Meridional Transport across a Zonal Channel: Topographic Localization

Transcription

1 JUNE 200 MACCREADY AND RHINES 427 Meridional Transport across a Zonal Channel: Topographic Localization PARKER MACCREADY AND PETER B. RHINES School o Oceanography, University o Washington, Seattle, Washington (Manuscript received 29 September 999, in inal orm 5 September 2000) ABSTRACT Experiments are perormed using a two-layer isopycnic numerical model in a zonal channel with a large meridional topographic ridge in the lower layer. The model is orced only by a steady meridional volume transport in the upper layer, and develops a current structure similar to the Antarctic Circumpolar Current. Meridional volume lux across time-mean geostrophic streamlines is ound to be due to a combination o the geostrophic eddy bolus lux and the lateral Reynolds stress. The proportion o each depends on the strength o the orcing. The Reynolds stress increases with the orcing, while the bolus lux is relatively constant. Topography localizes the eddy luxes at and downstream o the topography, where eddy energies are greatest. The strength o the zonal transport is governed by the onset o baroclinic instability and so is relatively insensitive to the strength o the meridional transport.. Introduction This work is a numerical study o meridional transport across a zonal channel in the absence o direct wind or bottom boundary layer ageostrophic transports. Although highly idealized, it is motivated by observed and modeled properties o the Antarctic Circumpolar Current (ACC). The ACC has a large potential density range that does not contact the surace or bottom topography on a circumpolar path. Killworth and Nanneh (994, their Fig. 3) ind this lack o contact to apply in the FRAM model in the density range o kg m 3 (with only about 2% outcropping up to 26 kg m 3 ) over the latitude band 65 56S. Ivchenko et al. (996, p. 766), looking on a time-mean barotropic streampath in the middle o the FRAM ACC also ind a broad range o nonoutcropping or nongrounding density suraces, between o kg m 3 (500 to 2000 m). The meridional overturning circulation o the Southern Ocean, sketched in Fig., is orced by the creation o bottom and surace/intermediate water masses, which are exported equatorward in deep boundary currents and the wind-driven Ekman layer. The poleward return low, nominally in the North Atlantic Deep Water (NADW) potential density range, brings in relatively warm, salty water in the Atlantic sector, and oxygen poor old water in the Paciic sector (Toggweiler and Samuels 992). The return low is largely in the density range lacking signiicant surace or bottom contact in a broad circumpolar region, and is the ocus o this study. Corresponding author address: Parker MacCready, University o Washington, Oceanography, Box , Seattle, WA parker@ocean.washington.edu The dynamics o the ACC have been the subject o a great deal o research in the last decade, particularly numerical modeling. The Fine Resolution Antarctic Model (FRAM: FRAM Group 99) was the irst eddyresolving model o the Southern Ocean to use realistic orcing. Results rom FRAM (Killworth and Nanneh 994; Ivchenko et al. 996) largely conirm the conjecture o Munk and Palmén (95) that the wind stress driving the ACC is balanced by bottom orm stress on topographic ridges. Olbers (998) gives a concise review o these dynamical results. FRAM s meridional circulation was weaker than is thought realistic, due to our poor knowledge o wintertime orcing and convection (Saunders and Thompson 993). Nevertheless, the meridional circulation that developed, when analyzed in potential density coordinates by Döös and Webb (994), is seen to have a middepth poleward low. Killworth and Nanneh (994) ind that the vertical divergence o orm stress balances the time-mean meridional circulation. Marshall et al. (993) point out that transient eddies must be undamental to the orm stress in an isopycnal analysis since by orienting the horizontal path o integration to be along a time-mean geostrophic streamline the mean geostrophic mass lux (and orm stress) must vanish. Gille (997b) and Best et al. (999) analyze Southern Ocean numerical model balances along mean streampaths. Ivchenko et al. (996) and Gille (997a) analyze momentum and potential vorticity budgets in coordinate systems that ollow both isopycnals and mean streampaths. These studies generally conirm Marshall et al. s view o the importance o transient eddies. However many questions remain, particularly concerning the geographic structure o the eddy eects. 200 American Meteorological Society

