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A Laboratory Model of Thermocline Depth and Exchange Fluxes Across Circumpolar Fronts*

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A Laboratory Model of Thermocline Depth and Exchange Fluxes Across Circumpolar Fronts* 656 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 34 A Laboratory Model of Thermocline Depth and Exchange Fluxes across Circumpolar Fronts* CLAUDIA CENEDESE Physical Oceanography Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts JOHN MARSHALL Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts J. A. WHITEHEAD Physical Oceanography Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts (Manuscript received 6 January 2003, in ®nal form 7 July 2003) ABSTRACT A laboratory experiment has been constructed to investigate the possibility that the equilibrium depth of a circumpolar front is set by a balance between the rate at which potential energy is created by mechanical and buoyancy forcing and the rate at which it is released by eddies. In a rotating cylindrical tank, the combined action of mechanical and buoyancy forcing builds a strati®cation, creating a large-scale front. At equilibrium, the depth of penetration and strength of the current are then determined by the balance between eddy transport and sources and sinks associated with imposed patterns of Ekman pumping and buoyancy ¯uxes. It is found 2 that the depth of penetration and transport of the front scale like Ï[( fwe)/g9]L and weL , respectively, where we is the Ekman pumping, g9 is the reduced gravity across the front, f is the Coriolis parameter, and L is the width scale of the front. Last, the implications of this study for understanding those processes that set the strati®cation and transport of the Antarctic Circumpolar Current (ACC) are discussed. If the laboratory results scale up to the ACC, they suggest a maximum thermocline depth of approximately h 5 2 km, a zonal current velocity of 4.6 cm s21, and a transport T 5 150 Sv (1 Sv [ 106 m3 s 21), not dissimilar to what is observed. 1. Introduction of a streamwise average view of the ACC. The ACC is imagined to ¯ow along the frontal outcrop. Equatorward In the Southern Ocean, meridional gradients in air± of the front, light ¯uid is pumped down from the surface sea buoyancy ¯ux act to create a strong polar front along through the action of the prevailing winds; polewards which the Antarctic Circumpolar Current (ACC) ¯ows of the front heavy ¯uid is sucked up to the surface. in thermal wind balance. Westerly winds also drive the Equatorward ¯ow in the surface Ekman layer carries ACC eastward and, through associated Ekman currents, ¯uid meridionally at the surface balancing regions of induce an Eulerian meridional circulation (the Deacon upwelling and downwelling. However, what happens cell), which acts to overturn isopycnals enhancing the below the surface Ekman layer? How is the ¯uid re- strong frontal region. The potential energy stored in the turned poleward? front is released through baroclinic instability, and the Here we set up and study an idealized laboratory ensuing eddies are thought to play a fundamental role model designed to address the possibility that eddy in the dynamical and thermodynamical balance of the transfer may play an important role in this problem. The ACC. idea is sketched in Fig. 1b. Rather than suck and pump Figure 1a shows a highly idealized schematic diagram from the surface, we represent the action of the wind by pumping ¯uid in to and out of a rotating tank through * Woods Hole Oceanographic Institution Contribution Number many small holes drilled in its base. The ¯uid pumped 10887. in at the periphery of the tank from below is dense; (ambient) ¯uid pumped out in the center of the tank is less dense. The dense ¯uid pumped in from below rep- Corresponding author address: Dr. Claudia Cenedese, Physical Oceanography Department, Woods Hole Oceanographic Institution, resents, we imagine, the light ¯uid pumped down from MS #21, Woods Hole, MA 02543. the surface in the subtropics, as sketched in Fig. 1a. E-mail: [email protected] As we shall see, in our laboratory experiment, the q 2004 American Meteorological Society MARCH 2004 CENEDESE ET AL. 657 height of the dense ¯uid pumped in from the periphery torÐwhen this parameter is less than ; unity, baroclinic increases, but the dense ¯uid is prevented from moving waves with subsequent eddy formation appear at the radially inward in an axisymmetric manner because of density front. Again, these models capture some aspects the Coriolis force due to the rotation of the tank. Instead of the ACC, but only recently have laboratory models it forms a circumpolar front that becomes baroclinically that combine both buoyancy and wind-driven compo- unstable and the radial transfer of ¯uid in to the central nents been developedÐsee Marshall et al. (2002) who sucking region is achieved by unsteady, eddying mo- studied a warmed, pumped