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Loop Current Eddy Interaction with the Western Boundary in the Gulf of Mexico S. A. FROLOV Accurate Environmental Forecasting, Inc., Narragansett, Rhode Island
G. G. SUTYRIN Graduate School of Oceanography, University of Rhode Island, Narragansett, Rhode Island
G. D. ROWE Accurate Environmental Forecasting, Inc., Narragansett, Rhode Island
L. M. ROTHSTEIN Graduate School of Oceanography, University of Rhode Island, Narragansett, and Accurate Environmental Forecasting, Inc., Narragansett, Rhode Island (Manuscript received 22 August 2003, in final form 25 March 2004) ABSTRACT A two-layer, intermediate equations model that, uniquely, allows for the intersection of the bathymetry with the layer interface is used to study the interaction of isolated Loop Current Eddy (LCE)-type anticyclones with western-boundary topography. Two idealized topography configurations representative of the Gulf of Mexico (GoM) coastal topography at 258 and 238N are studied; the 258N topography configuration is characterized by a relatively wide shelf and a narrow continental slope, and the 238N configuration is characterized by a relatively narrow shelf and a wide continental slope. The physical mechanism that has the most significant effect on the evolution of the LCE in both topographic configurations is the interaction of the LCE with cyclones formed directly to its north through the process of off-shelf advection of potential vorticity in the upper layer. The LCE interaction with those cyclones that are generated through this mechanism results in the LCE becoming elliptic and rotating clockwise with its center following a cyclic trajectory. The amplitude of the cyclic motion produced by LCE interactions with cyclones is controlled by a different physical mechanism. The mechanism consists of the LCE interacting with deep eddies that can be generated beneath the LCE over regions of flat topography adjacent to the continental slope. The deep eddies are generated by stretching and compression of the lower layer by a rotating elliptic LCE. The net effect of these eddies is to amplify significantly the cyclic motion of the LCE. The width of the continental slope is the critical parameter controlling the strength of the LCE interaction with deep eddies and, therefore, the amplitude of the cyclic motion. The characteristic pattern of LCE evolution seen in the numerical experiments can be identified in some observed cases of LCE interaction with the western boundary in the GoM.
1. Introduction Large, baroclinic, anticyclonic eddies [the so-called Loop Current Eddies (LCEs)] formed in the eastern Gulf of Mexico (GoM) typically propagate southwestward from their formation region until reaching the western boundary where their continued evolution and motion are strongly influenced by interactions with the continental slope and shelf. Observations of LCE interactions with the western slope and shelf do not easily lend them-
Corresponding author address: Dr. S. A. Frolov, Accurate Environmental Forecasting, 165 Dean Knauss Road, Narragansett, RI 02882. E-mail:
[email protected]
q 2004 American Meteorological Society
selves to a canonical description of either the interaction process or its results. LCEs may remain near the slope or move offshore, they may move north or south, and there may be significant modification of the shelf water mass. The only consistently observed characteristic of LCE interactions with the slope and shelf are weakening of the LCE and formation of other (smaller) eddy-like features (Vukovich and Crissman 1986; Kirwan et al. 1988; Lewis et al. 1989; Vukovich and Waddel 1991; Vidal et al. 1992; Hamilton et al. 1999). This variability of LCE interactions with the slope and shelf indicates that there should be a number of variables that govern these interactions, and a number of authors have contributed theoretical insight likely to be relevant in explaining the myriad observed behav-
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iors. Some of the earliest studies of eddy–topography interaction were those of Smith and O’Brien (1983) and Smith (1986). In a series of numerical experiments using a primitive equations two-layer model, they showed that b- (both planetary and topographic) induced dispersion leads to an asymmetric eddy structure that then gives the eddy a nonlinear self-advective tendency, and that eddies with a weak lower-layer expression evolve quickly to upper-layer features in the presence of topography due to dispersion of the lower-layer feature by topographic Rossby waves (TRWs). These eddies then propagate independently of topography. Grimshaw et al. (1994) also showed that eddies in contact with the bottom rapidly disperse under the influence of TRWs when they encounter strongly sloped topography. More realistic models by Sturges et al. (1993) and Welsh and Inoue (2000) that used 12- and 15-layer models, respectively, demonstrated that the deep circulation in the vicinity of an LCE is dominated by vortex-like motions that are highly vertically coherent below 1300 m in the deep regions of the GoM. These authors also found that each LCE is associated with a deep cyclone– anticyclone pair, and that the deep cyclone strengthens relative to the anticyclone as the LCE migrates westward in the surface layer until the deep circulation dissipates near the western boundary. The vertical coherence of the deep motions present in these simulations suggest that in its simplest form, the GoM is dynamically well represented as a two-layer system. In contrast to the above studies that are focused on eddy interactions with sloping topography away from boundaries, the dynamics of eddy interactions with boundaries have been studied in both the context of a reduced-gravity model (see, e.g., Nof 1999, and the references therein) and in a two-layer intermediate equations model (Sutyrin et al. 2003). In the reduced-gravity studies the western boundary was represented as a vertical wall while the two-layer study considered a more realistic western boundary. Numerical experiments from Sutyrin et al. (2003) included an idealized representation of the continental slope and shelf characteristic of the real topography in the western GoM. However, the continental shelf was unrealistically deep allowing LCEs to penetrate all the way onto the shelf and reach the shoreline. These studies identified a common physical mechanism involved in the LCE interaction with the western boundary: the so-called image effect, which results in a northward migration of anticyclonic rings. In addition to this mechanism, the study of Shi and Nof (1993) indicated that in some cases anticyclonic rings can propagate northward during interactions with the western boundary due to the ejection of mass southward from the eddy. The presence of an unrealistically deep shelf in the numerical experiments of Sutyrin et al. (2003) led to additional southward motion of the LCE induced by the circulation beneath the LCE as it moves onto the shelf. In the present study we continue to investigate LCE
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interactions with the western boundary in the GoM in the two-layer intermediate equations context. Similar to the experiments of Sutyrin et al. (2003) the anticyclone is initialized in the upper layer over the abyssal plane away from the topography; the lower layer is initially at rest. The eddy then naturally develops a lower-layer flow and propagates westward driven by the b effect where it encounters the meridionally uniform slope and shelf. The important new feature of our investigation is the incorporation of a realistic continental shelf that is allowed to penetrate all the way into the upper layer. Two types of shelf configuration are studied. In the first configuration, which corresponds to the GoM coastal topography profile at 258N, the shelf is relatively wide while the continental slope is relatively narrow. In the second configuration, which corresponds to the GoM topographic profile at 238N, the shelf is relatively narrow while the continental slope is relatively wide. By contrasting the LCE evolution in experiments with different topography configuration, we identify physical mechanisms controlling the LCE interaction with the western boundary and make some conclusions about their relative importance. The rest of the paper is organized as follows. In section 2 we discuss the set of intermediate equations solved by the numerical model and describe briefly some of the numerical techniques implemented in the model. The results of numerical experiments and their interpretation are described in section 3. Some observational evidence supporting the numerical results is presented in section 4. Last, section 5 provides a summary and conclusions. 2. Model formulation a. Two-layer equations We consider a stratified, rotating, hydrostatic, Boussinesq fluid with a rigid lid on the b plane. In particular for a two-layer inviscid flow, the momentum and continuity equations are
1
] t v i 1 ( f 1 z i )k 3 v i 5 2= p i 1 ] t h i 1 = · (h i v i ) 5 0,
v i2 2
2
and
(1) (2)
where the subscript i 5 1 (2) denotes the upper (lower) layer, v 5 (u, y) is the horizontal velocity vector (u is the zonal velocity in the x direction; y is the meridional velocity in the y direction), z 5 k · = 3 v is the relative vorticity, f 5 f 0 1 by is the Coriolis parameter, = is the horizontal gradient operator, and k is the vertical unit vector. The layer depths are h1 5 D1 (x, y) 2 h
and h 2 5 D 2 (x, y) 1 h, (3)
where D1 is the depth of the upper layer in a horizontally uniform ocean, D 2 (x, y) 5 D(x, y) 2 D1 is the depth of the lower layer including topography, and h is the
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interface displacement; in the regions where D 2 , 0, that is, bottom depth is less than the upper-layer thickness, h 2 5 0 and h1 5 D(x, y). The reduced pressure (p i , the pressure divided by density) and the interface displacement (h i ) are related by the hydrostatic equation: g9=h 5 =(p 2 2 p1 ),
qi [
f 1 zi . hi
yg 5
(5) (6)
v5
(7)
(8)
and that the ratio of interface slope to bottom slope, f 0V ø 0.3. g9|=D|
2
1
Given a typical reduced gravity in the GoM of g9 ø 0.02 m s 22 , a typical upper-layer depth D1 ø 300 m, a typical topographic slope | =D | ø 0.01, and assuming the eddies are in geostrophic balance at leading order, we find that the ratio of the interface displacement to the upper-layer depth, f 0 VL ø 1, g9D1
1
1 1 k 3 =b 2 =] t p , f 1 zg f0
(21) i PTi ] ( p 2 p2 ) 1 = · =] t p i g9 t 1 f0
Since LCEs represent a typical circulation pattern in the GoM, the scaling analysis presented below is based upon the flow parameters associated with a typical LCE. A typical LCE has maximum velocity V ø 1 m s 21 , at radius L ø 100 3 10 3 m. Choosing f 0 ø 6 3 10 25 s 21 , we find that the Rossby number R 0 , which characterizes eddy strength relative to the planetary vorticity, is V ø 0.16. f 0L
(10)
(9)
These nondimensional parameters indicate that the flow is essentially in geostrophic balance, and that depth variations in both layers cannot be assumed small. This combination suggests an ‘‘intermediate’’ simplification of the primitive equations, that is, between quasigeostrophic and primitive equations dynamics. For this study we choose a specific way of derivation of the intermediate equations described by Sutyrin (1994). This form of the intermediate approximation is also called the general vorticity approximation according to the classification of Allen et al. (1990) who has shown it to be one of the most accurate among its class. Since this approximation is not widely used by the numerical modeling community a quick derivation for the example of a two-layer system is presented below.
