SEPTEMBER 2002 STRANEO ET AL. 2603

Effects of on in Strongly and Weakly Baroclinic Flows with Application to the Labrador *

FIAMMETTA STRANEO,MITSUHIRO KAWASE,ϩ AND ROBERT S. PICKART Department of , Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

(Manuscript received 18 July 2001, in ®nal form 25 February 2002)

ABSTRACT Large buoyancy loss driving deep convection is often associated with a large wind that is typically omitted in simulations of convection. Here it is shown that this omission is not justi®ed when overturning occurs in a horizontally inhomogeneous . In strongly baroclinic ¯ows, convective mixing is in¯uenced both by the background horizontal density gradient and by the across-front advection of buoyancy due to wind. The former processÐknown as slantwise convectionÐresults in deeper convection, while the effect of wind depends on the relative orientation of wind with respect to the baroclinic front. For the case of the Labrador Sea, wintertime act to destabilize the baroclinic Labrador Current causing a buoyancy removal roughly one-third as large as the air±sea buoyancy loss. Simulations using a nonhydrostatic numerical model, initialized and forced with observed ®elds from the Labrador Sea, show how the combination of wind and lateral gradients can result in signi®cant convection within the current, in contrast with previous ideas. Though the advection of buoyancy due to wind in weakly baroclinic ¯ows is negligible compared to the surface buoyancy removal typical of convective conditions, convective plumes are substantially deformed by wind. This , and the as- sociated across-front secondary circulation, are explained in terms of the vertical advection of wind-generated vorticity from the surface boundary layer to deeper depths. This mechanism generates vertical structure within the convective layer, contradicting the historical notion that properties become vertically homogenized during convection. For the interior Labrador Sea, this mechanism may be partly responsible for the vertical variability observed during convection, which modeling studies have until now failed to reproduce.

1. Introduction vection in the interior Labrador Sea using Large Simulations (LES). In these simulations, however, as in Open-ocean deep convection occurs as a result of many of the modeling studies of ``chimney convection,'' large surface buoyancy loss that is generally associated it is assumed that the convective region is void of any with large surface wind stress. For example, convection large-scale horizontal gradients. When this is not the in the Labrador Sea and the northwest Mediterranean caseÐgiven the relatively slow mixing timescales of Sea is driven by wind outbreaks that advect cold, dry air off the continents at speeds often exceeding 20 m deep convection (on the order of a day)Ðit is conceiv- sϪ1 (Schott et al. 1996; P. Guest 2001, personal com- able that wind will affect the mixing of properties. An munication). So far, however, most simulations of deep understanding of the dynamical coupling of convective convection have failed to include the effects of wind. overturning, baroclinicity, and a surface wind stress is This assumption is typically justi®ed on the basis of therefore necessary before these processes can be pa- scaling arguments since in the regime of deep convec- rameterized in models that are not capable of resolving tion the overturning is predominantly buoyancy driven small time and space scales. and the mechanical stirring due to wind is comparatively The present study is motivated in part by two recent unimportant. Neglect of the wind is also suggested by observations from the Labrador Sea, suggesting signif- studies such as Harcourt et al. (2002), who studied con- icant impact of wind and baroclinicity during convec- tion. The ®rst observation is that convection can occur within the on the western side of the * Woods Hole Oceanographic Institution Contribution Number Labrador Sea, previously believed to be a region where 10609. ϩ Current af®liation: Department of Physical Oceanography, Uni- only limited overturning occurred because of the large versity of Washington, Seattle, Washington. vertical strati®cation there. The second observation is the high degree of vertical structure present during ac- tive convection in the interior of the Labrador Sea. This Corresponding author address: Dr. Fiammetta Straneo, Dept. of Physical Oceanography MS. #21, WHOI, Woods Hole, MA 02543. is contrary to the general assumption that convection E-mail: [email protected] results in complete vertical homogenization of proper-

