Although the upper-layer dynamics of the Loop Current and eddies in the Gulf of Mexico are well studied, the understanding of how they are coupled to the deep flows is limited. In this work, results from a numerical model are analyzed to classify the expansion, shedding, retraction, and deep-coupling cycle (the Loop Current cycle) according to the vertical mass flux across the base of the Loop. Stage A is the “Loop reforming” period, with downward flux and deep divergence under the Loop Current. Stage B is the “incipient shedding,” with strong upward flux and deep convergence. Stage C is the “eddy migration,” with waning upward flux and deep throughflow from the western Gulf into the Yucatan Channel. Because of the strong deep coupling between the eastern and western Gulf, the Loop’s expansion is poorly correlated with deep flows through the Yucatan Channel. Stage A is longest and the mean vertical flux under the Loop Current is downward. Therefore, because the net circulation around the abyssal basin is zero, the abyssal gyre in the western Gulf is cyclonic. The gyre’s strength is strongest when the Loop Current is reforming and weakest after an eddy is shed. The result suggests that the Loop Current cycle can force a low-frequency [time scales ∼ shedding periods; O(months)] abyssal oscillation in the Gulf of Mexico.
The Loop Current is the extension of the Yucatan Current and is the most prominent circulation feature in the Gulf of Mexico. Mainly confined in the upper 1000 m, the Loop Current has very strong speeds that can exceed 2 m s−1 (for a review and references, see Oey et al. 2005). Large warm-core rings (Loop Current eddies, 200–350 km wide and 500–1000 m deep) episodically separate from the Loop Current at time intervals that range from 3 to 18 months (Sturges and Leben 2000). Upper-layer (z ≳ −1000 m) mass influx from the Yucatan Channel feeds the Loop Current, which accumulates mass and grows larger and deeper (Pichevin and Nof 1997, hereafter PN97). Because the Gulf of Mexico is closed in the west, the expanding (and deepening) Loop forces some water out of the Straits of Florida and also through the upper Yucatan Channel (e.g., on the Cuban side). Because the Straits of Florida has a shallow sill depth (800–1000 m) and a rather narrow width compared to the Loop, some of the displaced water also leaks into the Caribbean Sea through the deep sill of the Yucatan Channel (∼2040 m). As the Loop Current grows, the westward Rossby wave speed (which is ∝ −βR2, where R is the Rossby radius based on the matured deep Loop) overcomes the growth rate and the Loop sheds an eddy (Nof 2005, hereafter N05). As the eddy migrates westward, it also displaces water from the western Gulf (WG), and this also generates deep flows. This cycle (expansion → Yucatan’s deep flows → separation → retraction → eddy migration → deep flows in the Gulf → expansion) will be referred to as the Loop Current cycle.
Some (surface) aspects of the Loop Current cycle can be seen in animations of sea surface height (SSH) from satellite product [e.g., Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO); available online at http://www.aviso.oceanobs.com] and/or numerical models. Deep outflows (in Yucatan Channel) were observed by Burkov et al. (1982) and Maul et al. (1985) and in a numerical model [the Princeton Ocean Model (POM)] by Oey (1996). Oey summarized his and Maul et al.’s findings: “… correlation between shedding events and reversed bottom flow can be identified …. The bottom reversed flows last from a few weeks to as long as 6 months … and in general precede sheddings.... The evidence for the two processes to be related is overwhelming. In analyzing the near-bottom current meter time series in the Yucatan Channel, Maul et al … noted prolonged (weeks to months) southward flow, which appeared to correlate with eddy shedding inferred from satellite imagery ….” Oey (1996) was more interested in relating the Yucatan deep outflow and Loop Current eddy shedding but noted also that the model deep outflow is correlated with upper-layer (defined as z > −750 m) inflow, at time scales of 1–3 months (see his Fig. 6). Because the upper-layer inflow contributes to the growth of the Loop (PN97; N05), the Yucatan deep outflow may also correlate with the Loop Current’s expansion area. The idea was first put forth by Maul (1977), as summarized in Maul et al. (1985): “… this deep southward flow (in the Yucatan Channel) is part of the continuity adjustment process associated with eddy formation in the Gulf Loop Current: excess upper-layer inflow required to form the eddies is partially compensated by time-dependent outflow in the deep layer.”
Maul et al.’s (1985) idea is later examined by Bunge et al. (2002) using mooring data from September 1999–June 2000 collected during the CANEK observational program in the Yucatan Channel (Candela et al. 2002; Sheinbaum et al. 2002). The analysis was for 6 months from November 1999 to April 2000 and excluded eddy shedding. The authors found some correlation between Loop Current expansion rate and Yucatan deep outflow. Subsequent analyses by Ezer et al. (2003; also a POM simulation, described in Oey et al. 2003) suggested also that deep outflow in the Yucatan Channel may be related to the Loop’s expansion rate.