(11)
where z g 5 (1/ f 0 )¹ 2 p is the geostrophic vorticity and b 5 p 1 (1/2)y g2 is the geostrophic Bernoulli function. Inserting the expression (11) into the continuity equation (2) yields a predictive system of equations for p that involves only the pressure field,
b. Scaling and the intermediate equations
R0 [
1 k 3 =p , f0
and the next-order flow is expressed as
(4)
where g9 [ g(r 2 2 r1 )/r1 is the reduced gravity. The potential vorticity q i of fluid parcels is conserved in each layer; that is, (] t 1 v i=)q i 5 0;
To leading order in the Rossby number, the flow is geostrophic,
2
5 J(b i , PTi ) 1 M i 1 Q i ,
(12)
where PT 5 h/( f 1 z g ) is the potential thickness (inverse potential vorticity), M is diapycnal momentum flux (due to bottom friction), and Q is horizontal diffusion: Qi 5 ]x
[
1
] [
2 1]
A h = =] p f 1 zg f0 x
y
1
2
]
A h = =] p . f 1 zg f0 y
This expression suggests a simplified form for the effect of momentum diffusion Qi 5
Ai 2 ¹ (PTi¹ 2 p i ) f0
that is used in the current version of the model. The diapycnal mass flux is modeled by the Ekman boundary layer with the characteristic thickness h E either in the lower layer: M 2 5 2h E¹ 2 p 2 , or in the upper layer: M1 5 2h E¹ 2 p1 , over the shelf where h 2 5 0. These intermediate equations are uniformly valid for arbitrary layer depth perturbations, including diabatic processes, and permit the interface to intersect the bathymetry. However, an important restriction on the form of the bathymetry applies: the intersection of the bathymetry and the layer interface has to be confined horizontally to a single grid point during the entire integration. This restriction is satisfied in situations where the bottom slope at the mean layer interface depth is so steep that the depth change over a single horizontal grid is large than maximum vertical motions of the interface. In this case the intersection point of the layer interface with topography still moves freely up and down, however, because of the steepness of the topographic slope it remains within one horizontal grid. Given model horizontal resolution of 10 km and maximum variation of layer interface of about 400 m, this restriction requires the bottom slope to be steeper than 0.04 around 300 m (mean interface depth), which is well below realistic values for a typical topographic slope in the shelfbreak region.
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FIG. 1. The zonal sections of bathymetry and initial interface displacement for the two IE1 model experiments. The wide shelf bathymetry is from 258N, and the narrow shelf bathymetry is from 238N. The initial interface displacement is shown with the dotted line.
c. Numerical model The core of the intermediate equations (IE) model consists of a custom-designed over-relaxation iterative elliptic solver capable of solving Eqs. (11) and (12). The solver is capable of restricting the area where the solution is calculated to the grid points with finite layer thickness. This feature allows the solver to handle situations in which the lower layer thickness vanishes because of the topography penetrating through the layer interface. Other notable features of the model include a conservative Arakawa spatial approximation for the Jacobian on the right-hand side of Eq. (12), and a second-order Adams–Bashforth approximation for each time step. The model is implemented on a uniform rectangular grid. 3. Numerical experiments a. Experiment design The model was configured for a rectangular 540 km 3 1000 km basin with a uniform 10-km horizontal resolution. No-flux boundary conditions were assigned on the western, eastern, and northern boundaries; open boundary conditions were assigned on the southern boundary to allow TRWs to propagate out of the domain. The bottom topography in the eastern part of the domain is flat (3500 m) representing the bathymetry of the central GoM. A meridionally uniform slope is introduced along the western boundary representing the western shelf. Two types of shelf configuration were used in simulations. In the first configuration, which corresponds
to the GoM coastal topography profile at 258N, the shelf is relatively wide while the continental slope is relatively narrow. In the second configuration, which corresponds to the GoM topography profile at 238N, the shelf is relatively narrow while the continental slope is relatively wide. The prescribed basin margin bathymetry included vertical walls on the northern and eastern boundaries. The exact bottom topography profiles were prescribed as specific cross sections from the ETOPO5 bathymetric database and are shown in Fig. 1. Even though both characteristics of the topography profile are important—that is, the shelf width and the slope width— for simplicity we will further refer to these two configurations as ‘‘wide shelf’’ and ‘‘narrow shelf,’’ respectively. The vortex was initialized away from the topography with a circular potential vorticity perturbation in the upper layer, q1 5
f , D1 1 Z(r)
Z 5 Zc r5
(13)
1 1 tanh(1 2 r 2 ) , 2
and
Ï(x 2 x 0 ) 2 1 (y 2 y0 ) 2 Lc
,
(14) (15)
where Z c 5 900 m and L c 5 80 km. This potential vorticity perturbation corresponds the upper-layer eddy about 400 km in diameter with maximum velocity of 1 m s 21 and maximum interface slope of 0.003 at 100km radius. The resulting eddy structure as shown in Fig. 2. The lower layer was initially at rest.