᭧ 2002 American Meteorological Society

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC 2604 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 ties. We argue how both of these features can be ex- the Labrador Current and explore the relative contri- plained via the interaction of wind, baroclinicity, and butions of slantwise and wind effects. surface buoyancy ¯ux. This work is a natural extension The second observation of interest from the Labrador of a previous study addressing the effect of the ocean's Sea is the high degree of vertical structure observed horizontal density gradients (baroclinicity) on convec- within the convecting water in the interior of the basin. tive mixing (Straneo et al. 2002, hereafter SKR) and of This was seen in both the hydrographic measurements previous studies such as Haine and Marshall (1998). (Pickart and Torres 1998) as well as in the Deep La- Straneo et al. demonstrated how convective plumes are grangian Float (DLF) data of Steffen and D'Asaro deformed due to background horizontal gradients, which (2002). The hydrographic pro®les revealed the presence drives nonvertical mixing. Hence, parameterizations of of ``multiple mixed layers,'' whereby two (and some- convection as a one-dimensional mixing process in a times three) uniform layers were vertically stacked upon baroclinic ocean can lead to erroneously shallow and each other (PCT). The pro®les also contained a rich light convective layers. variety of intrusions interspersed throughout the mixed A recent hydrographic survey of the Labrador Sea layers. Such variability (though generally less pro- during the winter convective season revealed that clas- nounced) was seen in the ¯oat data as well. A detailed sical Labrador Sea Water (CLSW) can be formed within comparison of the DLF measurements with ``model the western boundary current (Pickart et al. 2002, here- ¯oats'' reveals that this vertical structure is one of the after PCT). Speci®cally, deep mixed layers were ob- few features that LES simulations cannot reproduce served in the offshore barotropic branch of the Labrador (Harcourt et al. 2002). Convection in a weakly baro- Current (Lazier and Wright 1993), in addition to the clinic interior ocean, in the presence of a surface wind interior basin. Due to the dif®cult working conditions stress, is addressed in the second part of the paper. on the cruise, the inner baroclinic branch of the Labrador We employ a variety of data and models throughout Current could not be properly sampled, hence it was the study. To address the problem of convection in a impossible to determine the extent of overturning there. highly baroclinic ¯ow we utilize the hydrographic mea- However, previous evidence suggests that convection surements from the recent Labrador Sea Deep Convec- can at times extend into the baroclinic branch of the tion Experiment (Lab Sea Group 1998). These data are Labrador Current as well. For example, an eddy of new- used to determine the initial conditions and forcing ¯ux- ly ventilated water, less dense than CLSW, was sampled es appropriate for convection (section 2). This infor- in early spring near Flemish Cap (Pickart et al. 1996). mation is then used in a series of numerical runs ad- This water , referred to as Upper LSW (ULSW), dressing the convective layer deepening and water mass is believed to be the source of the middepth CFC max- formation due to vertical mixing alone, slantwise con- imum in the upper portion of the deep western boundary vection, and wind (section 3). Finally, we investigate current. Pickart et al. (1997) argue that ULSW is formed the combined effect of wind and baroclinicity on con- by convective overturning in the baroclinic branch of vection in the interior basin (section 4). The numerical the Labrador Current, which subsequently forms eddies model used is the same high-resolution, nonhydrostatic due to baroclinic instability. Further evidence of con- model employed by SKR, which assumes invariance vection in the baroclinic portion of the Labrador Current along the direction of the mean ¯ow. is provided by time series measurements from a suc- cession of mooring deployments (see Rhines and Lazier 1995; Pickart et al. 1997). 2. The western Labrador Sea currents and forcing The idea of convection in a baroclinic boundary cur- a. Overview rent is somewhat new. Given the large vertical strati- ®cation, it has generally been assumed that convection, The boundary current system of the Labrador Sea if any, would be very shallow. There is reason, however, comprises a series of wind and buoyancy driven currents to suggest otherwise. For example, SKR have shown ¯owing cyclonically around the basin (Fig. 1). On the that convection in a baroclinic ¯ow deviates from one- Labrador side, the baroclinic (inner) branch of the Lab- dimensional mixing due to slantwise effects, which re- rador Current resides just offshore of the shelf break, sults in deeper mixed layers. Second, the strong winds centered above the 1000-m isobath. This buoyancy-driv- that accompany convection will cause a lateral transport en current is supported by a hydrographic front sepa- of buoyancy across a baroclinic current and, given the rating cold, fresh arctic water from the warmer and more relatively slow timescales of convection, likely in¯u- saline waters of subtropical origin. The width of the ence the deepening of the convective layer. For the case baroclinic Labrador Current is roughly 50 km and trans- of the baroclinic Labrador Current, the prevailing north- ports approximately 11 Sv (Sv ϵ 106 m3 sϪ1) (Lazier westerly winds tend to advect dense water from offshore and Wright 1993). Seaward of this lies the barotropic over lighter water, effectively destabilizing the water (outer) branch of the Labrador Current located over the column. Convection in such a baroclinic boundary cur- middle of the continental slope (Lazier and Wright 1993; rent is addressed in the ®rst part of this paper. We ex- Pickart et al. 1997). This is believed to carry the bulk amine the water formed in the inner branch of of the subpolar Sverdrup return ¯ow (order 26 Sv) in

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC SEPTEMBER 2002 STRANEO ET AL. 2605