2 428 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 FIG.. Diagram o the presumed meridional circulation o the Southern Ocean. Surace water is driven equatorward by the zonal wind stress, then subducted at latitudes north o Drake Passage to orm Antarctic Intermediate Water (AAIW). Antarctic Bottom Water (AABW) is ormed by cooling in the Weddell Sea and entrainment o overlying Circumpolar Deep Water. North Atlantic Deep Water (NADW), and other waters in the same potential density class, are assumed in this paper to low poleward to balance the equatorward low above and below. Ivchenko et al. (996) show plots o crosspath velocity rom FRAM, and ind that it tends to occur in eddyrich regions downstream o topography. But they ind no clear sign or pattern to the luxes. By carrying out the analysis in a simpler model we are able here to delineate some o these patterns. One important issue is the exact deinition o the streampath: oten the barotropic streamunction is used, but on any depth or layer the baroclinic structure may cause the local geostrophic velocity to veer o the barotropic streampath. We carry out our meridional transport analysis in the same layer where the geostrophic streampath is deined and so avoid this veering contribution, which may easily overwhelm the eddy mass transport o interest. In this paper we explore volume transport balances between two isopycnals, particularly across curving time-mean geostrophic streamlines. We use an idealized numerical model coniguration to analyze the eddy luxes, the localization o the meridional lux by topography, and the sensitivity o the circulation to dierent orcing strengths. In section 2 the numerical model setup and basic output are presented. In section 3 the mass lux across both zonal and time-mean geostrophic streamlines is analyzed. Section 4 presents results rom experiments with dierent orcing. Section 5 is a discussion o the implications o these results. 2. Numerical model setup We use the Hallberg Isopycnic Model (Hallberg and Rhines 996). The model solves the shallow-water equations in a series o layers o dierent density, solving or layer thickness and horizontal velocity at each time step. The vertical discretization is the time-varying layer interaces. We use two layers (Fig. 2), the minimum to allow baroclinic instability and a orced layer ree rom topographic intersections. We orce the upper layer by steadily adding volume to it on a strip near the northern channel wall and removing volume on a strip near the southern wall. Thus, the upper layer is analogous to the NADW potential density class in the Southern Ocean, and we are ignoring the wind-orced upper layer. The initial upper and lower layer thicknesses are 000 and 3000 m, respectively, and deviate rom this by 250 m, so there is no outcropping or grounding o the interace. The bottom topography is a Gaussian ridge, 500 m in height, with a width o 4 (893 km, e- olding to e-olding). Treguier and Panetta (994) perormed a number o numerical experiments using a quasigeostrophic model, with 2 3 layers, and a variety o bottom topographies. They ind that even airly small topographic heights (5% 0% o the total depth) may exert a strong net orm drag on the low and that the stress increases markedly as the topographic length scale becomes large compared with the internal Rossby radius. Our experiments have relatively large topography, which causes blocked /H contours in the lower layer and also eectively blocks the development o much zonal transport in that layer. There is a linear bottom riction with stress approximating that due to a drag coeicient o The sidewalls are ree slip. The internal density jump gives a 50-km internal Rossby radius, while the (spherical) grid spacing is 6 in latitude and ⅓ in longitude, yielding a nominal grid spacing o 8.6 km, all at the central latitude o 55. The channel extent is 20 in latitude and 80 in longitude (zonally