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FIG. 2. Initial meridional section of zonal velocity and interface displacement across the eddy center.
Friction parameters were chosen to provide the LCE decay rate consistent with observations. Horizontal friction coefficients were prescribed as follows: A1 5 10 m 2 s 22 and A 2 5 1 m 2 s 22 . Vertical friction characterized by the Ekman layer depth was prescribed as h E 5 15 m. b. Experiment results and discussion Both the narrow (238N) and wide (258N) shelf experiments exhibit similar patterns of LCE evolution and associated eddy features during interactions with the bathymetry. In this section we describe the results of these two numerical simulations, discuss the physical processes involved, and analyze important differences. An additional numerical experiment was designed to analyze the relative importance of physical mechanisms identified in the first two experiments. The results of this experiment and the relevant discussion are presented in section 3b(3). 1) ‘‘WIDE
SHELF’’ EXPERIMENT
Figure 3 shows the simulated interface displacement at 5, 35, 60, and 150 days of integration for the wide shelf experiment. Similar to the simulations of Sutyrin et al. the eddy propagates westward driven by the b effect until its western edge reaches the shelf break on day 5 of integration. After 30 days of the anticyclone interacting with the shelf a cyclone forms next to it at its northern edge, which causes the anticyclone to become elliptic. The cyclone–anticyclone pair starts rotating anticyclonically causing the anticyclone to follow
a cyclic trajectory. By day 80 the cyclone–anticyclone pair completes the first rotation at which point the anticyclone moves back to the shelf about 100 km south of its initial position and the cyclone comes to the shelf just south of the anticyclone. As soon as the anticyclone moves back to the shelf a new cyclone starts to form north of it. Meanwhile, the first cyclone remains pushed against the shelf by the circulation of the anticyclone south of it and gradually dissipates. When the newly formed cyclone becomes sufficiently strong it pushes the anticyclone away from the shelf and the cycle repeats. The anticyclone gradually dissipates and the amplitude of the cyclic motion decreases. The integration is stopped after 150 days at which point the anticyclone intensity drops to approximately 30% of its initial magnitude as measured by the magnitude of the pressure anomaly in the upper layer. The evolution of the LCE-type anticyclone described above is considerably different from that simulated in previous studies with more idealized representations of the western boundary. In particular, there is no significant northward propagation of the LCE, which was seen in both the reduced-gravity experiments (e.g., Nof 1999) and in the two-layer IE experiments of Sutyrin et al. (2003) and was attributed, in both cases, to the image effect. The presence of a realistic shelf in our experiments does not allow the LCE to come close enough to the western boundary to permit a significant interaction with its ‘‘image.’’ As one can see in Fig. 3, the center of the LCE remains more than 200 km away from the western boundary, which is more than the radius of the anticyclone. Experiments of Sutyrin et al. demonstrated
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FIG. 3. Upper-layer interface displacement at 5, 35, 60, and 150 days of integration for the wide shelf experiment. Positive displacement is shown with thick solid contours; negative displacement is shown with dashed contours. The gray line indicates the LCE track. Bathymetry is contoured with thin lines.
that the center of an LCE has to approach the western wall within a distance less than its radius for the image effect to come into play. Another notable feature of our simulation is the generation of cyclones to the north of the LCE. The process of cyclone generation is related to off-shelf advection of potential vorticity (PV) in the upper layer by the circulation of the anticyclone. This process is illustrated in Fig. 4 showing day 35 of the wide shelf simulation with the PV in the upper layer indicated by shading. One can see that the cyclone forming north of the LCE is associated with a positive PV anomaly, which is pro-
duced by the stream of high PV carried along the periphery of the LCE from the shelf. Similar mechanism of off-slope PV advection was first suggested by Rhines (1998) and it was recently analyzed by Williams and Roussenov (2003) in a high-resolution general circulation isopycnal PE model. In their numerical experiments a baroclinic current separating from a sloping bottom carried high-PV water from the slope into the ocean interior, significantly affecting the character of the general circulation. Even though there were no isolated cyclones produced in our experiments, it is quite feasible that surrounding mesoscale features that are
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FIG. 4. Illustration of the cyclone formation by the off-shelf PV advection mechanism. Shading indicates the PV field in the upper layer, and arrows show geostrophic velocities. The interface elevation is shown with black contours, solid contours indicating negative values (anticyclones) and dashed contours indicating positive values (cyclones).