FIG. 1. Averaged 10-m winds for Feb±Mar 1997 from the NCEP reanalyzed dataset (courtesy of G. W. K. Moore). The dashed black FIG. 2. Section II from the R/V Knorr's hydrographic survey taken line indicates the location of the repeat hydrographic section from on 25 Feb 1997. The location of the section is indicated in Fig. 1. the R/V Knorr wintertime cruise in 1997. Gray arrows indicate the (a) Potential density referenced to the surface (␴␪), contour interval approximate locations of the West Greenland Current (WGC; solid), is 0.02 kg mϪ3. (b) Velocity perpendicular to the section, contour the Labrador Current (LC; solid), and the bottom intensi®ed DWBC interval is 0.05 m sϪ1, solid is equatorward, dashed is poleward. The (dashed). The bathymetric contours shown are 1000 m, 2000 m and locations of the baroclinic Labrador Current (BCLC), the barotropic 3000 m. Labrador Current (BTLC), and the deep western boundary current (DWBC) are indicated in (b). The portion of the section used to initialize the numerical simulations of section 3c is indicated by the a very narrow jet (order 70 km). Throughout this study vertical solid lines. The vertical dashed lines indicate the location of we refer to the baroclinic branch of the Labrador Current the three pro®les shown in Fig. 5. as the BCLC, and the barotropic branch as the BTLC. These should not be confused with the bottom-inten- March 1997 aboard the R/V Knorr (PCT). As part of si®ed deep western boundary current (DWBC), which this survey, a section on the western side of the basin is located farther downslope and transports over¯ow was occupied twice within a 10-day period [following water from the Norwegian and Greenland . (PCT), we refer to the ®rst occupation as section II and In wintertime the winds in the Labrador Sea are pre- the second as section IV]. The density and velocity dis- dominantly out of the northwest, resulting in cold, dry tributions for section II are shown in Fig. 2. In this ®gure air being blown off the continent over the relatively the BCLC is located roughly inshore of 40 km, and the warm ocean. This is exempli®ed by the average Feb- BTLC between 40 and 80 km. The location of the sec- ruary±March wind ®eld based on 20 years of National tion is shown in Fig. 1. A large buoyancy loss occurred Centers for Environmental Prediction (NCEP) data1 between the ®rst and second occupations, resulting in (Fig. 1). A similar mean ®eld is shown in Fig. 5 of Lab deepening convection in both the interior basin and in Sea Group (1998) for the winter months (December± the BTLC. Because section IV did not extend into the March) between 1968 and 1997. The winds in this quad- BCLC, however, it was impossible to document the ex- rant are associated with the largest buoyancy losses in tent to which convection occurred in the BCLC. To the subpolar North Atlantic, as shown by Lilly et al. make up for the lack of direct observations of convec- (1999) in the analysis of European Centre for Medium- tion within the BCLC, we use data from the ®rst oc- Range Weather Forecasts model results. cupation as the initial density distribution, and model The recent wintertime hydrographic survey of the its evolution (in the next section) using surface ¯uxes Labrador Sea was conducted during February and derived as follows.

b. Buoyancy ¯ux estimate 1 The NCEP heat ¯ux ®elds have been calibrated using in situ measurements collected in the northwest Atlantic during winter 1996± The surface buoyancy ¯ux during the 10-day period 97 (Renfrew et al. 2002). between the two occupations can be estimated in a num-

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC 2606 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32

the mean heat ¯ux during this time is within a range of 400±600 W mϪ2.

c. Wintertime wind forcing Realistic surface wind stresses can be obtained from direct atmospheric measurements collected during the hydrographic cruise (courtesy of P. Guest). Since the Knorr was away from the region of section II/IV be- tween the two occupations, we do not have a direct measurement of the forcing in this area during the 10- day period. Instead, we use a representative wind stress obtained by averaging all the data from the cruise (ap- proximately 40 days during the months of February and March) when the vessel was in the western half of the Labrador Sea. The mean wind stress calculated as such is 0.26 N mϪ2, equivalent to a wind speed of 15 m sϪ1 from west-northwest. In terms of the effectiveness of the wind at transporting buoyancy across the BCLC, we FIG. 3. Averaged ␴ pro®les for the Labrador Sea interior, from ␪ are interested in the component of the wind that is par- sections II and IV, taken on 25 Feb and 10 Mar 1997. allel to the current. Taking this to be the direction of the isobaths, the magnitude of the mean wind stress along the axis of the BCLC is 0.17 N mϪ2 (equivalent ber of ways. One could apply bulk formulae using di- to a surface wind speed of 12 m sϪ1). Note that the rectly observed meteorological and hydrographic vari- wind direction computed for the winter of 1996/97 is ables. However, given the extreme wintertime weather more westerly than the 20-yr mean ®eld of the Lab Sea conditions of the Labrador Sea these formulas are sub- Group (1998). Hence, the cross-frontal advection of ject to considerable uncertainties (Renfrew et al. 2002). buoyancy estimated below would be even greater for Instead, we use the difference in buoyancy content of the case of a ``canonical'' winter in the Labrador Sea. the interior pro®les between the two occupations to de- rive an approximate net buoyancy loss. This method 3. Convection in the boundary current system relies on the assumption that lateral ¯uxes are negligible so that any difference is due to the surface ¯ux alone. We now use a series of models to address the extent This is likely true only in the interior of the Labrador to which convection can occur in the two branches of Basin where at least two of the processes driving lateral the Labrador Current, with particular focus on the ¯uxes (slantwise convection and the advection of buoy- BCLC. In all simulations the initial condition is pro- ancy by wind) can be neglected due to the small hori- vided by the ®rst occupation of the hydrographic section zontal strati®cation. The net buoyancy loss is obtained (Fig. 2). Following the above analysis, we use a buoy- by calculating the difference in the vertically integrated ancy ¯ux of 10Ϫ7 m2 sϪ3 and, unless otherwise stated, buoyancy content of the horizontally averaged interior a surface wind stress of 0.17 N mϪ2. In all cases we pro®les (those offshore of 100 km in Fig. 2) for the two show results for two different forcing times, 10 and 20 sections (Fig. 3). By integrating from the surface to 2000 days. The 10-day simulation represents the time that m we ®nd this difference to be 9 kg mϪ2. elapsed between the two hydrographic sections and If this change is assumed to be driven by a uniform hence provides us with a ``simulated completion'' of surface buoyancy ¯ux acting for 10 days, it yields an the repeated section (done on 10 March). We use the average ¯ux of 10Ϫ7 m 2 sϪ3. This is roughly equivalent 20-day simulation as an estimate of the extent to which to a heat loss of 490 W mϪ2 if the typical compressibility overturning may have occurred by the end of the con- for the Labrador Sea is assumed to be 8.7 ϫ 10Ϫ5 J vective season. kgϪ1 KϪ1 and under the assumption that the freshwater To investigate the contribution of different mecha- ¯uxes are negligible. The same calculation, repeated nisms in driving convection in the boundary current, using the difference in the vertically integrated heat con- we make use of a series of progressively more complex tent (instead of total density), yields a similar mean heat models. First we use a one-dimensional model to sim- ¯ux of 450 W mϪ2. Though we are implicitly neglecting ulate overturning due to vertical mixing alone, which the net buoyancy transport resulting from eddy activity, is driven solely by buoyancy ¯ux. This scenario is in strong support for this value comes from measurements line with the results of Harcourt (1999) and others, who by Lagrangian ¯oats that were released during the hy- argue that the mechanical stirring due to wind is neg- drographic cruise in roughly the same region (Steffen ligible in the interior of the Labrador Sea during con- and D'Asaro 2002). The ¯oat measurements reveal that vection. Next we investigate the impact on convection

