THE RETROFLECTION PARADES

The classical question of what happens when a warm western boundary cu rrent, such as the North Brazil Current (NBC), retroflects is addresse d analytically using a reduced-gravity nonlinear model. The traditiona l view is that the northwestward Bowing current separates from the wal l, turns to the right (looking offshore), and forms a zonal boundary c urrent that Bows eastward. Integration of the steady inviscid momentum equation along the boundary gives the longshore momentum Bur (or flow force) and shows that such a scenario leads to a paradox. To resolve the paradox the separated current must constantly shed anticyclones, w hich propagate to the northwest due to beta and an interaction with th e boundary. This new eddy shedding mechanism, which is not related to the traditional instability of a zonal jet, may explain why the NBC mu st produce rings. A nonlinear analytical solution to the problem is co nstructed with the aid of a powerful theoretical approach based on the idea that nonlinear periodic flows can be integrated over a control v olume. This method enables us to extract all the details of the result ing features without solving for the details of the incredibly complic ated three-dimensional and time-dependent generation process. Due to t he strong nonlinearity of the problem, the method is quire different f rom the familiar averaging technique that requires the existence of a ''mean'' current. To employ the above method, however, it was necessar y to derive a new nonlinear formula for the beta-induced migration of eddies adjacent to a zonal boundary that slopes in the N-S direction. It turns out that the general problem involves an eddy retroflection l ength scale R(d)/epsilon(1/6) (where R(d) is the parent current Rossby radius and epsilon = beta R(d)/f(0)) that is greater than that of mos t eddies (R(d)). Calculations show that, for the retroflected NBC, whi ch transports about 45 Sv, eddies are shed approximately once every 90 days.