normally present during an LCE interacting with the western boundary can cause the separation of cyclones formed in this fashion from the LCE. Thus, the mechanism of off-shelf PV advection produced by LCEs interacting with the shelf can be an important source of small-scale cyclones found in the northern and the western GoM (Berger et al. 1996). A closer look at the results of the experiment reveals yet another feature that was not simulated in previous studies with more idealized western boundary topography. Figure 5 shows the circulation in the lower layer that develops beneath the anticyclone–cyclone pair by day 60 of the simulation. As one can see, a pair of a deep cyclone and anticyclone forms beneath the LCE; its net effect appears to be to push the LCE eastward— that is, away from the shelf—thus contributing to the cyclic motion of the LCE. It is not immediately clear how important are the deep eddies in contributing to the cyclic LCE motion relative to the surface cyclones. We leave the relevant discussion of this until section 3b(3), where we describe an additional experiment designed to isolate physical mechanisms primarily responsible for the cyclic motion of the LCE. The mechanism of deep eddy formation beneath a moving LCE and its effect on the LCE propagation was analyzed in a number of studies. Most recently this mechanism was discussed in the two-layer study of Sutyrin et al. (2003). In their experiments an LCE-type anticyclone moving over flat topography was shown to generate a wake of deep eddies, which produced a south-
FIG. 5. Wide shelf topography configuration experiment, day 45 of model integration. Thick contours indicate pressure in the upper layer, and vectors show the velocity in the lower layer. A deep cyclone– anticyclone pair is formed underneath the surface eddy over flat topography. The net effect of the deep circulation is to push the surface eddy away from the shelf. Solid contours correspond to positive values; dashed contours correspond to negative values.
ward component to the LCE direction of propagation. With application to our particular configuration the mechanism of deep eddy formation can be described as follows. A rotating elliptic eddy causes compression of the lower-layer water columns in front (in the rotational sense) of the eddy and stretching behind the eddy. The process of water column squashing (stretching) in the lower layer generates anticyclonic (cyclonic) relative vorticity. The bottom slope west of the LCE leads to radiation of the lower-layer relative vorticity in the form of topographic Rossby waves. On the other hand, the eastern part of the LCE is located over a flat bottom, allowing the relative vorticity generated in the lower layer to form a deep cyclone–anticyclone pair. In our experiments the deep eddy formation becomes possible because of the realistic representation of the continental slope. The profile of the bottom slope representing the western topography is a zonal cross section of the actual GoM bottom depth at 258N where the continental slope is approximately only 150 km. Thus, approximately one-half of a typical size LCE remains over flat topography during its interaction with the shelf. This is in contrast to the experiments of Sutyrin et al. where the continental slope was represented with an
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FIG. 6. Same as in Fig. 3 but for the narrow shelf experiment.
idealized linear slope 300 km wide resulting in the LCE located entirely over the slope during its interaction with the boundary. 2) ‘‘NARROW
SHELF’’ EXPERIMENT
The simulated interface displacement in the narrow shelf experiment is shown in Fig. 6. Since the topography configuration in this experiment includes a wider continental slope, it takes the anticyclone approximately 20 days longer to reach the shelf break. Consequently, the entire sequence of LCE interaction with the shelf is delayed by 20 days relative to the wide shelf case—that is, days 35 and 80 shown in Fig. 3 correspond to days 55 and 100 in Fig. 6. The evolution of the LCE and the
associated eddy features simulated in the narrow shelf experiment are similar to the wide shelf experiment. Cyclonic circulation forms immediately to the north of the LCE; the resulting cyclone–anticyclone pair (lopsided dipole) rotates clockwise causing the anticyclone to move offshore, then south, and then back onshore. As the lopsided dipole comes back to the shelf another cyclone starts forming north of the LCE while the first one remains south of the LCE and dissipates because of its interaction with the shelf. When the cyclone north of the LCE becomes sufficiently strong, the cycle repeats. Despite the similarities there are some important differences. The most notable difference is the substantially smaller amplitude of the cyclic motions exhibited
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by the LCE (shown in Fig. 6 with a thick gray line). Weak cyclic motions lead to prolonged LCE interaction with the shelf and its faster decay, the LCE intensity drops to 30% of its original intensity 125 days after encountering the shelf, as compared with 145 days for the wide shelf simulation. Another, more subtle difference is the weak northward motion of the LCE as it approaches the shelf. The discussion below focuses on these two differences and on the physical mechanisms responsible for them. In the previous section we have identified two physical mechanisms leading to the cyclic motion of the LCE. Both of these mechanisms are still present in the narrow shelf configuration; however, their impact on the LCE propagation is reduced leading to significantly less pronounced cyclic motion of the LCE. One of the mechanisms was the interaction of the LCE with the cyclone formed to its north through the process of off-shelf PV advection in the upper layer. The same mechanism is present in the narrow shelf experiment but the intensity of the cyclones is notably weaker. The weaker cyclone intensity is related to the weaker offshore PV flux caused by the steeper topographic slope over the shelf (see Fig. 1). This result is consistent with the result of Williams and Roussenov (2003) who have shown that the amount of high PV water carried offshore by a baroclinic current separating from a sloping bottom is inversely proportional to the bottom slope; that is, steeper bottom slopes produce lower offshore PV flux. The LCE interaction with deep eddies was identified as the second mechanism producing the cyclic trajectory of the LCE. Figure 7 shows the deep circulation during the eddy–shelf interaction in the narrow shelf