lens on an `` f'' plane. Fur- tions (the horizontal wiggly arrows in Fig. 1b). Ulti- thermore, Ivey et al. (1995) and Rosman et al. (1999) mately an equilibrium is set up in which (i) the radial preconditioned a convective region with cyclonic or an- volume transport by eddies balances the input of dense ticyclonic circulation using both buoyancy and me- ¯uid and (ii) the height to which the dense ¯uid reaches chanical forcing. They then investigated the effects of is controlled by the ef®ciency at which eddies carry preconditioning on the lateral spreading of deep water ¯uid radially. formed during open ocean convection. Here we present Elsewhere (e.g., Marshall et al. 2002; Karsten et al. a laboratory experiment designed to address the com- 2002; Marshall and Radko 2003) it has been argued that bined mechanical and buoyancy forcing of an initially meridional eddy transfer, as described above, is the cen- unstrati®ed rotating ¯ow in a geometry relevant to cir- tral mechanism that sets the depth and strati®cation of cumpolar ¯ow. the ACC. Here we study this mechanism in a controlled Our paper is set out as follows. In section 2 we de- laboratory setting. The external parameters of our sys- scribe the apparatus used in the experiment and the mea- tem are the scale of the forcing region L, the volume surements taken. In section 3 we describe the phenom- ¯ux pumped in to the tank Q, the buoyancy anomaly ena and evolution of typical circumpolar ¯ows obtained. of the pumped ¯uid g9, and the rotation rate of the tank We formulate a theory in section 4 and apply it to in- V. Our goal is to understand how the height of the dense terpret our results. The possible implications of this circumpolar front h and its velocity scale u depend on study to our understanding of oceanic circumpolar ¯ows these external parameters. are described in section 5. Of particular interest is the manner in which this sim- ple experiment combines both mechanical and buoyancy 2. Experimental setup forcing of the ¯uid. Previous laboratory studies have concentrated on either mechanical or buoyancy forcing As discussed in the introduction, instead of pumping but seldom in combination. Laboratory studies of the light ¯uid down from above as in Fig. 1a, in our labo- wind-driven circulation started with the ``sliced cylin- ratory abstraction we ¯ip things in the vertical and gently der'' model introduced by Pedlosky and Greenspan pump (i.e., small ¯ow rate) dense ¯uid r1 up from below (1967) and Beardsley (1969). These studies have been around the periphery of a rotating tank (representing light followed up by further experimental, analytical, and nu- water being pumped down in the subtropics) and gently merical studies (Beardsley 1973, 1975; Beardsley and withdraw lighter ¯uid of density r2 at the center (rep- Robbins 1975; Becker and Page 1990; Grif®ths and Ve- resenting the pole) as shown on Fig. 1b. ronis 1997, 1998). Although these models apply to gyre The experiments were conducted in a glass tank of circulation, they are not directly relevant to circumpolar radius R 5 50 cm, ®lled with ¯uid of density r 2 to a ¯ow because here Sverdrup dynamics do not apply. Na- depth H 5 30 cm, and mounted on a direct-drive turn- rimousa and Maxworthy (1985, 1987) studied a two- table rotating counterclockwise. A sketch of the appa- layer strati®ed model of coastal upwelling. Some aspects ratus is shown in Fig. 2. We simulate the action of of that modelÐthe horizontal density gradient and the Ekman layers on the interior ¯uid by introducing and wind stress forcingÐhave processes in common with withdrawing ¯uid through a perforated base at a con- the ACC front. However, the presence of a coastline and trolled rate. By adjusting the rate of pumping and the a prescribed strati®cation prohibit its direct application density of the pumped ¯uid, we can independently con- to the problem at hand. Some laboratory studies of baro- trol both the rate of the simulated Ekman pumping and clinic zonal currents are reviewed by Rhines (1994) in- the magnitude of the buoyancy ¯ux. Underneath the cluding the dynamics and transport of Rossby waves perforated false bottom, there is a reservoir divided into and currents explored by, for example, Sommeria et al. an inner region of radius R1, an intermediate annular (1989, 1991). region of width (R 2 2 R1), and an outer annular region The instability of a buoyancy-driven current in the of width (R 2 R 2) (see Fig. 2b). Dense water, created absence of wind stress has been comprehensively dis- by salt solution of density r1, is fed into the outer an- cussed by Eady (1949), Phillips (1954), Hide (1971), nular region by means of a pump positioned in a dense Hart (1972, 1980), Douglas et al. (1972), Saunders water (r1) source. This mechanical source simulates the (1973), Grif®ths and Linden (1981a,b, 1982), Chia et vertical Ekman pumping, we, due to winds at the free al.
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