3 JUNE 200 MACCREADY AND RHINES 429 FIG. 2. Sketch o the domain or the numerical simulations. The model has two layers with original thickness 000 and 3000 m. The bottom topography is a single Gaussian ridge extending the entire meridional width o the channel. The low is orced by continuously adding water to the upper layer in a band o the northern wall (black band), and removing the same amount o water rom the upper layer in a similar band near the southern wall (white band). reentrant). The run is designed to resolve the most unstable baroclinic eddies, the wake rom the ridge, and the jets associated with the current. The main run we discuss is orced with a poleward volume lux in the upper layer o 2.2 Sv (Sv 0 6 m 3 s ). This would be equivalent to 0 Sv i the channel, and the orcing, were o 360 longitudinal extent. The model is spun up rom rest and takes about 5000 days to equilibrate (Fig. 3). We analyze output, saved every 0 days, rom day 5000 to The model spinup is quite similar to that described by Straub (993). The irst eect o the orcing is to immediately set up a 2.2 Sv poleward transport in the lower layer (Fig. 3d). The meridional transports in Fig. 3 are calculated at midlatitude. The lower layer transport is required to allow the eventual north-to-south shoaling o the interace. The rapid north south connection in the lower layer is caused by low along the ridge on / H contours. The Coriolis orce acting on the orced southward low in the upper layer near the orcing strips accelerates a zonal low to the east. As the upper layer thickens at the north and thins at the south, the magnitude o the meridional potential vorticity (PV) gradient decreases in the lower layer. As the PV gradient goes to zero in the lower layer (Fig. 4), baroclinic instability develops, initially near the walls at about day This is also the time at which the poleward meridional transport begins to be elt in the upper layer. The baroclinic eddies have two well-known eects (reviewed in Rhines 994): they cause an interacial orm stress that accelerates the lower layer and redistribute momentum laterally, concentrating it here into one strong and two weak sinuous jets. These are evident in the mean upperlayer surace height (Fig. 5), which ollows contours o the time-mean geostrophic streamunction. The tendency to orm multiple jets, sometimes called zonation, in regions where the orcing scale is many Rossby radii wide, is described in Panetta (993) and Treguier and Panetta (994). The jets exist in both layers downstream o the ridge due to the eddy orm stress coupling. The undulations in the lee appear to be barotropic short Rossby waves, with zonal wavelength approximately 640 km. The time-mean energy ields are plotted in Fig. 6. The KE o the mean low, and eddy KE and PE, are concentrated within the jets, particularly downstream o the ridge where the mean low is strongest. 3. Meridional transport across closed paths Within a layer the momentum equations may be written exactly as u k u( ) B D. (3.) Here u (u, ) is the horizontal velocity, x u y is the relative vorticity, is the Coriolis requency, and k the vertical unit vector. Subscripts x, y, and t denote

4 430 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 FIG. 3. Zonal and meridional volume transport vs time or both layers o the larger numerical simulation. The run equilibrates in about 5000 days. partial derivatives. The Bernoulli unction is B p/ o (u u)/2, where p is the pressure anomaly and o is a reerence density. The dissipative terms used in the model are a biharmonic lateral riction and interacial and bottom riction; however only bottom riction is important to the balances that we present, the other terms being negligible. Adopting subscripts and 2 or FIG. 4. Time-mean (days ) potential vorticity (0 7 m s ) in upper (a) and lower (b) layers o the numerical simulation. the upper and lower layers respectively, the bottom riction is given by F x y D id jd u, (3.2) h 2 where F 0 4 ms. Multiplying (3.) by the layer thickness h and rearranging to solve or the volume transport, hpy 2 y hu hu huy h t hd (3.3) 2 o hpx 2 x h h hux hut hd. (3.4) 2 o The irst term on the right is the transport due to the correlation o layer thickness and geostrophic velocity, the next three are the nonlinear and time-dependent terms, and last is the rictional contribution. The analysis o Marshall et al. (993) highlights the utility o looking at the balance along time-mean geostrophic streamlines, because upon such a path the large-scale meandering o the current is removed. Recasting our balance upon an arbitrary curvilinear path with alongpath and crosspath velocities U (U, V) and coordinates (s, n), the crosspath transport may be written as hps 2 s hv hv hus hut hd. (3.5) 2 o Separating all dependent variables into time-mean (ov-

5 JUNE 200 MACCREADY AND RHINES 43 FIG. 5. Time-mean surace height contours (m) with vectors showing the lower-layer transport. erbar) and eddy (prime) parts and taking the time average o (3.5) we ind hps hp s 2 s hv hv hus hut hd. 2 o o (3.6) We have only explicitly separated out the eddy and mean contributions in the pressure term because it is only there that the choice o path will cause a signiicant simpliication. Along a path with p const the irst term on the right drops out, and only the eddy pressure term contributes. Physically this is the geostrophic eddy bolus lux (Rhines and Holland 979) due to the correlation o thickness anomalies and crosspath geostrophic velocity. Evaluating (3.6) in upper and lower layers, we use p / o g and p 2 / o g g 2, where g is gravity, g the reduced gravity o the interace, and,2,3 are the elevations (positive up) o the ree surace, interace, and bottom topography, respectively. Note that h 2, h 2 2 3, and we will take paths such that s 0. In upper and lower layers then, (3.6) may be written (ocusing only on the pressure term) as hv [g( ) 2 s other terms] (3.7) hv 2 2 [g(2 3)2s g 2 s g 2 2s other terms]. (3.8) Integrating around a closed path ater a statistically steady balance has been reached and assuming no signiicant correlation o terms with (as is the case in our simulations), we ind orced volume transport hv ds [ ] g ds other terms ds (3.9) 2 [ 0 hv ds 2 2 2s g ds g ds 3s (i) ] 2 s (ii) other terms ds. (3.0) The eddy bolus lux term is written as a orm stress (pressure times interace slope) in (3.9) ater the path integration, and typically acts as a drag on the upperlayer low. In the lower layer the same bolus lux term [(ii) in (3.0)] appears with opposite sign and generally accelerates the low in that layer. Thus, even though the eddy pressure terms are dierent in the two layers in (3.7) and (3.8), they almost exactly mirror each other in the path integrals (3.9) and (3.0) due to other terms dropping out. This eect is quite clear in the analysis o the numerical results below. The lower-layer time-mean geostrophic lux term [(3.0) term (i)] is a orm stress (not necessarily a drag) on the bottom topography. Obviously there is no eddy orm stress on the bottom because the topography is stationary. One may instead choose a path on which the lowerlayer pressure is constant, in which case the bottom orm stress, term (i) in (3.0), would vanish and bottom ric-