topography configuration. As one can see, the width of the continental slope, which is representative of the real continental slope at 238N, is nearly 100 km wider than in the wide shelf experiment. The LCE is located almost entirely over the sloping bottom resulting in substantially weaker deep eddies due to the TRW radiation over the slope. Small deep eddies still form over the flat topography region east of the slope; however, they can hardly have a significant impact on LCE propagation. The wide shelf simulation predicted only a very weak northward motion of the LCE during its approach to the western boundary. In contrast to this result a considerably stronger northward motion can be seen in the trajectory of the center of the LCE (shown in Fig. 6 with a thick gray line) as it approaches the shelf. The LCE moves approximately 40 km north, compared to less than 20 km in the ‘‘wide’’ shelf experiment. This northward motion can be attributed to the image effect, which is substantially stronger than in the wide shelf experiment due to the simple fact that the eddy can come closer to the western boundary. However, the image effect still cannot produce a sustainable northward LCE propagation seen in the experiments of Nof (1999) or Sutyrin et al. (2003). The northward motion of the LCE
FIG. 7. Same as in Fig. 5 but for narrow shelf experiment. The wide continental slope prevents the formation of a deep cyclone– anticyclone pair underneath the surface eddy.
quickly stops as the circulation of the cyclone, forming to the north of the LCE, pushes the LCE offshore. 3) ‘‘HYBRID
SHELF’’ EXPERIMENTS
The two previous numerical simulations indicated that two different shelf configurations produce two types of LCE behavior. In the first configuration, which corresponds to the GoM coastal topography profile at 258N, the LCE propagates southward following a cyclic trajectory with large (;50 km in zonal direction) cycles. In the second configuration, which corresponds to the GoM topography profile at 238N, the LCE also propagates southward along a cyclic trajectory, but the amplitude of the cycles is substantially smaller (;10 km) and the resulting southward propagation speed is slower. We have identified two physical mechanisms leading to the cyclic motion of the LCE: 1) the interaction of the LCE with the cyclone formed to its north via the process of off-shelf PV advection in the upper layer, and 2) the interaction of the LCE with deep circulation. The fact that the cyclic motion of the LCE becomes less pronounced in the narrow shelf configuration, where the impact of both mechanisms on the LCE propagation is reduced, confirms our conclusion about the role of these mechanisms in the process of LCE interaction with the western boundary. These experiments, however, do not
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FIG. 8. (right) Modified bottom topography profile in comparison with the (left) 238N shelf profile.
allow definitive conclusions to be drawn regarding the relative importance of the two mechanisms. In this section we describe two additional experiments that was specifically designed to address the question about the relative importance of the mechanisms leading to the cyclic motion of the LCE during its interaction with the western boundary. The basic idea is to design a topographic configuration that would reduce the impact of one of the mechanisms without affecting the other. Thus, the impact of only one mechanism on the LCE trajectory can be isolated for analysis. A new coastal topography profile was constructed by combining the 258N profile with the profile from 238N. The hybrid profile (Fig. 8) includes the shallow portion (shallower that 1000 m) from the 238N profile (narrow shelf ) and the deep portion from the 258N profile (narrow continental slope). The resulting topography has the same configuration in the upper layer as in the narrow shelf experiment, leading to the generation of weaker cyclones by the LCE interaction with the shelf. However, the narrow continental slope in the lower layer allows the generation of deep eddies similar to the wide shelf experiment. The resulting LCE trajectory in this hybrid experiment was found to be very similar to the trajectory in the 258N (wide shelf, narrow slope) experiment (see Fig. 9)—that is, it had amplified cyclic motion—proving that the large amplitude cyclic motion of the LCE at 258N is related to the deep eddies. The resulting LCE behavior indicates that the effect of deep eddies (when they can be generated) on the LCE trajectory is substantially stronger than the effect of the off-shelf advected surfaceintensified eddies. This conclusion is further confirmed by the second
hybrid topography experiment. The hybrid topography profile in this case (Fig. 10) includes the shallow portion (shallower than 1000 m) from the 258N profile (wide shelf ) and the deep portion from the 238N profile (wide continental slope). The resulting topography has the same configuration in the upper layer as in the wide shelf experiment, leading to the generation of stronger cyclones by the LCE interaction with the shelf. However, the wide continental slope in the lower layer prevents the generation of deep eddies similar to the narrow shelf experiment. The resulting LCE trajectory in this case is very similar to the narrow shelf experiment (see Fig. 11) indicating that the width of the continental slope is the key parameter determining the amplitude of the cyclic motion of the LCE. It is important to emphasize, however, that the LCE interaction with the cyclones is still the primary reason for the cyclic motion of the LCE during its interaction with the shelf. The cyclone–LCE interaction causes the LCE to become elliptic and rotate, which then generates deep eddies over flat topography that significantly amplifies the cyclic motion. Thus, the LCE–cyclone interaction can be considered as a process triggering the cyclic motion of the LCE, while the LCE interaction with deep eddies is responsible for the amplitude of this motion. The width of the continental slope is the critical parameter controlling the strength of the LCE interaction with deep eddies and, therefore, the amplitude of the cyclic motion. 4. Comparison with observations Our two-layer simulations of LCE-type anticyclone interactions with a realistic western boundary reveal two
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FIG. 9. (right) Hybrid topography experiment in comparison with the (left) wide shelf experiment. Trajectory of the anticyclonic eddy is very similar to the trajectory in the wide shelf (258N) configuration.
