakened state of the AMOC. This AMOC-control mechanism provides an additional hypothesis on the age old question of why the Gulf Stream separates from the North American coast south of the zero-wind stress curl line.

Henri Drake ‪@henrifdrake.bsky.social‬ brought up an excellent point of whether the Gulf Stream separation issue in low-resolution models has anything to do with the AMOC-control hypothesis. I think that is fundamentally a different issue related to the wall boundary layer separation problem. A separation of wall-boundary flow is critically influenced by the flow speed, not the integrated transport. So, even if the Gulf Stream transport is the same in low- and high-resolution models, the Gulf Stream speed is much weaker in the low-resolution model; thus, the flow cannot separate from the coast. So, in a low-resolution model, the AMOC has to be unrealistically strong to overcome the wall-boundary layer dynamics issue to separate below the zero-wind stress curl line.

Figure 6 from Killworth (1985): A steady state solution of the two-level model driven by both wind and buoyancy forcing (density in the upper and lower layer, and velocity vectors in the upper layer).

Killworth, P. D., 1985: A two-level wind and buoyancy driven thermocline model. Journal of Physical Oceanography, 15, 1414–1432, https://doi.org/10.1175/1520-0485(1985)015<1414:ATLWAB>2.0.CO;2.