6 432 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 FIG. 6. Mean KE o the mean (a) and eddy (b) ields, and mean PE (c) o the eddy ield, or both layers o the numerical simulation. The energies are given in J m 2 and the basin averages are shown in the panels. The eddy energies are greatest in the jets in the lee o the ridge. The basin average APE o the mean ield is J m 2. tion would be the only term available to slow the lower layer. In act, such a statement holds or any closed geostrophic streampath, whether in the ACC or a subtropical gyre. We choose to consider only the case where the upper-layer pressure is constant on integration paths, because that is the layer in which we diagnose mechanisms o crosspath volume transport. While the ormulation o the numerical model makes it simple to carry out an integration within a given isopycnal layer, it is more diicult to evaluate terms upon curving horizontal paths. This is particularly true as one tries to look at small lows across the much larger mean geostrophic current. Small errors in interpolation or path orientation combine and may lead to large spurious crosspath luxes rom the mean geostrophic low. In practice we will evaluate all the terms on the rhs o the Cartesian equations (3.3) and (3.4) and then interpolate each term to points along a given path with const. We will assume that the upperlayer mean pressure term is zero on this path. The other terms (the ones which are not negligibly small) are generally oriented enough across the path so that their crosspath contributions may be reliably calculated. We will also present results rom standard zonal integrations, in which case the mean pressure terms are, o course, retained. The statistically steady zonal and meridional ( Cartesian ) transport equations in each layer are