characteristic patterns of LCE evolution: 1) a cyclonic eddy is produced north of the LCE, and 2) after some period of interaction with the shelf the LCE moves east away from the shelf, and then comes back to the shelf
south of the initial point of impact. The last pattern should be especially pronounced in case of a LCE impacting the shelf around 258N, where the continental slope is narrow enough to allow the formation of deep
FIG. 10. (right) Second modified bottom topography profile in comparison with the (left) 258N shelf profile.
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FIG. 11. (right) Second hybrid topography experiment in comparison with the (left) narrow shelf experiment. Trajectory of the anticyclonic eddy is very similar to the trajectory in the narrow shelf (238N) configuration.
eddies beneath the LCE. South of 258N the simulations predict substantially weaker cyclic motion of the LCE, which could be hard to detect in observational data. The two characteristic patterns of LCE evolution identified in our experiments have, indeed, been observed in the western GoM. Figure 12 taken from SAIC (1988) shows ellipses fitted into drifter trajectories observed in 1985–86. The drifters were seeded in the socalled ‘‘fast eddy’’ and tracked the eddy until 26 June 1986 throughout the process of eddy interaction with the western shelf. The eddy was observed to impact the western shelf in the vicinity of 258N and reflected back (move southeastward) from the shelf following the cyclic motion similar to what we see in our experiments. A high-resolution hydrographic survey was conducted during the interaction of fast eddy with the shelf (SAIC 1988). Figure 13 taken from SAIC (1988) shows the height of the 158C isotherm derived from the survey, which reveals a cyclone forming north of the LCE very similar to the results of our simulations. 5. Summary and conclusions The interaction of an LCE-type anticyclone with a realistic western boundary topography in the western GoM has been investigated numerically with a two-layer intermediate equations model that, uniquely, allows for the intersection of the bathymetry and the layer interface. The key new feature of our investigation is a process study in the setting of a realistic continental shelf
that penetrates all the way into the upper layer. Two types of shelf configuration were studied. In the first configuration, which corresponds to the GoM coastal topography profile at 258N, the shelf is relatively wide while the continental slope is relatively narrow. In the second configuration, which corresponds to the GoM topography profile at 238N, the shelf is relatively narrow while the continental slope is relatively wide. The anticyclone was initialized in the upper layer over the abyssal plane away from the topography with the lower layer initially at rest. The eddy then naturally develops lower-layer flow and propagates westward, driven by the b effect until it encounters the coastal topography. As a result of our investigation, two physical mechanisms controlling the LCE interaction with a realistic western shelf were identified. The most robust mechanism—that is, the mechanism that has significant effect on LCE evolution in all topographic configurations that were considered—is the mechanism of LCE interaction with cyclones formed to its north via the process of offshelf PV advection in the upper layer. Similar mechanism of off-slope PV advection by a baroclinic current separating from a sloping topography has been previously identified and studied in a general circulation context. Our experiments indicate the importance of this same mechanism in the mesoscale process of LCE interaction with the western shelf. The LCE interaction with the cyclones generated via off-shelf PV advection mechanism results in the LCE becoming elliptic and
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FIG. 12. Figure 4.5-4 from SAIC (1988). Stylized representation of the paths of drifters 3353 and 3378 during the period of Feb–Mar 1986. The center of the eddy ellipse is observed to move in a southeasterly direction.