The Loop Current cycle is not exact: no two realizations of Loop Current are the same and eddy sizes differ. Also, the intervals between eddy separations, as well as the inflow and outflow transports, vary with time. It is, however, a useful concept. Although the previous research suggests that the Loop’s expansion may be correlated with deep outflow, we do not yet have a clear description of this and other processes involved. We do not, in particular, have a clear understanding of the upper–lower layer coupling during a Loop Current cycle. This is due to the lack of an observational dataset that can adequately provide the three-dimensional and time-dependent evolution of the Loop Current cycle. There are now many good numerical models of the Gulf of Mexico (see review in Oey et al. 2005). Models now have high resolution that reduces their truncation errors and makes up for their lack of true physics with self consistency (e.g., mass is conserved), fine spatial coverage, and multiyear outputs. Here, we use the POM to examine the Loop Current cycle. An 8-yr process simulation is conducted such that the model sheds eddies at a nearly constant rate of 1 eddy per 8.1 months (12 eddies total). The nearly constant rate of eddy shedding produces nearly repeatable Loop Current cycles. The model therefore yields more easily identifiable patterns that provide insight into the coupling between the Loop Current and deep flows. The following questions will be addressed: What is the distribution of mass that enters and exits the deep Gulf during a Loop Current cycle? What is the time-dependent coupling between the Loop Current and various inflows and outflows? How does the western deep Gulf respond to the Loop Current cycle, and why is the circulation there cyclonic?
Our focus will almost exclusively be on deep flows and their relation to the Loop Current and eddy-shedding, as these are topics that are least understood. The approach is to compute (deep) mass transport budgets and then relate them to the Loop Current cycle. This work therefore complements Oey (2008), who examined deep eddies and how they may generate topographic Rossby waves. It will be seen also that some of Oey’s (2008) analyses support our results.
Mass budget analyses do not directly tell us about cause and effect. However, mass conservation imposes powerful constraints on the dynamics of a semienclosed sea. In the case of the Gulf of Mexico, westward mass transport by eddies necessitates a return (i.e., eastward) transport, which will be used in this work to provide an improved understanding of the dynamics of the Loop Current cycle. A similar approach was previously used as one of the analysis tools to explain eddy-shedding behaviors of the Loop Current and heat exchanges between the Gulf and the Caribbean Sea (Chang and Oey 2010a,b). As indicated above, PN97 and N05 suggest that the separation of an eddy from the Loop Current is primarily an upper-layer process in which the tendency for the “bulged” Loop to bend westward because of Rossby wave dynamics overcomes the growth rate of the Loop by inflow through the Yucatan Channel. Chang and Oey’s (2010a) work supports PN97 and N05. By analyzing the results of a three-dimensional model with Gulf’s topography and stratification, the authors demonstrate that eddy shedding depends on Gulf-wide mass balance and zonal momentum flux in the upper layer. In this work, we will present results that also support the idea of PN97, N05, and Chang and Oey (2010a) of a dominantly upper-layer forcing by the Loop Current and eddies. This idea is central to understanding the results contained herein. The following “thought experiment” is useful: Fluid in the Gulf is initially at rest. Yucatan inflow, which is primarily in the upper layer (as observed by Sheinbaum et al. 2002; see also Fig. 2 in Oey et al. 2005), then initiates a growing Loop Current in the eastern Gulf (EG).1 The abyssal ocean then responds; an example is Maul et al’s (1985) idea of a deep outflow through the Yucatan Channel. As the Loop bends westward and as the eddy separates from the Loop and migrates westward, water that is displaced in the western Gulf produces return (i.e., eastward) transports both near the surface and in deep layers (Chang and Oey 2010a). Chang and Oey (2010a) show that an eddy typically transports about 13 Sv (1 Sv ≡ 106 m3 s−1) of water westward (see their Table 2). Most of this water is returned eastward in the upper layer, but the deep return flow (under the eddy, deeper than z ≈ −800 m) is not insignificant, roughly 1–2 Sv, and the accompanying vertical mass flux in the western Gulf is downward. As the eddy decays and in the absence of other external forcing (i.e., surface fluxes, rivers, and time-dependent large-scale transports, e.g., from the Atlantic, etc., are nil), isopycnals flatten, resulting in upwelling in the western Gulf that is accompanied by westward deep flow from the eastern to western basins. In this idealized experiment, the causes of all these originate in the upper layer: Yucatan inflow, Loop Current, and eddies. The goal is then to describe and understand this simple case. The results presented herein will suggest that, for deep motions to significantly affect the upper-layer dynamics, the forcing would be external and the likely source is the deep flow through the Yucatan Channel.
The outline of the paper is as follows: Section 2 describes the numerical model. Section 3 describes the Loop Current cycle using mass balances to analyze the coupling between Loop Current, eddy-shedding, and time-dependent deep flows. In section 4, we show how the Loop Current cycle is coupled to the central and western Gulf’s deep circulation. Section 5 uses a vorticity constraint for the deep Gulf to show that a cyclonic gyre must exist in the western Gulf. Section 6 is conclusions and discussion.