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC SEPTEMBER 2002 STRANEO ET AL. 2607

front characterized by a uniform horizontal density gra-

dient ␴y, where y is the cross-stream coordinate. We assume that the surface stress acts over a layer of thick- ness d. Let Q be the surface buoyancy ¯ux and ␶ the zonal component of the wind stress. According to lam- inar Ekman theory, the vertically integrated meridional

transport VE induced by the wind acting over the layer of thickness d is

␶ VE ϭϪ , (1) f ␳ 0

FIG. 4. Plot of ␴␪ vs distance in the for the one- where f is the Coriolis parameter and ␳ 0 is the reference dimensional model simulations after 10 and 20 days of forcing. Also density of seawater. To estimate the relative contribution shown is ␴ at 100 m for sections II and IV, and the location of the ␪ of surface buoyancy ¯ux versus wind, consider the rate baroclinic and the barotropic portions of the Labrador Current (BCLC and BTLC, respectively). Shaded regions indicate the density ranges of change of mass per unit area over the depth d. If we for ULSW and CLSW. assume that the only lateral ¯uxes are those induced by wind, and given a surface buoyancy ¯ux Q, this is giv- en by due to the presence of horizontal strati®cation in the boundary current in conjunction with the wind stress. 0 d ␳␳␶ We use basic Ekman theory to argue that the wind- 00 ␴ dz ϭ Q ϩ ␴yEV ϭ Q Ϫ ␴ y . (2) dt͵ g g ␳ 0 f driven advection of buoyancy across the density front Ϫd is nonnegligible. Finally we use a nonhydrostatic nu- merical model to investigate the deviation from vertical The ®rst term on the right-hand side of (2) accounts mixing due to slantwise convection and to the coupling for the density change due to the surface buoyancy ¯ux of baroclinicity and wind effects. Q, which is positive for buoyancy leaving the ocean's surface, while the second term accounts for the buoy- ancy transport due to wind. In this term, the horizontal a. One-dimensional mixing density gradient in (2) is a mean gradient, vertically In the ®rst model we assume that a surface buoyancy averaged over the depth of the layer affected by the

loss results in the vertical homogenization of a layer of wind. For the BCLC, ␴y Ͼ 0 and VE Ͻ 0 for a positive ¯uid (the mixed layer) and that there is no discontinuity wind stress. Note, incidentally, that by the same argu- at its base. The potential density distribution across the ment we expect wind to have a stabilizing effect on the section, within the mixed layer, after 10 and 20 days of West Greenland Current. The ratio of the two terms for forcing is shown in Fig. 4. Included in the ®gure are the BCLC can be calculated by using the parameters 7 2 3 2 the density ranges corresponding to ULSW (␴␪ ϭ derived above (Q ϭ 10Ϫ m sϪ , ␶ ϭ 0.17 N mϪ ) and 3 27.68±27.72 kg mϪ ) and CLSW (␴ ϭ 27.74±27.78 Ϫ6 ␪ a mean horizontal density gradient of ␴y ϭ 2.5 ϫ 10 Ϫ3 kg m ), as de®ned by Pickart et al. (1997). The mixed Ϫ4 kg m . This estimate of ␴y is obtained by vertically layer model shows that CLSW can be formed in the averaging the horizontal density gradient over the top BTLC, while water mass formation in the BCLC is lim- 500 m at the center of the BCLC (the central pro®le in ited mostly to ULSWÐeven in the 20-day forcing sce- Fig. 2). This yields a ratio for the wind-driven buoyancy nario. These results are in line with Pickart et al. (1997) ¯ux to the vertical buoyancy ¯ux of who did a similar calculation using historical data. The mixed layer depths in the present simulation range from g␴␶ 100±700 m (150±900 m) in the BCLC to 800±900 m y 0.32. (3) 2 ഠ (1000 m) in the BTLC for 10 (20) days of forcing. ␳0 Qf Thus, based on this simple calculation, we expect the b. Impact of wind-driven lateral ¯uxes wind-induced lateral advection of buoyancy to provide The model presented above does not include the ef- an effective buoyancy loss that is approximately one- fects of the large wind stress that is parallel to the ¯ow. third that due to the surface ¯ux. Note that this calcu- Given the orientation of the BCLC and the surface lation does not include slantwise convection effects, nor stress, we expect the wind-driven advection of buoyancy does it account for any coupling of wind and baroclin- to be directed onshore and hence to be effective at de- icity that may modify the mixing. Yet this ®rst attempt stabilizing the . How does this compare shows that, in regions of strong horizontal gradients, with the destabilization due to the buoyancy ¯ux? For destabilization due to wind can make a substantial con- simplicity consider the case of an in®nitely extended tribution to the net buoyancy loss.

