LOOP CURRENT DYNAMICS IN LABORATORY EXPERIMENTS

Sergei N. Bulgakov and Ángel R. Meulenert Peña

Sergei Nikolaevich Bulgakov. D.Sc. in Physical Oceanography, Marine Hydrophysical Institute, Ucraine. Professor-Investigator, Institute of Astronomy and Meteorology, Universidad de Guadalajara, Mexico. Address: Av. Vallarta 2602, C.P. 44130, Colonia Arcos, Guadalajara, Jalisco, Mexico, e-mail: sbulgako@udgserv.cencar.udg.mx

Ángel Reinaldo Meulenert Peña. Meteorologist. Ph.D. in Geography. Senior Scientist and Director of the Institute of Astronomy and Meteorology, Universidad de Guadalajara, Mexico. e-mail: ameulene@astro.iam.udg.mx

Two aspects of the Loop Current (LC) dynamics in the Gulf of Mexico were studied in a series of laboratory tests: 1) the variation of its penetration distance into the Gulf, and 2) the process of ring detachment by this current. The experiments were conducted in a square tank with a scaled coastal geometry of the Gulf. A flow field was generated by pumping waters of different densities into the Caribbean Sea through the two major channels of the Greater and Lesser Antilles. The flow characteristics depend upon the horizontal and vertical scales of the basin, influx, density differences, and rate of rotation. They can be classified according to the dimensionless parameters of Reynolds (Re) and Burger (Bu). The results of the flat bottom barotropic/baroclinic experiments with constant flux demonstrate that the major phenomena of the LC dynamics can be reproduced in a laboratory. We find that the penetration distance of the LC is governed by the Reynolds number, which is the ratio of the inertial force to the frictional force, while eddy shedding occurs for a Burger number less than unity (Bu<1).

Dos aspectos de la dinámica de la Corriente de Lazo (CL) en el Golfo de México son estudiados en una serie de pruebas de laboratorio: 1) la variación de la distancia de penetración en el Golfo de México, y 2) el proceso de desprendimiento de giro por ésta corriente. Los experimentos fueron realizados en un tanque cuadrado con una geometría costera a escala del golfo. El campo de flujo se generó bombeando agua de diferentes densidades dentro del Mar Caribe, a través de los dos grandes canales de las Antillas Mayores y Menores. Las características del flujo dependen de las escalas horizontal y vertical de la cuenca, el influjo, la diferencia de densidades y la razón de rotación, y pueden ser clasificados atendiendo a los parámetros adimensionales de Reynolds (Re) y Burger (Bu). Los resultados de los experimentos de fondo plano barotrópico/baroclínico con flujo constante demuestran que el principal fenómeno de la CL puede reproducirse en el laboratorio. La distancia de penetración de la CL es gobernada por el número de Reynolds, que es la razón entre la fuerza inercial y la fuerza de fricción, mientras que el desprendimiento de giro ocurre cuando el número de Burger es menor que 1 (Bu<1).

Received: 04/21/03. Modified: 06/02/2003. Accepted: 06/03/2003

An anticyclonic meander of the Loop Current (LC), consisting of inflow through the Yucatan Channel and outflow through the Florida Strait, is the principal element of the Gulf of Mexico (GM) water circulation. Two interesting aspects of the LC are the variability of its penetration distance into the Gulf and its quasi-periodic eddy shedding by the LC. The latter process transports waters of the Caribbean Sea into the Gulf, contributing to the exchange of mass and momentum with the surrounding waters. The eddies and LC front have been studied using remote sensing, hydrographic measurements, and numerical calculations.

An investigation of the LC path variability based on hydrographic observations and satellite data (see review in Lavin, 1997) indicated that the LC path varies significantly. The characteristic LC paths are shown schematically in Figure 1 as the standard position (S), cut-way (C), northward (N) and westward (W) fronts. Although the LC fronts are frequently close to their standard positions, the cut-way and deep meanders of the LC are also statistically probable (Maul, 1977; Vukovich and Hamilton, 1989). The period of eddy separation is also variable, but it is close to the mean annual value of 11 months, with a range of 6 to 17 months (Vukovich, 1995).

