APPENDIX B

Fundamental Understanding of the Loop Current System

The Gulf LC is known to affect all of the oceanographic and meteorological phenomena of the Gulf and the adjacent continental land masses, including the moisture flux into the U.S. heartland. Thus, understanding the LC’s behavior as it enters through the Yucatan Channel and exits through the Florida Straits is important for maritime commerce, fisheries, oil and gas operations, farming, and weather prediction. Observations, particularly the nearly continuous ones, over the recent era of satellite altimetry measurements show a complex set of behaviors, including periods of time when the LC is confined to the region of inflow and outflow, versus other times when the LC extends far into the Gulf of Mexico. Accompanying the large intrusion is the shedding of an anticyclonic eddy, upon which the LC tends to (but not always) retract back to its more direct inflow–outflow pathway. Numerous studies describe these behaviors along with some satellite altimetry era examples, which include Alvera-Azcárate et al. (2009), Leben (2005), Liu et al. (2016), Sturges and Leben (2000), and Zeng et al. (2015b).

The most vexing theoretical issues regarding the behavior of the LC remain twofold: first, what controls the penetration of the LCS into the Gulf of Mexico, and second, what determines the shedding of an anticyclonic eddy and the retraction of the LC back into its more southern inflow/outflow position.

The theories begin with the work of Reid (1972), who argued that the LC loses its topographic control when heading north upon leaving the vicinity of the Campeche Bank, where the water depth increases abruptly from about 1,000 meters deep to the abyss at about 3,500 meters deep. As a result of this rapid depth transition, the LC flow field is largely limited to the upper 1,000 meters of the water column. Thus, a reduced gravity model was argued as being appropriate for considering subsequent LC evolution. By virtue of the planetary beta effect (due to the gradient in the Coriolis parameter b = ∂f/∂y), further northward translation of the LC results in an increase of negative relative vorticity. Negative relative vorticity (or clockwise spin) tends to turn the LC to the right, causing it to eventually loop around and head back toward the south before exiting through the Florida Straits as the Gulf Stream, hence the name Loop Current. Hurlburt and Thompson (1980) built on this work with a series of idealized numerical model simulations using barotropic, reduced gravity, and two-layered models, with

and without planetary beta. The basic argument of Reid (1972) was demonstrated, the shedding of eddies were further shown to be a result of planetary beta, and both bathymetry and dissipation were argued to also be important. A corollary to this work is that eddy shedding and subsequent westward movement are intrinsic properties of the LCS. Triggering by time-dependent inflows is not necessary for eddy generation, but as with any instability, further forcing may hasten the process.

A requirement for eddy shedding was identified by Pichevin and Nof (1997), who argued on analytical grounds that the northward inflow and eastward outflow resulted in a momentum imbalance paradox. By considering the area as an integrated, steady, inviscid, zonal momentum equation, they found that such a flow configuration was not possible to balance the zonal momentum outflow through the Florida Straits without eddies being shed to the west. Eddy size, speed, and shedding period estimates resulting from this theory appeared to be in reasonable agreement with the observed LC statistics. This theory was extended by Nof (2005), who used a multiple–time scale approach to show that the integrated Coriolis force on a growing eddy is also able to provide momentum closure.

Being that eddy shedding occurs aperiodically (e.g., Sturges and Leben, 2000), Lugo-Fernández (2007) chose a nonlinear time-series approach to determine if the LC behaved as a chaotic oscillator. Despite the limited available data, such analysis suggested that the LC is not chaotic, but instead acts as a nonlinear oscillator responding to variations in forcing conditions.

The next emergent line of thought was by Sheremet (2001), who considered the conditions under which a western boundary current in Munk (1950) balance (i.e., horizontal friction dissipating planetary vorticity advection) would either penetrate a gap (i.e., intrude into the Gulf of Mexico), or leap across that gap (proceed directly from the inflow to the outflow). For narrow gaps (less than twice the Munk boundary-layer scale defined by a horizontal friction parameter and the planetary beta), it was found that the current leaps over the gap, except for a small portion that leaks through, bends around, and then exits the gap. For larger gap widths, the boundary current enters the gap and flows west as a zonal jet eventually returns as an oppositely directed zonal jet exits the gaps and flows north. Nonlinear effects modified the linear solution, as did an increasing Reynolds number (increasing turbulence) that further facilitated eddy shedding. Given that the distance is several hundred kilometers between the 1,000-meter isobaths on the Campeche Bank and the West Florida Shelf, the gap across which the LC must leap is large (according to the original values used by Munk in his seminal paper on western boundary currents), and consequently, an LC penetra-

tion into the Gulf of Mexico was a reasonable expectation according to Sheremet’s gap leaping theory.

