Volodymyr Zharkov

The Arrested Agulhas Retroflection

Paleoceanographic proxy data indicate that the Agulhas leakage into the South Atlantic was dramatically reduced during glacial times. In our former papers, we suggested that this was due to a northward shift of the zero wind stress curl that, in turn, forced the retroflection to occur farther north, where the slant of the coastline relative to the north is steep. In the present paper, we propose that strong westerlies (0.4 Pa, implying a wind speed of ∼12 m s−1 at zero degrees centigrade), which were supposedly common during glaciations, can also arrest the leakage. This arrest occurred because the wind stress opposed the momentum flux associated with the retroflection; such an arrest did not require the retroflection to shift in latitude. We use a simple, nonlinear, “reduced gravity” model to show analytically and numerically that, under the above conditions, the eastward wind stress compensates for the zonal westward flow-force associated with the retroflection, thus avoiding the development and shedding of rings. For a nearly zonal wall, westerly winds, and small upper layer thickness along the wall, the arresting wind stress is found, theoretically, to be, τ = 0.042α3/2ρf0[(2f0Q)3/g′]1/4, where α is twice the retroflection eddy vorticity, ρ is the water density, Q is the Agulhas Current volume flux, and the remaining notation is conventional. A few words on Stern’s contribution to the field of eddies Eddies, the oceanic analogs of tornadoes and hurricanes, were one of Melvin’s specialties. In an elegant paper that most people originally referred to as “esoteric” (1974, JMR), Melvin showed that much can be learned about eddies by looking at groups of two adjacent vortices, each spinning in a different direction. For reasons known only to him, he coined this counter-spinning vortex a “Modon”. (A modon actually means a collection of cities in Arabic.) Despite the initial skepticism by some (evidently, one editor of a respectable 1. Department of Earth, Ocean and Atmospheric Science, Florida State University, Tallahassee, Florida, 32306, U.S.A. 2. Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, Florida, 32306, U.S.A. 3. Corresponding author. email: doron@fsu.edu 4. Center for Oceanic-Atmospheric Prediction Studies, Florida State University, Tallahassee, Florida, 32306, U.S.A. 5. Department of Geology, Kent State University, Kent, Ohio, 44242, U.S.A. 6. Department of Atmospheric Science, The Hebrew University of Jerusalem, Jerusalem, Israel. 7. Instituto de Matemática, Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, RJ, Brazil.

Comments on “On the Steadiness of Separating Meandering Currents”

AbstractUsing integration constraints and scale analysis, van Leeuwen and De Ruijter focused on the steady aspect of the downstream flow in the momentum imbalance articles of Nof and Pichevin appearing in the 1990s and later on. They correctly pointed out that when the steady downstream flow is exactly geostrophic then it must obey the additional downstream (critical) condition (where u is the speed, g′ is the reduced gravity, and h is the thickness). They then further argue that this additional condition provides “a strong limitation on the generality of their results.” These results for steady flows have been incorrectly generalized by the typical reader to eddy generating unsteady flows, which was the focus of Nof and Pichevin.The current authors argue that, although the van Leeuwen and De Ruijter condition of is valid for a purely geostrophic and steady flow downstream, it is inapplicable even for the steady aspect of the Nof and Pichevin solutions because the assumption of a purely geostrophic flow (...

Why Does the North Brazil Current Regularly Shed Rings but the Brazil Current Does Not

Abstract Both the North Brazil Current (NBC) and the Brazil Current (BC) are western boundary currents (WBCs) that separate from the western Atlantic coast. The NBC retroflects and sheds several rings per year (at the retroflection region), whereas the BC rarely sheds rings near its separation point. Traditionally, the difference between these two WBCs has been attributed to the Malvinas Current (MC), whose momentum flux opposes the poleward momentum flux of the BC, thus preventing rings shedding at the point where the current leaves the coast. Even in the absence of the MC, rings from the separating BC would have never been regularly generated because of the relatively large slant of the coastline relative to the zonal direction. Using the recently proposed theory of Zharkov and Nof, it is demonstrated that the large inclination of the coastline between 20° and 45°S (approximately 50°) lies within the regime that does not allow the BC a continuous shedding of rings. In contrast, the inclination of the co...

A New Model of Current Retroflection Applied to the Westward Protrusion of the Agulhas Current

AbstractThe dynamics of current retroflection and rings shedding are not yet fully understood. In this paper, the authors develop an analytical model of the Agulhas Current retroflection dynamics using three simple laws: conservation of volume, momentum balance, and Bernoulli’s principle. This study shows that, for a retroflecting current with a small Rossby number, this theoretical model is in good agreement with numerical simulations of a reduced-gravity isopycnal model. Otherwise, the retroflection position becomes unstable and quickly propagates upstream, leaving a chain of eddies in its path. On the basis of these findings, the authors hypothesize that the westward protrusion of the Agulhas retroflection and the local “zonalization” of the Agulhas Current after it passes the Agulhas Bank are stable only for small Rossby numbers. Otherwise, the retroflection shifts toward the eastern slope of the Agulhas Bank, where its position stabilizes due to the slanted configuration of the slope. This study show...