A long-standing hypothesis is that the variation of the LC penetration into the Gulf and its ring detachment are caused by the variation in the rate of inflow through the Yucatan Channel. On the contrary, a numerical study (Hurlburt and Thompson, 1980) has shown that these phenomena can be reproduced in numerical experiments without time variations in the inflow. It was noted, in particular, that for realistic parameter values, eddy shedding occurred in baroclinic, but not barotropic models. It was also found that this phenomenon occurs only if the beta-effect and bottom topography are included.

In contrast, Blaja and Sturges (1981) presented evidence for a wind-driven circulation in the GM, and anticyclonic gyre caused predominantly by wind stress curl. It was found that the north-south component of the wind is coherent with the LC position.

These theoretical studies have been continued and extended in other numerical models. The sensitivity of the GM to variations of heat forcing through the Yucatan Channel was studied by Skiba and Adem (1995). Oey (1996) found a strong correlation between eddy shedding and decreasing or reversing the lower-layer (>750m) transport in the Yucatan Channel. Dietrich and Lin (1994) noted the influence of Caribbean eddies on the vorticity of the LC and eddy shedding. Murphy et al. (1999) stated that some Caribbean eddies squeeze through the Yucatan Channel into the GM, where they can influence the timing of LC eddy-shedding events.

Kuo and Ichiye (1979) simulated the barotropic circulation of the GM in a circular tank. The flow field was generated by the injection and withdrawal of homogeneous water through two wall openings. Somewhat different results were obtained. The authors concluded that the westward penetration of the LC intensifies as the Rossby number and Ekman number (Ek=v/fL²) decrease. They noted that eddies formed in this series of laboratory experiments and that the eddies remained embedded in both sides of the main stream, rather than detaching and migrating from the main current.

A constrained model with a scaled coastal geometry of the GM that included only barotropic flow was developed by Sugimoto and Ichiye (1988). Wider ranges of volume transport, lateral shear, mean inflow thickness and bottom slope were included in their series of experiments. The sensitivity of the LC to these parameters was examined. Their results show that the northward penetration length of the loop is proportional to a parameter called penetration Rossby number (Rp=(2QLe/Wa)^1/4/L) where Q is the inflow volume transport, Le is the equivalent length of the approaching channel, W is the angular velocity of the table, a is the bottom slope, and L is the distance between the inlet and the outlet. The authors proposed this parameter as indication for the development and penetration of the loop and the transition to the short-cut path. They also showed that eddy shedding could be reproduced in the barotropic experiments. The mechanism they used to explain the ring detachment included the sea-level difference in the Florida Strait.

Thus, even a brief discussion of the problem of Loop Current dynamics in the laboratory experiments shows that there are different points of view regarding the mechanisms responsible for LC variations and eddy shedding. Two major reasons have motivated a new series of laboratory tests to extend the experimental studies of Ichiye (1972), Kuo and Ichiye (1979), and Sugimoto and Ichiye (1988). 1) The barotropic motion was studied in the previous experimental runs, whereas the role of the baroclinicity is still open to question. 2) The flow field in the previously reported laboratory experiments was generated by the water pump located in the Yucatan Channel. Observations in the real strait indicate the existence of a current-counter-current system (Emilson, 1971). This means that it is important to investigate the flow patterns both in the Gulf and in the Caribbean and to allow the water exchange through the Yucatan Channel to be free.

The purpose of the present study is to simulate the LC dynamics in barotropic/baroclinic experiments, to compare the results to previous laboratory runs, and to understand the role of various model parameters (such as barotropic/baroclinic effects, steady transport and flow rate oscillations through passages, vorticity of inflowing water, rotation, friction, beta-effect, orographic anomalies) in circulation patterns, using a laboratory model of the Gulf.

The circulation in the Gulf-Caribbean basin was investigated in a square tank (0.60x0.60m²) mounted on a rotating turntable. Due to the importance of the characteristic horizontal scales of the basin, including the widths of the straits, the scaled coastline configuration of the Gulf was reproduced in detail using styrofoam walls.

