The eddy cannon

A new nonlinear mechanism for the generation of “Meddies” by a cape is proposed. The essence of the new process is that the flow-force associated with any steady current that curves back on itself around a cape cannot be balanced without generating and shedding eddies. The process is modeled as follows. A westward flowing density current advances along a zonal wall and turns eastward after reaching the edge of the wall (i.e. the Cape of St Vincent). Integration of the steady (and inviscid) momentum equation along the wall gives the long-shore flow-force and shows that, no matter what the details of the turning process are, such a scenario is impossible. It corresponds to an unbalanced flow-force and, therefore, cannot exist. Namely, in an analogy to a rocket, the zonal longshore current forces the entire system to the west. A flow field that can compensate for such a force is westward drifting eddies that push the system to the east. In a similar fashion to the backward push associated with a firing cannon, the westward moving eddies (bullets) balance the integrated momentum of the flow around the cape. Nonlinear solutions are constructed analytically using an approach that enables one to compute the eddiesʹ size and generation frequency without solving for the incredibly complicated details of the generation process itself. The method takes advantage of the fact that, after each eddy is generated, the system returns to its original structure. It is based on the integration of the momentum equation (for periodic flows) over a control volume and a perturbation expansion in ϵ, the ratio between the eddiesʹ westward drift and the parent current speed. It is found that, because of the relatively small size of the Mediterranean eddies, β is not a sufficiently strong mechanism to remove the eddies (from the Cape of St Vincent) at the observed frequency. It is, therefore, concluded that westward advection must also take place. Specifically, it is found that an advection of 2 cm s−1 will remove (and generate) a Meddy once every 50 days or so and an advection of 5 cm s−1 will remove a Meddy every 17 days. “Kitchen-type” laboratory experiments on a rotating table show that, indeed, a flow that curves back on itself produces an eddy next to the tip of the cape. However, since neither significant β nor advection was present in the laboratory, the laboratory eddy was not shed during the limited time that the experiment was in progress. Numerical simulations (using the Bleck and Boudra isopycnic model) demonstrate, however, that eddies are constantly shed as predicted by the model.