These ideas were then expanded on by Sheremet and Kuehl (2007) and Kuehl and Sheremet (2009) through a series of elegant rotating tank experiments viewed in light of the theory. Fluid inertia was found to promote a leaping state, planetary beta a penetrating state, and the flow state was also found to depend on prior evolution, that is, a hysteresis. The strength of the current was also found to be important, suggesting that variations in volume transport might play a role in LC intrusion. This may be important given that analyses of altimetry observations in the Caribbean (Alvera-Azcárate et al., 2009) suggested an interannual variation in volume transport that was correlated with the zonal component of wind stress and a wind stress curl dipole on the northern and southern sides of the Caribbean that tilted the thermocline, changing the circulation, and that these interannual findings were further related to the El Niño–Southern Oscillation (ENSO) index. Zeng et al. (2015b) subsequently argued for a similar teleconnection.

Stratification was added to both the analytical and laboratory treatments by Kuehl and Sheremet (2014), allowing for a more complete set of boundary-layer scaling (inertia, bottom friction, horizontal friction) findings. They conclude that the system admits three distinct states: a steady gap-leaping state (retracted LC state), a steady gap-penetrating, extended LC state, and an eddy-shedding LC state. The transition between the latter two appears to be due to the relative strengths of vorticity advection into the gap and vorticity dissipation due to friction (predominantly Ekman friction). If friction is strong enough to balance vorticity advection, the system will assume a steady LC state. Once vorticity advection overcomes friction, the excess vorticity is dissipated by eddy shedding.

With LCE shedding shown by these previous works to be a consequence of planetary beta (due to relative vorticity becoming increasingly anticyclonic as the LC moves northward) and with the mechanism of energy conversion being either barotropic or baroclinic instability depending on the model setup (e.g., Hurlburt and Thompson, 1980), it remained to actually demonstrate the mechanism of instability observationally. This was accomplished recently by Donohue et al. (2016b) who argued for baroclinic instability being the primary mechanism. Known to be shed aperiodically and taking on different sizes, there remains a need to determine under what conditions LCEs may, or may not, be shed. For instance, a Hovmuller plot for sea surface height anomalies across the central Caribbean, the Nicaraguan Basin, and the Gulf of Mexico shows differing frequencies of occurrences from region to region (Alvera-Azcárate et

al., 2009), suggesting that triggering is not a simple matter (recall the Hurlburt and Thompson finding of a trigger not being a necessary condition for eddy shedding).

Whereas the LC may depend primarily on planetary beta once freed from topography, the Gulf is enclosed by steep escarpments that are also known to be important (Hurlburt and Thompson, 1980). These escarpments result in a topographic beta effect that may exceed the planetary beta effect by an order of magnitude along the escarpments. Thus, regions of steep bathymetric topography will result in the flow field tending to be oriented parallel to the isobaths and in the propagation of TRWs away from

regions where the flow may be temporarily perturbed to go across the isobaths. Such energy loss through TRW propagation may carry energy away from the LC, thereby reducing the ability of the LC to penetrate further into the Gulf and also reducing the energy available for eddy shedding, thus providing a stabilizing influence on the LCS.

In the search for simplicity in advancing LCS theory, an important knowledge gap may be the role of bathymetric topography. DeHaan and Sturges (2005) argued for a deep Gulf cyclonic circulation on the basis of the escarpments, and direct observations by Hamilton (1990, 2009) confirmed this. Oey and Lee (2002) and Hamilton (2009) considered TRWs to be implied in numerical model simulations and in situ observations, but only in the deeper portions of the Gulf of Mexico due to their model resolution. TRWs may also occur along the escarpments, and, with TRWs propagating with shallow isobaths to the right (in the Northern Hemisphere), an important point of origination is the West Florida Shelf, a region that remains relatively unobserved because of the absence of oil and gas exploration or operations there.

This absence of simplicity becomes clear when contrasting LCS behaviors between different years. For instance (and as described in Chapter 1), during 2014 through 2015, the Gulf witnessed an uncharacteristically active LCS behavior with the far northward penetration of the LC and subsequent eddy shedding repeating for some 18 months. In contrast, during 2017, the LC remained retracted and fairly stable for several months before settling into another state in which it extended partially northward with cyclonic and then anticyclonic features seeming to block it from further translation (see Figure B.1). These differing behaviors suggest that planetary beta effects, topographic beta effects, and the three-dimensional linkages between the LC and its sequential eddy structures must all be considered when improving on predictive capabilities.

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