7 JUNE 200 MACCREADY AND RHINES 433 [ ] hu ghy gh y hu negligible terms (3.) geox bolusx rvx [ ] h ghx gh x h negligible terms (3.2) geoy bolusy rvy [ ] hu 2 2 (gh2y gh2 2y ) (gh 2 y gh 2 2y ) hu F 2 negl. terms (3.3) geo2x bolus2x rv2x ric2x [ ] h2 2 (gh2x gh2 2x ) (gh 2 x gh 2 2x ) h2 2 2 Fu2 negl. terms. (3.4) geo2y bolus2y rv2y ric2y Short names or the various terms are given in (3. 3.4) such as bolusy ; each includes the / term and has units m 2 s, or volume transport per unit horizontal distance. For the path analysis the analogous terms will have names like bolusn or the eddy geostrophic bolus transport across the path. The upper-layer Cartesian bolus and rv terms, typically two orders o magnitude smaller than the geo terms, are plotted in Figs. 7 and 8. This scaling is consistent with the preponderance o APE in the timemean ields (Fig. 6). The bolus lux is strongest in the lee o the ridge (Fig. 7), and is oten directed almost normal to the mean geostrophic streamlines. The rv lux (Fig. 8), oten reerred to as the Reynolds stress (Marshall et al. 999), is larger than the bolus lux by about a actor o 3, but is mostly directed along mean geostrophic streampaths, particularly at and in the lee o the ridge. Interpolating these ields to the streampaths and evaluating the crosspath components we ind (Fig. 9) that the normal bolus lux is more oten directed poleward, consistent with the sign o the volume orcing. The normal bolus lux is greatest on the irst two meridional excursions o the current at and downstream o the ridge. The normal component o the rv term (Fig. 0) is also strongest on the ridge and in the lee. Marshall et al. (999), and previous work reviewed therein, ind that the bolus lux term is the dominant contribution to meridional transport when one considers large-scale averages. What is notable in Figs. 9 and 0 is that the lux terms normal to the streamline are localized in space by the topography. Such localization has been seen in the analysis o atmospheric eddy luxes (Lau and Wallace 979) and in the ocean (Cronin and Watts 996). The volume lux is clearly greater where the eddy energies are greater (Fig. 6), although there is not an exact correlation eature by eature. Ivchenko et al. (996) examined the velocity across the time-mean barotropic streamunction in FRAM. They plot locations where this velocity is signiicant and ind that it is strongest just downstream o topography, but without a consistent pattern in sign. Our analysis clariies this process by using the mean geostrophic streampath in the isopycnal layer where the lux is analyzed, so no standing-eddy low is aliased into the crosspath lux terms. Gille (997a) analyzed the PV budget in the Semtner Chervin model, looking on an isopycnal surace along a path o constant Montgomery potential. This is essentially identical to our streampath rame o reerence. Her major inding was that PV was not conserved along the path, varying by 25%, particularly in a large jump downstream o Drake Passage. In our model the mean PV is much more nearly constant along mean geostrophic streamlines. It is possible that the dynamics o the ACC in the region o Drake Passage, the Scotia Arc, and southern Argentina are similar to a deep western boundary current. This would suggest a more direct connection to dissipation in the bottom boundary layer. Our numerical model is designed to be more like the rest o the ACC, which does not pass through such constrictions. One might guess that the bolus lux in various locations could be due to speciic eddy processes such as thin eddies moving equatorward in one location and thick eddies moving poleward in another location. However, looking at scatterplots (not shown) o instantaneous eddy thickness versus normal geostrophic eddy velocity there were no clear patterns with location. Considering terms in the crosspath transport budget on a single contour, we may compare upper and lower layer budgets. In the upper layer the bolus and rv terms are strongly correlated in space in the undulations in the lee o the ridge. Thus, the two terms generally reinorce each other at a given location along a streamline. This contrasts markedly with the classical result rom zonal integrals o such lows (Shepherd 983; Panetta 993; Treguier and Panetta 994) in which the two

8 434 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 FIG. 7. Time-mean surace height contours (m) with vectors showing the upper-layer geostrophic eddy bolus lux. FIG. 8. Time-mean surace height contours (m) with vectors showing the upper-layer nonlinear rv lux (vector scale the same as in Fig. 7). terms tend to have opposite shapes as a unction o latitude. In the lower layer the bolus lux term generally mirrors that in the upper layer. The lower-layer rv term is much smaller than its upper-layer counterpart. Bottom riction is important only in the lee o the ridge where the deep jet is strongest. By ar the largest term in the lower-layer crosspath lux budget is the mean geostrophic term geo2n. This term is ( g/ )h 2 2s, which upon path integration (neglecting changes in ) is identical with the bottom orm stress, term (i) in (3.0). When the path integral o the geo2n term is nonzero, it is equivalent to having a net mean orm stress on the bottom topography. Path integrals o the various terms are evaluated or all circumpolar contours in Fig.. In the upper layer (Fig. a) both the bolus and the rv terms slow the jets, in about equal measure. This is dierent rom the pattern seen on zonal integrals in previous channel simulations. There the orm stress term tends to slow the jet, while the rv term tends to accelerate and sharpen it. This suggests that the large-scale meandering o the current, aliased by zonal averaging, may give rise to the accelerating tendency o the rv term in zonal averages. This pattern has been seen in zonal integrals in Treguier and Panetta (994) (although in their case the eddy orm stress was balanced by zonal wind stress instead o meridional transport) and in Marshall et al. (999). In the lower layer (Fig. b) the balance is mainly between the bolus term, accelerating the layer, and bottom orm stress geo2n which slows it, as in other simulations o the ACC (Ivchenko et al. 996). The upper and lower layer integrated bolus terms are essentially identical in magnitude and opposite in sign, as suggested by (3.9) and (3.0). The lower-layer terms should sum to zero,