2. The numerical model
The POM (Mellor 2002) is time dependent and three dimensional based on the primitive equations assuming hydrostacy and Boussinesq approximation. Model domain covers the western Caribbean Sea and the Gulf of Mexico west of 78°W. It is nested within a larger-scale, coarser-grid northwestern Atlantic Ocean model described in Oey et al. (2003). The nested model’s horizontal resolution is double, approximately 5 km in the Gulf of Mexico including the Yucatan Channel and Straits of Florida, and there are 25 vertical sigma levels (for publications that describe other details of the model, see online at http://www.aos.princeton.edu/WWWPUBLIC/PROFS/publications.html). All surface fluxes are nil, and transport through the Yucatan Channel is very nearly constant at 23.7 Sv. The model was integrated for 12 yr initialized from the coarse grid. A quasi-equilibrium state, in which the model Loop Current sheds eddies at a nearly constant rate of 1 eddy per 8.1 months, was reached in 4–5 yr. The analyses below are based on the last 8 yr of the model data.
3. The Loop Current cycle
In the model, eddies are shed at approximately (25.5°N, 88°W). After an eddy is shed, it migrates southwestward, at about 0.07 m s−1, and eventually decays in the southwestern Gulf. Meantime, the Loop Current reforms (i.e., expands) and the cycle repeats (see Oey et al. 2003, especially their Fig. 5; Oey 2004). This regularity is idealized but is an advantage for the present attempt to better understand processes. A description of how the deep flows (at Yucatan and between the western and eastern Gulf) are coupled to the Loop Current is nonexistence even for this idealized case.
The interaction between upper and lower layers (shallower and deeper than 1000 m, respectively) is examined by calculating mass balance beneath z = −1000 m. The reason for this will become clear shortly. Figure 1 shows the map of the eastern Gulf of Mexico. A control volume is defined in the deep portion of the eastern Gulf with the upper boundary at z = −1000 m. The northern, eastern, and southwestern boundaries are closed because of the continental shelf break, the shallow sill of the Straits of Florida, and the bank of Campeche. There are therefore three openings bounding the control volume: at 90°W (western thick line), the deep sill of the Yucatan Channel (southern thick line), and the upper boundary at z = −1000 m. The strong constraint imposed by mass conservation in this control volume will enable us to unambiguously describe the Loop Current cycle. We first present time series plots and then explain the physics involved.
Time series of transports across the three openings are plotted in Fig. 2. Thin vertical lines represent times when eddies detach from the Loop Current. Transports at 90°W (Tr90W), Yucatan Channel (TrYuc), and across z = −1000 m (TrZ1k) are time dependent, and they change signs (directions) at different stages of the Loop Current cycle. In the plots, the sign of transport is kept the same as the velocity: positive Tr90W and TrYuc are eastward and northward influx to the control volume, respectively, but positive TrZ1k is upward out of the control volume. The sign retention in TrZ1k is to keep its conventional physical meaning that downward is negative; for example, TrZ1k tends to be less than zero, representing downwelling when the Loop Current impresses upon the control volume from above as, for example, when the Loop expands into the Gulf of Mexico, etc. This relation between TrZ1k and the Loop Current’s expansion (and retraction, same below) is approximate (see the appendix), but for the time being it is quite helpful to keep a mental image of the connection. The curves and their relationships appear complicated, but on closer examination they reveal the following general pattern: Small time shifts of 1–2 months exist between Tr90W and TrYuc and also between TrYuc and TrZ1k (Fig. 2a). Transports at 90°W and Yucatan Channel (Tr90W and TrYuc, Fig. 2b) are anticorrelated: maximum Tr90W (i.e., maximum eastward transport at 90°W) leads minimum TrYuc (i.e., maximum southward transport at the Yucatan Channel) by 30 days [Fig. 2b; the correlation coefficient (CC) is −0.56 at 30-day lag].2 On the other hand, TrYuc and TrZ1k are positively correlated; the CC is +0.61 and is +0.72 at 30-day lag: TrZ1k lags TrYuc (Fig. 2c). These correlations (and their respective lags) suggest closely related dynamics between Loop Current expansion, eddy shedding, eddy passage across 90°W, which forces Tr90W, vertical mass exchanges across the base of the Loop (TrZ1k), and the Yucatan deep flows (TrYuc). To understand the relation, we choose one event from Fig. 2a to examine the interaction between TrYuc, Tr90W, and TrZ1k (Fig. 3, top). To confirm that our interpretations are robust (i.e., event independent) we also calculated the corresponding ensemble time series (Fig. 3, bottom). Because each event is distinct (each with a different time period), each ensemble is for simplicity taken as the average from 115 days before to 125 days after each eddy shedding. The two plots in Fig. 3 are similar, and the following descriptions apply to both of them. Three stages are defined based on the variation of TrZ1k as will be explained shortly. Figures 4a–c show the states of the Loop Current at these stages as plots of the corresponding ensemble averages of sea surface height and surface currents. Figure 5 gives schematic sketches that the reader may find useful in following the descriptions below.