The introduction of a dye into the tank made the flow patterns in the model visible and enabled to capture them on video. Current velocities were measured using a timer and a 0.05m grid drawn on the false bottom. Density measurements were made with an Anton-Paar densimeter with an accuracy of ±1×10^-2kg·m³.

The general mathematical statement of the buoyancy-driven circulation is based on a well known system of hydrodynamic equations that includes water motion and density diffusion. In the first approximation, it is assumed that the circulation is in geostrophic balance. This dictates a characteristic horizontal velocity scale , where L and H are the horizontal and vertical scales of the basin, is the baroclinic Rossby radius of deformation, is reduced gravity, Dr is the density difference over the vertical scale H, and f is the Coriolis parameter. If we introduce the characteristic scales of vertical movement (from continuity), and pressure P = r g'H (from the hydrostatic pressure approximation), it is then possible to rewrite the governing equations in dimensionless form:

  (1)

  (2)

(3)

  (4)

  (5)

Thus, the flow is controlled by the following non-dimensional parameters: the Rossby number  , which is the ratio of the inertial force to the Coriolis force;

the Ekman number  , which is the ratio of the viscous force to the Coriolis force; and the Prandtl number  , which is the ratio of the viscosity to the diffusivity, where n is a coefficient of kinematic viscosity and k is a coefficient of diffusivity. The Reynolds number is commonly used, which is the ratio of the inertial force to the viscous force. One of the most important dimensionless parameters controlling strait dynamics is the Burger number  , which is the ratio of the baroclinic or barotropic Rossby radius of deformation to the channel width. For the latter case the barotropic Rossby radius can be evaluated as  , with the scale of barotropic velocity then written as  , where Dx is a sea level difference between two connected basins (Whitehead, 1986).

Another important dimensionless parameter useful for comparing the similarity of the dynamical processes in the model and the prototype is the aspect ratio  . Moreover, the external forcing similarity of the buoyancy driven flows is based on a parameter  , where Q is the volumetric flux at the source (Bulgakov et al., 1996; Whitehead et al., 1998).

From Eqs. 1, 2 and 5 we identify three characteristic time scales. T1 = (f Ro)-1 is the time-scale of non-linearity or flow meandering. T2 = (f Ek)-1 is a time-scale of viscosity or decay for the gravity current. T3 = Pr (f Ek)^-1 is a time-scale of diffusivity or pycnocline steady state.

Thus, a group of independent parameters exists (L, l, H, f, g', Q, n, k). In addition, the circulation patterns produced in the experiments are governed by the relative vorticity of the inflows (z) and the topographic beta-effect (ß_H). The latter parameter replaces the planetary beta-effect  , and realizes as a sloping bottom in the laboratory. This could be evaluated from the complete potential vorticity conservation equation  = const, assuming that relative vorticity is constant. In this case the topographic beta-effect is derived from as .

The values of the dimensional and non-dimensional standard case parameters (SCP) of the Gulf and the laboratory model are presented in Table I. The Gulf-Caribbean basin is located in an area extending from approximately 10ºN to 30ºN (2.2×10⁶m) and from 60ºW to 98ºW (4×10⁶m). Therefore, its characteristic horizontal scale can be estimated as L=3×10⁶m. The Caribbean Sea is a deep-water basin, with a mean depth of approximately 4×10³m, whereas the mean depth in the Gulf is only 2×10³m. Therefore, the characteristic vertical scale of the Gulf-Caribbean basin was taken to be H=3×10³m.

In the laboratory model, a square tank was used with horizontal length L=0.60m and water depth H=0.06m. Thus, in the laboratory experiments, the aspect ratio H/L is larger by two orders of magnitude. However, since H<<L, both in the model and in nature, such a vertical distortion is permitted (see Ichiye, 1972; Kuo and Ichiye, 1979; Sugimoto and Ichiye, 1988).

Another important horizontal scale is the strait width. It is known that the Florida Strait is 80 miles wide and the Yucatan Channel is 84 miles wide. Therefore, the characteristic strait width for the Gulf was taken to be l=1.6×10⁵m. The water transport through the Yucatan Channel and Florida Strait is known to have a mean value of 30 Sv (Lavin, 1997).