9 JUNE 200 MACCREADY AND RHINES 435 FIG. 9. Time-mean surace height contours (m) with vectors showing just the normal component o the upper-layer geostrophic eddy bolus lux. FIG. 0. Time-mean surace height contours (m) with vectors showing just the normal component o the upper-layer nonlinear rv lux (vector scale the same as in Fig. 9). nominally. Errors are due to low-requency variability o the low, subsampling o the results in time, and the diiculty o accurately calculating the largest term, geo2n. Comparing the path integrals with a more standard zonal integral (Fig. 2) the main dierence is that the upper-layer mean geostrophic lux term geoly comes to dominate the bolus and rv terms. The growing importance o the geoly term is the expression o orm stress on the time-mean interace undulations associated with the standing wave structure o the jets. The rv term shows the classical tendency o accelerating the jet just south o 60S. This is one eect o including the standing wave into the zonal integral. In terms o physical processes the path integral provides a much clearer picture, as advocated by Marshall et al. (993). 4. Sensitivity to dierent orcing strengths Marshall et al. (999) perorm numerical experiments similar to those presented here, although without bottom topography. They typically use three layers in a channel, orced by maintaining speciied north south PV gradients in the upper layers. This results in a meridional transport, as in our simulations, although the strength o the transport is not speciied a priori. They ind that the meridional transport in a layer is approximately linearly proportional to the mean north south PV gradient in that layer. To test this in our case, where bottom topography is signiicant, we ran our numerical experiments using our channel model in a smaller domain, 0 in latitude and 20 in longitude, with the same meridional ridge as in the larger experiment. These runs,

10 436 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 FIG.. Path integrals o the cross-path transport terms. (a) Upper layer, (b) lower layer. The upper and lower bolus terms almost exactly balance each other. The upper-layer orced transport is 2.2 Sv. FIG. 2. Zonal integrals o the meridional transport terms. (a) Upper layer, (b) lower layer. The contribution rom the standing eddies geoly in the upper layer now becomes the dominant term.

11 JUNE 200 MACCREADY AND RHINES 437 FIG. 3. Path integrals o the cross-path transport terms rom a small-domain numerical simulation, orced by 0.28 Sv meridional transport. (a) Upper layer, (b) lower layer. especially those with stronger orcing, develop a single jet, locked to the ridge as beore. We vary the orcing strength, using., 0.56, 0.28, and 0.28 Sv (which would be 20, 0, 5, and 5 Sv i extended to a ull 360 domain; negative orcing means poleward transport). Due to the smaller domain the lows equilibrate rather quickly, and all have equilibrated by day The run with positive orcing is quite dierent rom the others. It does not develop a concentrated jet and has no coherent upper-layer PV structure or locking to the topography, but is included here or contrast with the more standard eastward lowing runs. The integrated time-mean cross-path transport analysis or two runs is shown in Figs. 3 and 4, or 0.28 and. Sv orcing, respectively. The primary dependence on orcing strength is that the run with stronger orcing develops a jet with larger north south excursions. The jet in the 0.28 Sv run (Fig. 3) is primarily slowed by the bolus lux, which accounts or most o the poleward mass transport. The rv lux tends to accelerate the jet. This is consistent with the classic pattern seen in zonal integrals (e.g., Treguier and Panetta 994). The situation is reversed however, in the. Sv case (Fig. 4), with the strongest slowing o the jet and most o the poleward lux being due to the rv term. The small-domain 0.56 Sv run (not shown) and the large-domain 2.2 Sv run (Fig. ) all midway between these two cases, with bolus and rv luxes being o equal importance. The path-integrated bolus lux is relatively insensitive to the strength o orcing, and instead it is the rv term that changes most to absorb the changes in net meridional transport. The relation between the time- and zonally averaged mass transport and meridional PV gradient, outside o the orcing strips, is plotted or all our runs in Fig. 5, using the same scaling as in Marshall et al. (999). In all our runs the transport is equilibrated with the orcing at all latitudes, and there is a spread o PV gradient because the jet structure tends to separate out the low into a ront with strong gradient surrounded by plateaus o weaker gradient. Nevertheless, looking at the mean values or each run, the pattern that emerges or the runs with negative orcing is that the PV gradient is approximately constant, and independent o orcing strength. The reason or this (Straub 993) may be argued as ollows. The PV gradient in the upper layer o our runs builds up until the PV gradient in the lower layer vanishes, at which point the eddy activity o baroclinic instability becomes a very eicient method o transporting mass poleward, and urther north south tilting o the interace is inhibited. Runs with stronger orcing have stronger eddy energy ields and, hence, the eddy lux terms are able to carry the extra transport or the same PV gradient. What makes our runs dierent rom those o Marshall et al. (999) is that in ours the eddy strength is set by the meridional transport in the layer that is orcing the overall low, whereas in their experiments the overall low structure was set by an imposed PV gradient in the upper layer, but the mass lux relation to PV gradient was evaluated in the intermediate layer.