a. Stage A
This corresponds to a state when the Loop Current is reforming and expanding after an eddy has shed and propagated away from the eastern Gulf of Mexico (Fig. 4a). The Loop Current at this stage is near the Yucatan Channel. Continuity requires that the Loop Current’s expansion is accompanied by downwelling beneath it so that TrZ1k < 0, though some mass may also leak into the Straits of Florida (cf. Maul et al. 1985; N05; Chang and Oey 2010a). This period of downwelling (TrZ1k < 0) is taken to define stage A. Figure 3 shows that it coincides in general with stronger deep outflow in the Yucatan Channel (TrYuc < 0). However, the responses in stage A are different prior to (stage A1) and after (stage A2) the shedding of an eddy. Although the Loop Current is reforming in both these substages, it is clear that, in stage A1, the deep, predominantly divergent flow in the eastern Gulf of Mexico is associated with the downwelling mass flux; that is, stage A1 is consistent with Maul et al.’s (1985) hypothesis. This is drawn in Fig. 5a. Stage A2 is different, however. Both deep eastward flow across 90°W (Tr90W > 0) and downward mass flux beneath the Loop Current (TrZ1k < 0) contribute to the strong outflow in the Yucatan Channel (TrYuc < 0). In fact, TrYuc reaches a minimum in stage A2 (i.e., maximum outflow; Fig. 3), balancing the summed contributions from Tr90W (>0) and TrZ1k (<0). However, the contribution from Tr90W is dominant. From Fig. 3, it is clear that the large Tr90W in stage A2 is caused by the continued forcing of the westward-propagating eddy (from stage C; see below) that forces an eastward returned deep flow (because the western Gulf is closed and mass is conserved; Chang and Oey 2010a). As stage A2 transits to stage A1, Tr90W weakens and TrZ1k reaches its minimum (strong downwelling). The strong downwelling feeds the deep outflow at Yucatan, TrYuc, and the latter continues to weaken because of the weakened contribution from Tr90W. All together, TrYuc appears to lead TrZ1k in Fig. 2c; that is, the minimum of TrYuc precedes the minimum of TrZ1k. The strong downwelling also squashes vortex lines and induces negative vorticity in the deep layers, consistent with Oey’s (2008) EOF analysis of the relative vorticity stretching term when the Loop is reforming (see his Fig. 4).
The existence of stage A2 (and stage C; see below) suggests that, within approximately 2 months after an eddy is shed, the deep outflow at Yucatan can be quite unrelated to the Loop Current’s expansion (which is related to TrZ1k < 0; see the appendix). This may explain why, in Fig. 3 of Bunge et al (2002), the rate of Loop’s expansion (and retraction) does not correlate well with the observed deep flow in the Yucatan Channel, especially at the beginning of the time series, which was 1–2 months after a huge eddy (Eddy Juggernaut) separated from the Loop Current.
b. Stage B
This corresponds to the period of incipient eddy shedding when TrZ1k changes sign to become positive or upwelling and continues to increase to its maximum value, around which time an eddy separates from the Loop (Fig. 3). The upwelling lags the sign change of deep eastward flow across 90°W (Tr90W > 0) and is almost entirely fed by it because the deep flow in the Yucatan Channel is very weak. This result shows that eddy shedding is related more to the westward movement of the Loop’s water mass (because westward Rossby wave speed exceeds the rate of mass influx from the Yucatan), proposed by N05, rather than to local instability (see also Hurlburt and Thompson 1980). The deep eastward flow Tr90W > 0 is therefore caused by pressure produced by westward-propagating eddy following Rossby wave dynamics. From the SSH plots in Fig. 3 (bottom),3 the steepest fall in eastern SSH occurs when the eddy separates from the Loop Current (from stage B to C; see below). This agrees with long Rossby wave dynamics, which, assuming geostrophy and reduced gravity for the upper layer, is
where h is the upper-layer depth. Thus, ∂h/∂t in the eastern Gulf is largest (and negative) for a matured Loop/eddy when the Rossby radius R is largest, and ∂h/∂x < 0 for an eddy exiting westward from the eastern Gulf. Westward detachment of the Loop’s water mass forces a deep returned (i.e., eastward) flow across 90°W (Tr90W > 0), leaves a “vacuum” in the area once occupied by the Loop, and “sucks” deep water upward (TrZ1k > 0). Upwelling stretches fluid column and results in deep cyclone that is often seen when an eddy separates from the Loop Current (Oey 1996, 2008; Schmitz 2005). The ensemble Loop Current takes on the shape of an elongated peanut (with shell; Fig. 4b). The narrowest region (or neck) of the peanut is where the most intense upwelling and cyclone reside. The fact that Tr90W precedes TrZ1k and that the two transports nearly balance each other prior to eddy shedding (i.e., when the matured Loop spreads westward) suggests that the cyclone is a byproduct of the shedding process rather than its cause.
