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. / A Dissertation submitted to the Geophysical Fluid Dynamics Institute in partial
fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Spring Semester, 2008. / Date of Defense: December 14, 2007. / Plant of the Coastline, Agulhas Current, Glacial periods, Rings injection, Retroflection, Eddies / Includes bibliographical references. / Doron Nof, Professor Directing Dissertation; Joel Kostka, Outside Committee Member; Carol Anne Clayson, Committee Member; Georges Weatherly, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_168680 |
| Contributors | Zharkov, Volodymyr (authoraut), Nof, Doron (professor directing dissertation), Kostka, Joel (outside committee member), Clayson, Carol Anne (committee member), Weatherly, Georges (committee member), Program in Geophysical Fluid Dynamics (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
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