Following parameter estimates in numerical models (Hurlburt and Thompson, 1980) the reduced gravity was taken as g'=0.03m·s^-2. Supposing the Coriolis parameter to have a value f=10^-4s^-1, it follows that the baroclinic Rossby deformation radius is R=9.5×10⁴m for the Gulf. The characteristic velocity in the Gulf-Caribbean basin from the geostrophic balance approximation, U=R²f/L, is 0.3m·s^-1. The Burger number for this case is Bu=0.35.

The external forcing parameter (q), as well as the Rossby number (Ro), had values of the order of 10^-3, and the horizontal Ekman number (Ek) was of the order of 10^-6 for both the model and the Gulf. Each of these models and Gulf non-dimensional parameters can be made equal by adjusting the rotation rate. Therefore, it can be spoken of the Burger-Reynolds and external forcing similarity in the laboratory experiments.

Comparison of the characteristic time scales shows that the time scale of non-linearity (T1), which is associated to the period of flow meandering and eddy shedding, has a value of about four months for the Gulf, and about 10 minutes for the laboratory conditions (Table I).

In the sets of baroclinic experiments, the horizontal density difference between inflowing waters varied in the range of 0< <2×10^-3, while total volume flux from the two inlets varied from 0.4×10^-6 to 3.0×10^-6m³·s^-1. Experiments were conducted at reasonable rotation rates (0<f<3s^-1) that satisfied Bu=O(1), Bu>>1 and Bu<<1. The water depth in the laboratory tank was varied from 0.06 to 0.10m.

In total, more than fifty barotropic and baroclinic laboratory runs were conducted with different combinations of the various model parameters. Each experiment started with the same initial conditions, with the water inside the tank at rest and homogeneous. Thereafter, the circulation was driven by two sources of inflowing waters. At the initial stages, an unsteady regime of circulation was observed in the Gulf in a form of a mushroom current through the Yucatan Channel. As the experiments progressed, this mushroom current transformed itself into a steady meander of the LC flowing out through the Florida Strait, and a general anticyclonic flow pattern in the western Gulf. Qualitative observations revealed that a minimum of 1.5 hours was required in order to reach a quasi-steady regime of circulation.

The influence of various model parameters on the LC path was first examined. In laboratory tests, the Rossby number was set between 1×10^-4 <Ro<2000×10^-4, and the horizontal Ekman number varied between 0·3×10^-6 <Ek<130×10^-6. As we experimented with wider ranges of rotation rates, water depths, gravity accelerations, and other model parameters, the ranges in the values of the dimensionless numbers exceeded those previously used (Ichiye, 1972; Kuo and Ichiye, 1979; Sugimoto and Ichiye, 1988). For baroclinic experiments, the results are summarized in a regime diagram with the scaled Rossby (Ro×10⁴) and Ekman (Ek×10⁶) numbers as axes (Figure 3). Four cases of LC paths were apparent for various combinations of the Ro and Ek numbers. These four regimes in Figure 3 are indicated by the symbols S, C, N and W, as in Figure 1.

The second case, a short-cut path (curve A in Figure 2), was observed by Ichiye (1972) for the same interval of small Rossby numbers and smaller Reynolds numbers (200<Re<500), caused by increased friction. In our experiments, a similar cut-way (when the loop did not develop as much and retreated to the southern coast) was realized for Rossby numbers less than 5×10^-4. We decreased Rossby numbers from SCP either by decreasing the influx or by using a smaller reduced gravity (up to zero for barotropic experiments). According to the observations, the major contribution of baroclinicity is a slightly intensified surface circulation (speeds of 0.005m·s^-1 for baroclinic and 0.002m·s^-1 for barotropic experiments).

Another limited case is the deep northward penetration (N). It is caused by a decrease in the rotation rate in the present experiments. As the Coriolis parameter f approaches zero, the Rossby number (Ro~f^-2) increases more rapidly than the Ekman number (Ek~f^-1). The slower rotation changes the balance between advection and friction, and a deep northward penetration of the LC results (curve N in Figure 1). Ichiye (1972) observed a deep northward penetration for large Rossby and Reynolds numbers as well (curve D in Figure 2). In contrast, in his experiments the inflow from the Yucatan Channel reaches the northern coast and then turns to the west to form a cyclonic meander.