The timing of eddy separation can depend on mass and momentum balances between the western and eastern Gulf of Mexico (i.e., fluxes across 90°W; Chang and Oey 2010a) and hence also on the deep transport Tr90W. The above result that the deep flow in the Yucatan Channel is weak during stage B then suggests that externally imposed small perturbations in the deep portion of the channel may sufficiently alter the balances across 90°W to delay or hasten eddy shedding. This is an interesting topic of potential importance, perhaps to be pursued in a future study.4
c. Stage C
This corresponds to the period immediately after an eddy has separated from the Loop Current and lasts approximately 1 month (Fig. 3). The ensemble Loop Current (Fig. 4c) shows a separated eddy that is crossing 90°W. As the eddy moves westward, the compensating deep eastward flow Tr90W > 0 continues to increase, whereas upwelling (TrZ1k > 0) weakens and Yucatan outflow increases (TrYuc < 0). The Yucatan outflow continues to increase and becomes a maximum (large negative TrYuc) in stage A2. The observational evidence of such a large outflow a few months after an eddy is shed may be seen in Bunge et al. (2002, their Fig. 3a near the beginning of the transport time series). Because in stage C the forcing for the outflow is due to Tr90W, Maul et al.’s (1985) hypothesis is not valid.
d. A summary of stages A, B, and C
Figure 5 shows a summary of the three stages discussed above. For simplicity, stage A1 only is given (Fig. 5a), whereas stage A2 is understood to be a continuation of stage C (Fig. 5c) with weak downwelling instead of upwelling. Figure 5a (stage A1) is when the Loop Current is reforming. There is downward transport under the Loop and flow divergence in the deep portion of the eastern Gulf, with outflow in the Yucatan Channel and westward flow to the deep basin of the western Gulf. Figure 5b (stage B) is when the Loop Current begins to shed an eddy. There is strong upward transport at the base of the Loop Current, induced by the rapid westward movement of the nascent ring separating from the Loop Current. The flow is therefore convergent in the deep basin of the eastern Gulf. The upwelling is primarily fed by the eastward deep flow across 90°W, whereas deep flow in the Yucatan Channel is weak. Figure 5c (stages C and A2) is when the eddy has separated and now propagates westward. The compensating eastward flow across 90°W is strong, and it is primarily balanced by the outflow at the Yucatan Channel.
It is clear that the Maul et al.’s (1985) hypothesis applies (approximately) only during stage A1. So far, we have only used TrZ1k to infer Loop’s expansion. In the appendix, we further examine the relations of the three transport time series (Fig. 3) with the Loop’s area. We find that, as can be expected from the above discussions, the correlation between the rate of Loop’s expansion with Yucatan outflow is not high, because the interaction with the western Gulf cannot be neglected.
The net transport is southward in the deep portion of the Yucatan Channel (TrYuc < 0). This is a consequence of the constraint imposed by the semienclosed Gulf. Mass transport into the Gulf by the Loop Current (TrZ1k < 0) and westward-propagating eddies (Tr90W > 0) must be returned out of the Gulf, and a portion of it exits the Gulf as deep outflow through the Yucatan Channel.
4. The Gulf of Mexico oscillator
What is the Gulf-wide deep circulation? Although numerous observational and modeling studies have been devoted to describing the upper-layer dynamics, the deep circulation is still poorly understood. Oey (2008) studied transient (deep) eddy motions (including topographic Rossby waves) but did not consider the Gulf-wide circulation. Oey and Lee (2002) showed that (see in particular their Fig. B1) the deep mean circulation is cyclonic. Lee and Mellor (2003) also obtained a deep cyclonic gyre in their Gulf of Mexico simulation. Based on historical data, DeHaan and Sturges (2005) gave observational evidence of the cyclonic deep gyre. Weatherly et al. (2005) presented SOFAR floats that indicated a cyclonic gyre at z ≈ −900 m. Several driving mechanisms have been proposed, some of which are local and quite detailed (see summary in Oey et al. 2005). Here, we offer a simple one related to the Loop Current cycle.
