Retroflection from Slanted Coastline Modeling Rings Injection into the South Atlantic during Glacials/Interglacials

Recent proxies analysis suggest that, at the end of the last glacial, there was a significant increase in the injection of Agulhas rings into the South Atlantic (SA). This brought about a dramatic increase in the salt-influx (from the Indian Ocean) into the SA helping re-start the then-collapsed meridional overturning cell (MOC), leading to the glacial termination. Here, we propose a mechanism through which large variations in ring production take place. To gain a preliminary understanding of the processes in question, we develop a nonlinear analytical model of retroflection from a slanted non-zonal coastline. In is known that the balance of long-shore momentum flux requires that the solution of retroflecting currents involves ring shedding on the western side. An important aspect of the ring dynamics is the ring intensity α (analogous to the Rossby number), which reaches its maximum value of unity when the upstream potential vorticity (PV) is zero. Friction leads to a slow-down and a decrease in α. The main difficulty is that the solution of the system of equations for conservation of mass and momentum of zonal currents leads to the conclusion that the ratio (Φ) of the mass flux going into the rings and the total incoming mass flux is approximately 4α/(1+2α) . This yields the "vorticity paradox"-- only relatively weak rings (α ¬ >1/2 ) could satisfy the necessary condition Φ ¬ >1. Physically, this means, for example, that the momentum-flux of zero PV currents upstream is so high that, no matter how many rings are produced and no matter what size they are, they cannot compensate for it. We show here that when the slant of coastline (γ) exceeds merely 15°, Φ does not reach unity regardless of the value of α. Namely, the paradox disappears even for small slants. Our slowly varying nonlinear solution does not only let us circumvent the paradox. It also gives a detailed description of the rings growth rate and the mass flux going into the rings as a function of time. Interestingly, for significant slants (γ ¬1/2 ) could satisfy the necessary condition Φ ¬ >1. Physically, this means, for example, that the momentum-flux of zero PV currents upstream is so high that, no matter how many rings are produced and no matter what size they are, they cannot compensate for it. We show here that when the slant of coastline (γ) exceeds merely 15°, Φ does not reach unity regardless of the value of α. Namely, the paradox disappears even for small slants. Our slowly varying nonlinear solution does not only let us circumvent the paradox. It also gives a detailed description of the rings growth rate and the mass flux going into the rings as a function of time. Interestingly, for significant slants (γ ¬1. Physically, this means, for example, that the momentum-flux of zero PV currents upstream is so high that, no matter how many rings are produced and no matter what size they are, they cannot compensate for it. We show here that when the slant of coastline (γ) exceeds merely 15°, Φ does not reach unity regardless of the value of α. Namely, the paradox disappears even for small slants. Our slowly varying nonlinear solution does not only let us circumvent the paradox. It also gives a detailed description of the rings growth rate and the mass flux going into the rings as a function of time. Interestingly, for significant slants (γ ¬°) , the rings reach a terminal size corresponding to a balance between the β -force and both the upstream and downstream momentum fluxes. This terminal size is unrelated to the ultimate detachment and westward drift due to β. The developed model enables us to obtain the nonlinear analytical solutions for eddy shedding, including the theoretical ranges of detached eddies radii, their propagation speeds, and their periods of detachment, as well as the average amount of mass flux going into the rings. Using the dependence of these aspects on the coastline slant, we show that there are restricted possibilities for ring detachment when the coast is oriented in the north –south direction. We define a critical coastline angle below which there is rings shedding and above which there is almost no shedding. In the case of the Agulhas region, the particular shape of the African continent implies that rings can be produced only when the retroflection occurs beyond a specific latitude where the angle is critical. During glaciation, the wind stress curl (WSC) vanished at a latitude lower than that of the critical angle, which prohibited the retroflection from producing rings. When the latitude at which the WSC vanishes migrated poleward towards its present day position, the corresponding coastline angle decreased below the critical angle and allowed for a vigorous production of rings. Simple process-oriented numerical simulations (using the Bleck and Boudra model) are in good agreement with our results and enable us to affirm that, during the glacials, the behavior of the Agulhas Current (AC) was similar to that of the modern East Australian Current (EAC), for which the coastline slant is supercritical.