12 438 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 3 FIG. 4. Path integrals o the crosspath transport terms rom a small-domain numerical simulation, orced by. Sv meridional transport. (a) Upper layer, (b) lower layer. Their intermediate layer was orced with a smaller PV gradient and thus did not control the eddy strength o the low. Our experiments support their general conclusion that thickness lux may be down the PV gradient, but the value o the lux apparently is also controlled by the eddy strength, and not just the size o the PV FIG. 5. Time-mean zonally averaged meridional volume transport or the our small-domain numerical simulations (upper layer), plotted vs normalized time-mean, zonal-mean meridional PV gradient. Points plotted or a run o a given strength cluster near a given value on the y axis, and the mean or a given run is plotted as a large illed circle. All runs with negative orcing develop about the same PV gradient. The run with positive orcing develops only a small PV gradient (the larger gradient being in the lower layer). gradient. Our experiments do, however, support the concept that the strength o the bolus lux may be controlled by the PV gradient. Also, as Marshall et al. (999) note, the downgradient lux concept may not work at all in some regions. This is clear in the lower layer o the 0.28 Sv experiment (not shown). There the magnitude o the zonal-mean meridional gradient o PV is relatively large, but it has zero mean meridional volume transport. This highlights the act that the eddy luxes rom baroclinic instability are really global properties, relating to the vanishing o the PV gradient somewhere in the domain, and are not controlled by a single layer. Stone (978) proposed the concept that the mean meridional density gradient in the atmosphere would be governed by the onset o baroclinic instability. Applying this idea to the Southern Ocean, Straub (993) develops a prediction or the zonal transport in a two-layer low when baroclinic instability has limited the meridional interace tilt. Assuming that the lower-layer zonal transport is blocked by topography he inds ghhy 2 upper layer zonal transport, (4.) 2 o where H and H 2 are resting layer thicknesses in a channel o meridional width y, o is at midchannel, and is the meridional gradient o. For our small-domain runs (using y 6, the width o the unorced region) (4.) gives about 50 Sv, somewhat larger than the three runs with poleward orcing, which develop transports between 36 and 4 Sv. Expression (4.) predicts 77 Sv or the larger-domain run, which has about 30 Sv.