The final case to be discussed is the westward spreading (W). As reported by Ichiye (1972), the inflow reaches westward (curve C in Figure 2) for large Rossby and small Reynolds numbers. On the contrary, Kuo and Ichiye (1979) concluded that westward penetration of the LC is intensified as the Rossby number and Ekman number decrease. Our qualitative results indicate that the westward spreading of the LC into the GM interior intensifies as the water depth increases. In addition, advection becomes important (Ro~H), and friction decreases (because of the suppressed vertical Ekman number, Ek~H-2). As a result, inertial forces prevail over viscous forces. The LC path for greater water depth (H=0.1m) and other SCP’s are shown by curve W in Figure 1.

The previously discussed experiments were conducted for the flat bottom case, with the Gulf of Mexico waters usually flowing out through the Florida Strait along Cuba due to the influence of Coriolis force. In the barotropic experiments, the topographic beta-effect was simulated by tilting the basin in the meridional direction, resulting in bottom slope of 4.8×10^-2. The principal effect of introducing the ß-effect is a general westward flow intensification in accordance with the well-known theory of Stommel. The schematic representation of the LC paths for various rotation rates, is shown in Figure 4. Deeper westward LC intrusion into the Gulf and westward intensification of the outflow through the Florida Strait occur for increased rotation rates.

The role of inflow vorticities was investigated by changing the inlet arrangement from vertical to horizontal. In the horizontal case, the constant vorticity of the inflowing water creates quasi-stational eddies in the Caribbean Sea. However, the vorticity and eddies were not observed to greatly affect the LC and general Gulf of Mexico circulation.

Another phenomenon that was investigated in the laboratory runs is eddy shedding. It is expected that rotation is one of the most important model parameters affecting the eddy shedding process. In the non-rotating case, outflow through the Yucatan Strait is an undisturbed curve of the LC. In this case and for slow rotation rates (when f approaches 0) the Rossby radius of deformation is much greater than the strait width (R>>l), and therefore the Burger number greatly exceeds unity (Bu>>1).

The principal result is that increasing rotation causes barotropic/baroclinic instability and flow meandering with an approximate time-scale of T1 = (fRo)^-1. Due to these LC sinusoidal oscillations, the anticyclonic (or cyclonic) vorticities from the western Gulf pulls some of the LC water into its rotation, thus initiating water detachment from the LC. A case of cyclonic vorticity and northward eddy penetration is schematically presented in Figure 5.

For slow rotation rates (f<0.6s^-1) and other SCP, when R>l and Bu>1, the eddy shedding appears as a filamentation process (Figure 6). For greater rotation rates (f>0.6s^-1) and smaller Burger numbers (Bu<1) a quasi-periodic eddy shedding was detected. The regime diagram presented in Figure 7 illustrates the undisturbed loop (L), filamentation (F) and eddy shedding (E) regions as a function of the Rossby radius of deformation (R) and strait width (l).

The fact that eddy shedding was observed both in the barotropic and baroclinic experiments is significant and suggests that it could be initiated by barotropic instability of the LC. Unfortunately, sea level differences could not be easily measured in laboratory tests. Therefore, evaluation of the barotropic Rossby deformation radius and corresponding Burger number is a topic for future studies.

To investigate the effects of changes in flow rate, variations of volume flux (regular and irregular in phase and amplitude) were used. We found no correlation between flux variation and eddy shedding, in agreement with numerical modeling results (Hurlburt and Thompson, 1980). In contrast, we have not found the baroclinicity and beta-effect to be essential for such a process, as it had occurred in our flat bottom barotropic experiments.

Two types of eddy shedding were observed in the laboratory tests. In the first case the detached eddy drifts westward. The second type of eddy is caused by the LC colliding with the coastal boundary of Florida. In the latter case, the eddy moves northward along the Gulf coastline. Two characteristic trajectories of eddies with westward (a) and northward (b) spreading from the barotropic experiments are shown in Figure 8. Positions of the eddy center at 30sec time intervals are derived from the experimental data. The maximum translational velocities of eddies for the barotropic experiment were about 0.002m·s^-1, with further deceleration and dissipation during movement. The horizontal scale of detached eddies varied from 0.02 to 0.05m. Photographs illustrating eddy shedding with westward propagation, and shedding with northward translation are shown in Figures 9 and 10, respectively.