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC 2608 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 c. Nonhydrostatic simulations can be written in terms u, the alongstream velocity, and ␰ the zonal horizontal vorticity: 1) THE NUMERICAL MODEL u ץ 22uץ Du Ϫ f ␷ ϭ ␯ ϩ ␯ yץ z22hץ To study the effects of slantwise convection, and of Dt ␷ the coupling of slantwise and wind effects on convection ␰ ץ 22␰ץ bץ uץ D␰ in the BCLC, we use a nonhydrostatic, high-resolution ϭ f ϩϩ␯ ϩ ␯ , (4) yץ z22hץ y ␷ץ zץ numerical model. It is the same model utilized by SKR Dt to investigate slantwise convection in more idealized where ¯ows. Two important simpli®cations are made in for- ץץץ mulating the model. First, it is assumed that subgrid- D ϭϩ␷ ϩ w , zץ yץ tץ scale unresolved processes can be parameterized in the Dt form of a constant Fickian diffusivity. This assumption, ␺ץ ␺ץ ;which has been employed in a number of convection ␷ ϭϪ , w ϭ , ␰ ϭٌ2␺ yץ zץ studies (see SKR and references therein), can be justi®ed on the basis that the model is capable of resolving the ␯ and ␬ are the eddy and diffusivity, and sub- dominant mixing agents during deep convectionÐthe scripts indicate horizontal and vertical coef®cients. Note convective plumes. Second, the model assumes invari- that the vorticity discussed throughout this section is ance in one horizontal direction, making it more suited that in the zonal direction, oriented perpendicular to the for problems where variations in one horizontal direc- y±z plane, and should not be confused with the vertical tion are much greater than in the other. This assumption vorticity that is more often referred to simply as vorticity is clearly satis®ed in the boundary current regime, ad- in the oceanographic literature. Similarly, the stream- dressed in this part of the study. Regarding convection function discussed below is in the vertical plane and in the interior of the Labrador Sea, addressed in the should not be confused with the more familiar horizontal second part of our study, the latter assumption is more streamfunction. Finally, we assume a linear equation of applicable for larger gyrelike, baroclinic structures as state such that the conservation of buoyancy, b ϭϪg␳Ј/ opposed to smaller eddies. However, three-dimensional ␳ 0, is given by convective simulations that include wind show how con- b ץ 22bץ Db vective cells tend to align along the wind direction, ϭ ␬ ϩ ␬ . yץ z22hץ effectively becoming convective rolls (Harcourt 1999). Dt ␷ This provides some support for the two-dimensional as- The model uses a staggered grid with the buoyancy sumption made here. and zonal velocity de®ned at the center of the grid rect- As shown in SKR, the model is successful in pro- angle, the meridional component of velocity at the sides, ducing plumes whose characteristics (width, velocities, and the vorticity and streamfunction at the corners. The and timescales) are in agreement with those observed Prandtl number is one, and the horizontal and vertical at a number of deep convective sites. There are, none- eddy diffusivities are 5 m2 sϪ1 and 0.03 m2 sϪ1, re- theless, a number of three-dimensional processes, such spectively. The lateral grid spacing is 125 m, vertical as baroclinic instability, or plume±plume interactions, grid-spacing 7 m, and the basin dimensions are 50 km which are not resolved in these simulations. While the by 2000 m. An Adams±Bashforth time stepping scheme model allows us to study the effect of wind on con- is used with a 30-s time step. Boundary conditions are vective plumes in its simplest setting, we are not able no ¯ux for buoyancy for the lateral and bottom bound- to resolve how such processes couple with the dynamics aries, while the ¯ux condition at the surface is given by described belowÐa question which needs further study. -z. Boundary conditions for the moץ/bץQ(y, t) ϭϪ␬␷ Regarding the role played by baroclinic instability dur- mentum equations are no stress at lateral boundaries, ing convection in the interior of the Labrador Sea, one x y no slip at the bottom and (␶ , ␶ ) ϭ ␳ 0␯z(uz, ␷ z) at the should recognize that, while it likely impacts the spread- surface. The wind stress ␶ is given by ing of convectively formed waters away from the for- xy mation region, previous studies of localized sinking may ␶ ϭ (␶ , ␶ ) ϭ cDaww␳ | U | U , Ϫ3 have unrealistically enhanced its effects (see Straneo where cD is the drag coef®cient (10 ), ␳a is the density Ϫ3 and Kawase 1999). This notion is supported by the fact of air (1.2 kg m ), and Uw is the wind velocity in m that recent wintertime observations from the Labrador sϪ1. In the simulations described below we take u to be Sea did not ®nd a large number of convectively formed the alongstream ¯ow component and limit our attention eddies, as one would expect from the classic chimney to the effects of a surface stress that is parallel to the collapse scenario for the interior region (Lilly et al. ¯ow (␶ y ϭ 0). The surface stress, when present, is ap- 2002, submitted to J. Phys. Oceanogr., hereafter LI). plied simultaneously along with the surface buoyancy Let x be the alongstream and y the across-stream di- ¯ux. The model is initialized with the potential density rections then, by assuming no variations in the alongs- and velocity ®elds from section II, limiting the domain x ϭ 0), the equations to the onshoremost 50 km shown in Fig. 2, roughlyץ/ץ) tream direction