We apply the same three-stage ensemble averaging but for the depth-averaged deep circulation below z = −1000 m (Figs. 4d–f; it is not necessary to distinguish between stages A1 and A2, which are therefore lumped into stage A). Stage A occurs 63% of the time (1803 days), stage B occurs 20% of the time (567 days), and stage C occurs 17% of the time (510 days). The anomaly is shown, but, because stage A is dominant, the 8-yr mean (not shown) is similar to Fig. 4d, with the corresponding cyclone being stronger and the anticyclone being weaker. Stage A has a cyclonic gyre in the western Gulf. In the eastern Gulf, a tripolar-circulation structure exists, with an anticyclone near (26°N, 87°W) sandwiched between two weaker cyclones north and south. The anticyclone also has a zonal “tail” that produces zonal eastward flow along 26°N; this eastward flow is sandwiched between two westward zonal currents south and north. In stage B, there is a cyclone in the eastern Gulf and an anticyclone in the western Gulf. Stage C is a transition stage when the western anticyclone strengthens, and in the eastern Gulf the cyclone weakens and an anticyclone appears. It is straightforward to see that these variations of the strengths of eastern and western circulations depend on stretching and compression imposed at the deep layer’s upper boundary at z = −1000 m: that is, on TrZ1kW and TrZ1kE (=TrZ1k), where the subscripts W and E denote region of the Gulf west and east of 90°W, respectively. Because TrZ1kW = −Tr90W [i.e., westward deep transport across 90°W is balanced by upwelling (across z = −1000 m) in the western Gulf and vice versa], we see from Fig. 3 (bottom) that, except during the short-period stage A2, TrZ1kW and TrZ1kE are anticorrelated; that is, upwelling or stretching of deep layer in one (sub)basin corresponds to downwelling or compression in the other. By conservation of potential vorticity, then, as the Loop Current is reforming in stage A (TrZ1kE < 0 and TrZ1kW > 0), the lower-layer vorticity in the eastern Gulf becomes more anticyclonic while the cyclone in the western Gulf strengthens (Fig. 4d). During incipient-shedding stage B, the deep layer of the eastern Gulf gains cyclonic vorticity because of the strong upwelling there, and the western Gulf’s cyclone weakens as downwelling there compresses vortex lines (i.e., anticyclonic anomaly; Fig. 4e). Stage C is a transition period when upwelling in the eastern Gulf wanes but downwelling in the western Gulf intensifies (Fig. 4f) as Tr90W continues to rise (Fig. 3). The process then repeats with a new Loop Current cycle. This coupled upper–lower layer response may be referred to as the Gulf of Mexico oscillator (see further discussions below). The amplitude of the deep vorticity (ζ) oscillation may be estimated using ∂(ζ/f )/∂t ≈ ∂w/∂z, which gives |ζ|/f ≈ 0.005 (using the values of w ≈ ±0.4 m day−1 and a time scale ≈30 days; Fig. 3), corresponding to a horizontal shear of about 0.05 m s−1 over 200 km (Figs. 4d–f).
5. Why is the deep mean circulation cyclonic?
It was mentioned previously that the 8-yr mean deep circulation in the western Gulf is cyclonic, similar to that shown in Fig. 4d. More detailed analyses indicate that the mean downwelling under the Loop penetrates below z ≈ −2000 m, and the western cyclonic gyre is also strongest below that level (not shown). Deeper than this depth, the abyssal basin of the Gulf of Mexico is closed and fluid motion shows little vertical variations (Oey 2008). We therefore model the abyssal Gulf as a homogeneous fluid layer with vertical mass flux across its top. A reduced-gravity model is used. Yang and Price (2000) show that for a basin with inflows or outflows across its lateral boundary and in steady state,
where (n, l) is the unit vector at the boundary of the basin with outward normal n and tangential unit vector l, s is the coordinate along the boundary (positive anticlockwise), r is the bottom friction coefficient, H is the depth of lower layer at rest (i.e., bottom topography), h is the depth anomaly, uh is the horizontal depth-averaged velocity, ζ = ∇ × uh is the corresponding relative vorticity, Uh = uh(H + η) is the depth-integrated transport, and r is the linear friction coefficient. For a closed basin, the LHS vanishes, so that the circulation ∮(uh · l)ds = 0 . Therefore, because the mean vertical flux in the eastern Gulf of Mexico is downward (the red curve in Fig. 3), the resulting anticyclonic circulation must be compensated by cyclonic circulation somewhere else in the basin. We use a numerical model to show that the cyclonic circulation is in the deep portion of the western Gulf of Mexico.
The reduced-gravity model is also based on POM. The domain is the Gulf of Mexico deeper than 1000 m and is closed at the Straits of Florida and the Yucatan Channel. (The choice of z < −1000 m to define the deep layer is for computational convenience only; it has no impact on the result because the Yucatan Channel is closed in the model.) Table 1 gives various model parameters and their meanings. Weak dissipation is included as AH for numerical stability. A mass influx of 0.25 Sv is specified (i.e., downward into the deep layer) over an area 250 km × 250 km under the Loop Current, and the model is integrated until steady state. The depth anomaly h and depth-averaged velocity uh are plotted in Fig. 6, which clearly shows a cyclonic gyre in the deep western Gulf. Apart from the weaker strength, the resulting circulation is in good agreement with Fig. 4d (the dominant stage A), including the weak eastward zonal flow just north of the 3000-m isobaths in the northern Gulf.