The Loop Current flow patterns in the Gulf of Mexico were investigated with a series of laboratory experiments using a rotating tank with a source-sink type flow. The inflow was introduced through two inlets in the Caribbean Sea using circulating pumps, and the outflow emptied to the Northern Atlantic. Both barotropic and baroclinic flows were considered. The coastal topography was reproduced using a scaled model of the Gulf-Caribbean basin, and the planetary beta-effect was simulated by a topographic beta-effect caused by a sloping bottom in barotropic experiments. The Burger and Reynolds numbers, as well as external forcing parameters were similar for the model and for the Gulf.

The following principal questions were investigated: 1) the origin of the LC and the variation of its penetration length, and 2) the mechanism of eddy shedding. The sensitivity of the flow patterns to various model parameters was also examined. The conclusions can be summarized as follows.

The anticyclonic meander of the LC, consisting of inflow through the Yucatan Channel and outflow through the Florida Strait, is the result of source-sink flow dynamics. It is consistently observed in barotropic and baroclinic experiments. The penetration distance of the LC (cut-way or deep meander) is governed by the Reynolds number (Re), which is the balance of inertial force (Ro) to the viscous term (Ek), as was shown in earlier laboratory experiments by Ichiye (1972). It depends on such model parameters as the volume flux (Q), density difference between inflowing waters (Dr), and water depth (H). Baroclinicity makes the flow more intense as compared to the barotropic circulation. Water depth controls the bottom friction. Experiments have demonstrated that the flow rate variations in phase and amplitude, in the range 0.4×10^-6<Q< 3.0×10^-6m³·s^-1, and vorticity at the inlets (zero or constant), have little effect on the LC dynamics. A general westward current penetration can be observed in experiments with the topographic beta-effect, while greater rotation rates cause deeper meanders of the LC.

Rotation rate affects the LC behavior to a greater degree. For the non-rotational case (f=0s^-1) an undisturbed loop was observed. Meandering of the LC commences with a period of non-linearity or flow meandering, estimated as T1 = (fRo)^-1. For slow rotation (f<0.6s^-1) and other standard case parameters, filamentation starts when the Rossby deformation radius exceeds the strait width (R>l) or when the Burger number is greater than unity (Bu>1). For greater rotation (f>0.6s^-1), quasi-periodic eddy shedding occurs when the Burger number is less than the critical value of approximate unity (Bu<1) or when the Rossby deformation radius is less than the strait width (R<l). Therefore, both the dynamical and geometric similarity of the model and Gulf are of great importance for reproducing this effect.

For this experimental study it is concluded that the LC can penetrate the Gulf, bend north- and westward, and shed realistic anticyclonic eddies with almost an annual frequency with no time variations in the inflow, in agreement with numerical modeling results (Hurlburt and Thompson, 1980). In the laboratory this phenomenon was observed both in the baroclinic and barotropic experiments for realistic parameter values, whereas in the theoretical studies eddy shedding occurred in the baroclinic, but not in the barotropic models.

The results of these laboratory experiments concerning the LC paths criteria are in general agreement with the experimental results (Ichiye, 1972), but differ somewhat from those proposed by Kuo and Ichiye (1979). This series of laboratory tests confirmed the conclusion (Sugimoto and Ichiye, 1988) that ring detachment occurs in barotropic experiments. We found that the criterion for this phenomena is the existence of a critical Burger number, rather than the sea level difference in the Florida Strait.

Laboratory runs were carried out at the Department of Physical Oceanography of Woods Hole Oceanographic Institution (travel grant provided by CONACyT-NSF project E120.1279) and at the Geophysical Fluid Dynamics Laboratory of Guadalajara University (support by CONACyT project No 32499-T). J. Almaguer Medina and A. Martínez Zatarain assisted in performing the laboratory runs. J.A. Whitehead and reviewer's comments were very useful for the manuscript preparation.

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