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC SEPTEMBER 2002 STRANEO ET AL. 2609

FIG. 5. Pro®les of ␴␪ after 20 days of buoyancy forcing for mixed layer model with no wind stress (dashed). nonhydrostatic numerical model with no wind (solid), and numerical model with wind (dotted). Locations for the three pro®les shown, (a)±(c) are indicated in Fig. 2: (a) the onshoremost location and (c) the offshoremost. coinciding with the BCLC. The surface forcing applied ing a weak stable strati®cation (see SKR). According is 10Ϫ7 m2 sϪ3 for the buoyancy ¯ux and 0.17 N mϪ2 to SKR, these effects are signi®cant only when the local for the wind stress. A more detailed description of the gradient Richardson number, de®ned as the ratio of the model and its success at representing convective over- vertical strati®cation to the square of the vertical shear turning can be found in SKR. in the alongstream velocity, is of order one (or equiv- alently when the strati®cation on the alongstream ab- solute momentum surfaces is different from the vertical 2) RESULTS strati®cation). Since both the horizontal and vertical The numerical model provides us with a tool to in- strati®cations vary across the front (Fig. 2), we expect vestigate the convective layer modi®cations induced by the deviation in density and depth of the convective slantwise effects as well as the coupling of baroclinicity layer due to slantwise effects to vary as such. Similarly, and wind. This is done by comparing two different non- we anticipate that the effect of wind will also vary across hydrostatic simulations: one in which the boundary cur- the front, for two reasons. First, the amount of buoyancy rent is subject to the buoyancy ¯ux alone and one in transported laterally is proportional to the magnitude of which it is simultaneously subject to a buoyancy ¯ux the horizontal buoyancy gradient [see (2)]. Second, the and a surface wind stress. In the buoyancy ¯ux only change in density within the convective layer is depen- simulation, we make the assumption that deviations dent on the thickness of the convective layer within from the mixed layer model dynamics discussed above which this denser ¯uid is mixed (greater impact on shal- are principally due to slantwise convection effects. In lower mixed layers). Since both vertical and horizontal the buoyancy ¯ux and wind forcing simulation, depar- strati®cation in the BCLC are largest onshore, this is tures from the mixed layer model are due both to slant- also the region where we expect to see the largest effect wise effects and to lateral advection of buoyancy by of wind. Given the orientation of the boundary with wind. Slantwise convection manifests itself in tilted respect to wind, both slantwise effects and wind forcing plumes that drive mixing along the absolute momentum will result in deeper and denser convective layers in the surfaces of the mean ¯ow. Because the strati®cation BCLC. along these surfaces is less than the vertical strati®ca- We begin the comparison by showing the density pro- tion, slantwise convection results in deeper mixing ®les, after 20 days of forcing, for the buoyancy ¯ux (compared to one-dimensional mixing) while maintain- only run, the wind plus buoyancy ¯ux run, and the one-

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC 2610 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32

dd0 ␳ S(x, t) ϭ ␴ dz ϭ 0 (Q ϩ Q ϩ Q ), (5) dt dt͵ g sl w Ϫd

where Q is the atmospheric buoyancy ¯ux, Qsl is the equivalent buoyancy ¯ux due to slantwise effects, and

Qw is the equivalent buoyancy ¯ux due to wind. We now use the nonhydrostatic simulations to calculate both

Qsl and Qw. Let Smlm(x, tt), Ssl(x, ), and Sw(x, t) be the vertically integrated density at x, after 20 days of forc- ing, for the mixed layer model, the nonhydrostatic sim- ulation with no wind, and that with wind, respectively. By integrating (5) in time, we can write expressions for the change in S(x, t) in each of the runs.