The mean cyclonic circulation in the deep western Gulf (say west of 90°W) requires an inflow (i.e., westward) across 90°W [Uh · n < 0 in Eq. (1)] below the sill depth of the Yucatan Channel, consistent with downwelling across z ≈ −2000 m in the eastern Gulf, mentioned above, and a corresponding upwelling in the western Gulf. The net transport integrated from z = −1000 m to bottom across 90°W, 〈Tr90W〉 (〈·〉 indicates the mean), must still be eastward however (Fig. 3), because it must balance the mean westward mass transport by LC eddies. The vertical flux across z = −1000 m in the western Gulf is therefore downward. There is then vertical convergence for −1000 m > z > −2000 m in the western Gulf, and the mean transport at 90°W has a three-layer structure as shown in Fig. 7. We caution however that, although useful for understanding the overall circulation, the three-layer structure hides a complex latitudinal flow structure (not shown).
6. Conclusions and discussion
Conclusions are summarized and discussed below:
The expansion, eddy shedding, and retraction of Loop Current and its coupling with the deep flows is classified into various stages depending on the vertical mass flux across the base of the Loop (z ≈ −1000 m) in the eastern Gulf:
(i) Stage A1 is the “Loop reforming” stage prior to eddy shedding; it has downward flux and deep divergence;
(ii) Stage B is the “incipient shedding” stage; it has deep convergence from the west (i.e., the central Gulf) that leads upward flux under the Loop, whereas the Yucatan Channel’s deep flow is weak;
(iii) Stage C is the “eddy migration” stage; it too has an upward flux, though a decreasing one, and deep flow from the west supplies the deep Yucatan outflow; and
(iv) Stage A2 is the beginning of the Loop-reforming stage after eddy-shedding; it has a downward flux but the deep influx (of stage C) from the central Gulf remains substantial, and together they contribute to strong deep outflow in the Yucatan Channel.
Stage B results support PN97 and N05 that eddy shedding is primarily by westward detachment of the matured Loop by Rossby wave dynamics. The dynamical response of a weak Yucatan deep flow during this stage suggests that eddy shedding may be sensitive to external deep perturbations (e.g., from the Caribbean), an interesting future research topic.
There exists significant deep coupling between the western and eastern basins of the Gulf, and this leads to a poor correlation between the Loop Current expansion (area) and deep outflow in the Yucatan Channel. The vertical flux TrZ1k is correlated with Yucatan deep flow TrYuc (CC = +0.72 at 30-day lag; TrZ1k lags TrYuc; Fig. 2c) and is negatively correlated (CC = −0.5) with the Loop’s area expansion rate d(ALoop)/dt (see appendix). The less-than-perfect correlations in both cases are caused by deep exchanges Tr90W between the western and eastern Gulf. We find therefore that d(ALoop)/dt and TrYuc are only weakly correlated with CC = −0.36, which is also the level of correlation found by Ezer et al. (2003) from a realistic numerical simulation and also by Bunge et al. (2002) from observations. In commenting on the latter’s work, Rivas et al. (2005) noted that “… there is little relation between the variation of the surface area extension of the Loop Current and the evolution of the near-bottom eddy flow in the Yucatan Channel … ,” except perhaps during a Loop growth period in October–November 1999) after an eddy (Eddy Juggernaut) was shed. During this period, a strong outflow lasting 40–50 days and with peak transport of −2 Sv in the Yucatan Channel occurred. This period corresponds to and agrees well with stages C and A2 (Fig. 3).
The net downward flux under the Loop is because the Loop Current spends a relatively longer time “reforming” (stage A: 63% time). Together with the compensating deep flow from the western Gulf, the net deep transport at Yucatan is southward. This is a consequence of the constraint imposed by the semienclosed Gulf. Mass transport into the Gulf by the Loop Current (TrZ1k < 0) and westward-propagating eddies (Tr90W > 0) are returned out of the Gulf, and a portion of it exits the Gulf as deep outflow through the Yucatan Channel.
The Yucatan’s deep outflow of about −1 Sv compares reasonably well with Sheinbaum et al.’s (2002) observation of −0.7 to −0.8 Sv below the 5.7°C isotherm (z ≈ −900 m; see also Rivas et al. 2005) over a 10-month period from September 1999 to June 2000. As noted above, the stronger deep outflow shortly after an eddy is shed has also been observed (Sheinbaum et al. 2002; Bunge et al. 2002).
The cyclonic gyre that appears west of approximately 90°W is because the mean vertical mass flux at the base of the Loop Current due to the Loop Current cycle is downward, which locally inputs a negative vorticity. Because the deep Gulf is closed for z < −2000 m, the net circulation around the abyssal basin is zero, and a deep cyclonic gyre must exist in the western Gulf. The gyre’s strength varies with the Loop Current cycle, being strongest when the Loop Current is reforming and weakest after an eddy is shed. The deep vertical mass fluxes in the western and eastern Gulf are nearly out of phase. These results suggest that, during a period when the Loop Current is growing, the deep cyclonic gyre in the western Gulf ought to be strengthened.