13 JUNE 200 MACCREADY AND RHINES 439 We conclude that the baroclinic instability governor on the interace tilt is a zeroth-order description o the basic dynamics. 5. Summary and discussion We have presented results rom numerical simulations o two-layer channel low over topography, orced by a meridional mass transport in the upper layer. Analyzing the cross-channel transport mechanism on timemean geostrophic streampaths we ind that both eddy orm stress and lateral Reynolds stress may retard the jets. The relative importance o the geostrophic eddy bolus lux versus the Reynolds stress as the meridional transport mechanism was ound to depend on orcing strength. The Reynolds stress grew with the orcing, while the bolus lux was relatively constant. Focusing on the transport mechanisms as a unction o position along a given path, we ind that both transport mechanisms were larger on and in the lee o the topographic ridge, where eddy energies were also highest. The two mechanisms tend to be correlated along the path, instead o being anticorrelated as seen in the path or zonal integrals. The reason or this correlation is not clear. A series o smaller numerical simulations were done to test the sensitivity o the low to dierent orcing strengths. It was ound that the total zonal transport (and with it the time-mean meridional potential vorticity gradient) was markedly insensitive to the strength o meridional orcing. The PV gradients instead appeared to be controlled by the onset o baroclinic instability. While the meridional mass transport in the orced layer was always down the PV gradient, it was not linearly related to that gradient, instead increasing with the eddy (and orcing) strength, while the PV gradient remained relatively constant. While these experiments are highly idealized, they may have important implications or the dynamics o the Antarctic Circumpolar Current. Regions o strong eddy activity have been observed (Ivchenko et al. 997; Gille 997a,b; Best et al. 999) downstream o topographic obstacles and channel constrictions. Our results suggest that these may be the main geographic locations or poleward transport o deep waters in the NADW potential density class. In addition, the meridional tilt o isopycnals across the ACC may be very insensitive to the strength o wind or buoyancy orcing, being governed by the onset o baroclinic instability instead o the orcing strength. This suggests that the role o the Southern Ocean as a connection point between surace and abyssal oceans may persist over many extremes o climatic orcing. Acknowledgments. This work was generously supported by the National Science Foundation under Grants OCE and OCE We are indebted to LuAnne Thompson and three anonymous reviewers or comments, to Robert Hallberg or the use o his numerical model, and to David Darr or programming assistance. REFERENCES Best, S. E., V. O. Ivchenko, K. J. Richards, R. D. Smith, and R. C. Malone, 999: Eddies in numerical models o the Antarctic Circumpolar Current and their inluence on the mean low. J. Phys. Oceanogr., 29, Cronin, M., and D. R. Watts, 996: Eddy mean low interactions in the Gul Stream at 68W. Part I: Eddy energetics. J. Phys. Oceanogr., 26, Döös, K., and D. J. Webb, 994: The Deacon Cell and other meridional cells o the Southern Ocean. J. Phys. Oceanogr., 24, FRAM Group, 99: An eddy-resolving model o the Southern Ocean. Eos, Trans. Amer. Geophys. Union, 72, Gille, S. T., 997a: Why potential vorticity is not conserved along mean streamlines in a numerical Southern Ocean. J. Phys. Oceanogr., 27, , 997b: The Southern Ocean momentum balance: Evidence or topographic eects rom numerical model output and altimeter data. J. Phys. Oceanogr., 27, Hallberg, R., and P. B. Rhines, 996: Buoyancy-driven circulation in an ocean basin with isopycnals intersecting the sloping boundary. J. Phys. Oceanogr., 26, Ivchenko, V. O., K. J. Richards, and D. P. Stevens, 996: The dynamics o the Antarctic Circumpolar Current. J. Phys. Oceanogr., 26, Killworth, P. D., and M. M. Nanneh, 994: Isopycnal momentum budget o the Antarctic Circumpolar Current in the Fine Resolution Antarctic Model. J. Phys. Oceanogr., 24, Lau, N.-C., and J. M. Wallace, 979: On the distribution o horizontal transports by transient eddies in the Northern Hemisphere wintertime circulation. J. Atmos. Sci., 36, Marshall, D. P., R. G. Williams, and M.-M. Lee, 999: The relation between eddy-induced transport and isopycnic gradients o potential vorticity. J. Phys. Oceanogr., 29, Marshall, J., D. O. Olbers, H. Ross, and D. Wol-Gladrow, 993: Potential vorticity constraints on the dynamics and hydrography o the Southern Ocean. J. Phys. Oceanogr., 23, Munk, W. H., and E. Palmén, 95: Note on the dynamics o the Antarctic Circumpolar Current. Tellus, 3, Olbers, D., 998: Comments on On the obscurantist physics o orm drag in theorizing about the Circumpolar Current. J. Phys. Oceanogr., 28, Panetta, R. L., 993: Zonal jets in wide baroclinically unstable regions: Persistence and scale selection. J. Atmos. Sci., 50, Rhines, P. B., 994: Jets. Chaos, 4, , and W. R. Holland, 979: A theoretical discussion o eddydriven mean lows. Dyn. Atmos. Oceans, 3, Saunders, P. M., and S. R. Thompson, 993: Transport, heat, and reshwater luxes within a diagnostic numerical model (FRAM). J. Phys. Oceanogr., 23, Shepherd, T. G., 983: Mean motions induced by baroclinic instability in a jet. Geophys. Astrophys. Fluid Dyn., 27, Stone, P. H., 978: Baroclinic adjustment. J. Atmos. Sci., 35, Straub, D. N., 993: On the transport and angular momentum balance o channel models o the Antarctic Circumpolar Current. J. Phys. Oceanogr., 23, Toggweiler, J. R., and B. Samuels, 992: New radiocarbon constraints in the upwelling o abyssal water to the ocean s surace. The Global Carbon Cycle, M. Heimann, Ed., NATO ASI Series, Springer-Verlag. Treguier, A. M., and R. L. Panetta, 994: Multiple zonal jets in a quasigeostrophic model o the Antarctic Circumpolar Current. J. Phys. Oceanogr., 24,

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