FIG. 6. Equivalent buoyancy ¯uxes due to slantwise effects (Qsl, t dashed) and wind effects (Q , dotted) from the nonhydrostatic sim- ␳␳00 w S (x, t) ϭ S (x) ϩ Qdtϭ Qt ulations calculated after 20 days of forcing. The equivalent buoyancy mlm 0 gg͵ 0 ¯ux from the Ekman model QEk is the solid black line. ␳ t S (x, t) ϭ S (x) ϩ 0 (Q ϩ Q ) dt sl 0 g ͵ sl 0 dimensional mixed layer model introduced in section ␳ 0 3a (Fig. 5). Pro®les shown are taken at three different ϭ (Q ϩ Qsl)t cross-stream locations, indicated in Fig. 2, and are rep- g resentative of different regimes within the front. As the ␳ t S (x, t) ϭ S (x) ϩ 0 (Q ϩ Q ϩ Q ) dt relative magnitude of the horizontal to the vertical strat- w 0 g ͵ sl w i®cation changes across the front, so too does the rel- 0 ative impact of wind and slantwise effects. At the most ␳ ϭ 0 (Q ϩ Q ϩ Q )t, (6) onshore location, wind causes the largest deviation in g sl w the mean density of the convective layer, while slantwise effects are unimportant. Hence the density pro®le in the where S 0(x) is the initial vertical integral, and Q sl and buoyancy only run is identical to that of the mixed layer Q w represent the time-averaged contribution of the slant- model (save for the slumping of the isopycnals), while wise and wind effects, respectively. The left-hand side in the wind and buoyancy forcing run the pro®le is on of (6) is evaluated from the three runs and used to de- Ϫ3 average 0.008 kg m denser and clearly deeper (Fig. termine Qsl and Qw. 5a). At the more central location, we see a departure g from the mixed layer model even in the buoyancy only Qsl(x) ϭ [S sl(x, t) Ϫ S mlm(x, t)] (7) run (Fig. 5b), suggesting that slantwise effects are no ␳ 0 t longer negligible. When wind is included, the departure g from the mixed layer is approximately doubled with Q (x) ϭ [S (x, t) Ϫ S (x, t)]. (8) ww␳ t sl respect to the buoyancy only run, suggesting that the 0 effects of wind and of slantwise mixing on the convec- Finally, the equivalent buoyancy ¯ux due to wind tive layer are comparable. Finally, at the most offshore from the nonhydrostatic simulation, Qw, is compared to location, we see that slantwise convection still causes that predicted by the laminar Ekman model, presented a noticeable departure from the mixed layer model, in section 3b [cf. (2)]: while wind effects are relatively less important (Fig. 1 ttg 5c). Q ϭ QdtϭϪ ␶␴ dt. Ek Ek 2 y t ͵ ␳0 f ͵ To make a more quantitative comparison of the de- 00 parture from vertical mixing due to slantwise effects Since the applied wind stress is constant in time, the and to wind, we modify (2) to include changes due to horizontal density gradient is the only time varying both processes. In practice, we ask what is the ``equiv- quantity in the above expression. This term cannot be alent'' buoyancy ¯ux, due to either process, in com- directly evaluated without an a priori knowledge of the parison to the surface buoyancy ¯ux? To answer this convective layer's evolution, so we approximate it with question we assume that the two effects are essentially the vertical average of the initial ␴y over the top 700 m decoupled and that, when acting in combination, their of the water column (the convective layer due to wind effect can be represented as the superposition of their varies between 600 and 800 m). A comparison of the individual contributions. Let the rate of change of S(x, three equivalent ¯uxes, after 20 days of forcing, is t), the vertical integral of density (integrated over a shown in Fig. 6. Only the interior portion of the domain depth greater than the convective layer), be is shown so as to eliminate the effects of the lateral

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC SEPTEMBER 2002 STRANEO ET AL. 2611 boundaries. Their magnitude should be compared to that of the applied surface ¯ux, 10Ϫ7 m2 sϪ3. This more quantitative analysis con®rms the scenario described above. Slantwise effects are relatively un- important onshore but increase to a maximum of 0.2 ϫ 10Ϫ7 m 2 sϪ3 in the center of the front, thus amounting to a correction that is one-®fth of the magnitude of the atmospheric buoyancy ¯ux (Fig. 6). This lateral varia- tion in amplitude is due to the decreasing vertical and horizontal strati®cation across the front. At the most onshore location, slantwise effects are inhibited by the large vertical strati®cation; isopycnals are mostly hor- izontal on the plume scale, making mixing along the slanted paths formally identical to vertical mixing in terms of depth and density of the convective layer. Mov- ing farther offshore, slantwise convection becomes more effective as the vertical strati®cation decreases but the horizontal strati®cation is still large. At the outer edge of the front the horizontal strati®cation decreases sig- ni®cantly; hence the impact of slantwise convection de- FIG. 7. Convective layer depth across the section after 20 days of creases accordingly. This behavior supports the analysis forcing for the mixed layer model (mlm), the nonhydrostatic with no of SKR, who ®nd that the importance of slantwise con- wind, and the nonhydrostatic with wind simulations. The portion of vection is determined by the relative magnitude of the the section shown is that used to initialize the numerical simulations, horizontal to the vertical strati®cation. Wind effectsÐ shown in Fig. 2. diagnosed from these numerical simulationsÐmono- tonically decrease in the offshore direction due to a reduction in the horizontal strati®cation (Fig. 6). The tive layer is much more pronounced. Wind stress results good agreement between Qw and QEk supports the as- in a thickening of the convective layer by up to 300 m sumption that the dominant effect of wind, in this in the onshore portion of the BCLC, decreasing to zero boundary current regime, is due to the horizontal ad- offshore with respect to the slantwise only case (Fig. vection of buoyancy. The magnitude of the equivalent 7). This thicker convective layer is also associated with ¯uxes for slantwise and wind effects con®rm that their a denser convective product (Fig. 8). The combination impact is not negligible with respect to the surface buoy- of slantwise and wind effects results in a mean increase ancy forcing. Indeed, their combined effect, over the in the density of the water masses formed of approxi- central portion of the front, can amount to an equivalent mately 0.01 kg mϪ3 (larger increases occurring on- increase in the buoyancy ¯ux of approximately 50%. shore). We now return to our original question: how easy is These simulations show that substantial convection it for convection to occur within the BCLC? Having in the boundary current is more likely than one might shown that slantwise and wind effects can result in a expect based on vertical mixing alone. This provides substantial deviation from one-dimensional mixing, we support to the theory that ULSW may be formed in the illustrate how this affects the convective layer's depth baroclinic branch of the Labrador Current (densities and density distribution across the front. The depth of may even reach the CLSW range, Fig. 8). Our simu- convection after 20 days of forcing in the three simu- lations are based on realistic wind and buoyancy forcing lations is shown in Fig. 7. In the nonhydrostatic sim- applied to observed hydrographic pro®les from the win- ulations, we use potential vorticity (PV) as an indicator tertime Labrador Sea in 1997. It is worth noting that of where convection has occurred; the low PV convected overall 1996/97 was a moderate winter (see PCT), hence waters are separated from the unconvected waters by a such water mass formation is even more likely for robust large PV gradient. Slantwise effects result in a deeper winters, such as those which occurred earlier in the de- convective layer than one-dimensional mixing. This de- cade. parture is limited to a few tens of meters at the on- shoremost part of the section, to about 100 m offshore. 4. Convection in the interior We note that the maximum in the convective layer depth in the one-dimensional model, located at the center of So far we have concentrated on the combined effects the section, is associated with horizontal inhomogene- of baroclinicity and wind stress on convection in a ities present in the original section data. This lateral strongly baroclinic ¯ow. We have shown that the ®rst- structure is absent in the nonhydrostatic simulations be- order effect of wind is a lateral advection of buoyancy cause of the lateral mixing that has occurred during the that is signi®cant with respect to the magnitude of the 20 days of forcing. The impact of wind on the convec- air±sea buoyancy ¯ux. In this section, we examine the