The coupled surface and deep motions in the Gulf of Mexico resulting from the separation of warm rings from the Loop Current may be idealized as a west–east oscillator (about a mean). The SSH curves in Fig. 3 (bottom) show the connection between flow and pressure. As the Loop Current expands, pressure builds up and the isopycnal tilts eastward (deeper east than west; eastern SSH rises). As a ring separates and propagates westward, strong transport from east to west ensues in the upper layer and the isopycnal tilts westward (deeper west than east; eastern SSH falls). Downwelling in the west pushes lower-layer fluid into the eastern Gulf’s deep basin, where it upwells as well as leaks into the Caribbean Sea through the Yucatan Channel. Then, in the western Gulf, the ring decays and produces upwelling, whereas, in the eastern Gulf, the Loop reforms and produces downwelling. The isopycnal tilts eastward, and the cycle repeats. Thus, rising SSH in the east corresponds to downwelling there and also to falling SSH in the west and upwelling there and vice versa for falling SSH in the east (Fig. 3).
The west–east oscillation is the dominant mode of variability in our idealized model. The standard deviation (of the oscillation) of the gyre-scale currents is O(0.05) m s−1 (Figs. 4d–f). The Loop Current cycle can therefore produce deep currents that vary slowly at the eddy-shedding time scales. Also, because the oscillation depends on the west–east pressure difference, the behaviors of the Loop Current, including how often it sheds eddies, may depend on the existing conditions of the Gulf itself (e.g., how many rings it already has). For the same reason, model parameterizations of dissipation and diffusion, which in part determine how eddies decay, can affect the shedding rate. These are interesting and important topics for future research.
The above idealization is useful for understanding the overall response of the Loop Current cycle, but there are also important details [e.g., the Loop Current cycle is also associated with transport fluctuations at the Straits of Florida; see Oey and Chang (2011)]. A three-layer mean transport structure at 90°W exists because of the strong potential vorticity constraints placed on the abyssal circulation (because the deep Gulf is closed), and also westward mass transport by eddies must be returned to the eastern Gulf.
We thank the two anonymous reviewers for their comments. This research is supported by the Minerals Management Service Contracts M08PC20007, M07PC13311, and M08PC20043 (SAIC 4400159982) and also by the GOMEX Project. We thank Drs. Alexis Lugo-Fernandez and Walter Johnson for their encouragements. YLC received a fellowship from the Graduate Student Study Abroad Program (NSC97-2917-I-003-103) of the National Science Council of Taiwan. Computation was done at NOAA/GFDL, Princeton.
Loop Area and Deep Transports
The Loop Current’s expansion and retraction are more readily observed (e.g., from satellite) than the vertical mass flux beneath the Loop Current, TrZ1k, so here we wish to see how closely they are related. We use the Loop’s area (ALoop) defined by SSH > 0.1 m as a proxy of its expansion and retraction (Fig. 1). Virtually the same results are obtained using time series of the Loop’s edge measured along the line that connects the southeastern to northwestern corners of the dashed box in Fig. 1.
Figure A1 shows ALoop plotted together with TrZ1k, TrYuc, and Tr90W. The ALoop is anticorrelated with and lags TrZ1k by 60 days (=π/2 for a shedding period of 240 days); the maximum lagged CC is −0.5. Thus, d(ALoop)/dt and TrZ1k are anticorrelated. As the Loop expands (retracts), it forces a downward (upward) flux across its base. On the other hand, Fig. 2 already shows that TrZ1k lags the Yucatan deep flow TrYuc by 30 days (CC = 0.72) so that TrYuc must lead ALoop by 90 days and is anticorrelated with it, with CC = −0.5 × 0.72 = −0.36, as shown in the middle panel of Fig. A1. The less-than-perfect correlations in all of the above cases, particularly in the CC between TrYuc and ALoop, are caused by deep exchanges Tr90W between the western and eastern Gulf. Indeed, there is a much more robust correlation between ALoop and Tr90W, with the latter lagging the former by 70 days and the corresponding CC = 0.55 (Fig. A1, bottom). Physically, although the expansion of the Loop Current causes the Yucatan outflow to strengthen, it is not the only cause. The maximum outflow is actually controlled more by eddy shedding and propagation (across 90°W) when Tr90W increases.
Corresponding author address: L.-Y. Oey, Princeton University, 300 Forrestal Rd., Sayre Hall, Princeton, NJ 08540. Email: firstname.lastname@example.org
All quoted correlation coefficients in the paper are significant at the 95% significance level.
Hurlburt and Thompson (1980) found in their two-layer model experiment that eddy shedding ceases if Yucatan deep inflow is increased, and they explained their finding in terms of topographic torque. Their results are also consistent with the reasoning of PN97, N05, and Chang and Oey (2010a) based on mass and momentum balances. The two are not contradictory, and their relative importance in more realistic simulations and/or observations should be investigated in the future.