rotating clockwise with its center following a cyclic trajectory. The amplitude of the cyclic motion produced by the LCE interaction with the cyclones is controlled by a different physical mechanism. The mechanism consists of the LCE interaction with deep eddies that can be generated beneath the LCE over regions of flat topography adjacent to the continental slope. The deep eddies are generated due to stretching and compression of the lower layer by a rotating elliptic LCE. The net effect of these eddies is to significantly amplify the cyclic motion of the LCE. The width of the continental slope is the critical parameter controlling the strength of the LCE interaction with deep eddies and, therefore, the amplitude of the cyclic motion. The amplitude of the cyclic motion is significantly larger for the western topography with a narrow continental slope, which allows the deep eddies to form beneath a large portion of the LCE. The presence of a realistic shelf in our experiments does not allow the LCE to come close enough to the western boundary to permit a significant interaction with its ‘‘image.’’ Thus, the role of the image effect, identified to be a significant factor in LCE interaction with
the western boundary in previous studies, is substantially reduced. The image effect can have a bigger influence on the LCE for western topography configurations with a narrow shelf, where the LCE can simply come closer to the shoreline. For these configurations, the image effect was shown capable of propagating the LCE up to 40 km northward. The process of cyclone formation, however, prevents the image effect from producing the continuous northward motion of the LCE seen in those previous studies that represented the western boundary as a vertical wall. A combination of the above physical mechanisms produces a characteristic pattern of LCE evolution during its interaction with the western boundary. The pattern consists of a cyclone formation north of the LCE and subsequent cyclic LCE motion, especially pronounced around 258N. This characteristic pattern can be identified in some observed cases of LCE interaction with the western boundary in the GoM. In particular, the interaction of fast eddy with the western boundary around 258N, which occurred during the fall of 1986, was observed to produce a cyclone north of the eddy. The eddy was then observed to move away from the
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FIG. 13. Figure 4.4-20b from SAIC (1988): Topography of the 158C isotherm based on the Jan–Feb 1985 XBT survey.
shelf and south, following the characteristic pattern identified in our experiments. Even though our idealized experiments are well suited for identifying important physical mechanisms involved in LCE interaction with the western boundary, they do not allow to make any definitive conclusions about preferred path of LCEs in the western GoM. In our experiments we consider an isolated LCE. Since LCE interaction with the boundary results in generation of predominantly cyclonic vorticity, a weak mean cyclonic circulation forms east of the eddy creating a tendency for southward eddy propagation. In reality, the GoM circulation has a significant anticyclonic component resulting from continuous supply of warm water by the Loop Current. This anticyclonic component is very likely to alter the southward LCE propagation tendency seen in our experiments. Furthermore, the effects related to
continuous stratification, wind forcing, zonally varying topography, etc., which were excluded from consideration in our experiments, are also likely to alter LCE behavior in many real cases. Thus, further numerical studies involving very realistic simulations that would include all of the above effects are necessary to address the question about the preferred LCE path in the western GoM. We believe the results of the present study will provide valuable insight for interpreting the results of these future realistic simulations. The physical mechanisms identified in our experiments have some important implications for the general circulation in the GoM. Even though no isolated cyclones were produced in our experiments, it is quite feasible that surrounding mesoscale features that are normally present during an LCE interaction with the western boundary can initiate the separation of cyclones
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from the LCE. Thus, the off-shelf PV advection produced by the LCEs interaction with the shelf can be an important source of small-scale cyclones found in the northern and the western GoM (Berger et al. 1996). The mechanism of LCE interaction with deep eddies revealed in our experiments implies that larger LCEs encountering the western boundary around 258N can move away from the shelf after some period of interaction and return back south of the initial point of impact. On the other hand, LCEs encountering the western boundary around 238N are likely to stick to the shelf, resulting in quicker dissipation. Acknowledgments. This work was supported by the Minerals Management Service, U.S. Department of the Interior, Washington, DC, under Contract 01-99-CT310289. Georgi Sutyrin was partially supported by the National Science Foundation and the Office of Naval Research. REFERENCES Allen, J., J. Barth, and P. Newberger, 1990: On intermediate models for barotropic continental shelf and slope flow fields. Part I: Formulation and comparison of exact solutions. J. Phys. Oceanogr., 20, 1017–1042. Berger, T., P. Hamilton, J. Singer, R. Leben, G. Born, and C. Fox, 1996: Louisiana–Texas Shelf physical oceanography program eddy circulation study, final synthesis report—Volume I. U.S. Department of the Interior Tech. Rep. MMS 96-0051, 324 pp. Grimshaw, R., D. Broutman, X. He, and P. Sun, 1994: Analytical and numerical study of a barotropic eddy on a topographic slope. J. Phys. Oceanogr., 24, 1587–1607. Hamilton, P., G. S. Fargion, and D. C. Biggs, 1999: Loop Current eddy paths in the western Gulf of Mexico. J. Phys. Oceanogr., 29, 1180–1207. Kirwan, A., J. Lewis, P. Reinersman, and I. Quintero, 1988: Observed and simulated kinematic properties of Loop Current rings. J. Geophys. Res., 93, 1189–1198.
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