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC 2612 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32

drographic and the DLF measurements is slantwise mix- ing. As shown by SKR, the weak horizontal gradients observed in the interior are still large enough to drive mixing of properties along slanted paths, thus poten- tially creating vertical variability from horizontal struc- ture. Straneo et al. did not, however, include the effects of a wind stress. In this section we extend the work of SKR to address how convective mixing in a weakly baroclinic ¯ow (the interior Labrador Sea) is modi®ed by a wind stressÐin particular how the plumes are dis- torted. We use the same nonhydrostatic numerical model of the previous section and limit our attention to the FIG. 8. Plot of ␴ within the convective layer after 10 days (solid ␪ case of a wind stress that is parallel or antiparallel to gray) and 20 days (solid black) of buoyancy and wind forcing from the numerical experiments. Mixed layer model density distributions the mean ¯ow since these conditions likely have the (dashed lines) for the same forcing periods are the same as those largest impact on the overturning. Because of the chang- shown in Fig. 4. The initial density distribution in section II (dotted ing direction of the ¯ow in a recirculation or an eddy, line) was also shown in Fig. 4. Shaded areas represent the CLSW the orientation of the coordinate system is arbitrary. We and ULSW density range. therefore limit our attention to the case of a westward, surface intensi®ed oceanic ¯ow and address the case of impact of wind on convection in the interior of the Lab- a wind stress that is parallel or antiparallel to this ¯ow. rador Sea, where the bulk of CLSW is formed. Here, It should be recognized, however, that the results pre- horizontal density gradients result from features such as sented are only sensitive to the relative orientation of eddies (LI) or horizontal recirculations (Lavender et al. wind and of the oceanic ¯ow, and not on their absolute 2000), with magnitude typically an order of magnitude direction. less than that found in the baroclinic boundary current (PCT; LI). Because of this and because the surface buoy- ancy loss varies over larger spatial scales, we anticipate a. Laminar in terms of vorticity that the lateral advection of buoyancy due to wind is negligible with respect to the surface buoyancy ¯ux. It is instructive to consider ®rst the wind-only prob- Instead, motivation for investigating the effect of wind lem within the simpli®ed framework of Ekman dynam- on convection in the interior of the Labrador Sea is ics, which will then be compared to the full nonhydro- provided by the lack of an explanation for the large static model. For our purposes, it is more appropriate degree of spatial variability (especially vertical) ob- to cast the laminar Ekman problem in terms of relative served during wintertime surveys of the interior Lab- vorticity, as follows. rador Sea. Such variability was evident both in the Let ␻ be the relative vorticity vector, towed CTD measurements undertaken in the winter of

,( ϫ u ϭ(wyzzxxyϪ ␷ , u Ϫ w , ␷ Ϫ u ١ as well as in the measurements made by the ␻ ϭ (␰␩, ␨) ϭ 1996/97 convecting DLFs (Steffen and D'Asaro 2002). This var- iability is at odds with the notion that convection can where subscripts indicate partial derivatives. In terms be represented as a purely vertical mixing process. Even of vorticity, the steady laminar Ekman balance, typically complex nonhydrostatic simulations of convection have, written as a momentum balance between the ageostroph- so far, been unable to reproduce it. For example, Har- ic part of the Coriolis terms and the vertical viscous court et al. (2002) compared data collected by ``model terms, becomes ¯oats,'' released in the LES simulations of convection in the Labrador Sea, with those collected by the DLFs f ␰ ϭ ␯␩␷ zz f ␩ ϭϪ␯␰␷ zz, (9) (Steffen and D'Asaro 2002). Overall the agreement was excellent, except that the model ¯oats were unable to where we have neglected horizontal derivatives of the reproduce the large degree of temperature variance ob- vertical velocity in comparison with vertical derivatives served by the DLFs while moving up and down the of the horizontal velocities. Boundary conditions for (9) convective layer. As suggested by Harcourt et al., this, are and other less dramatic discrepancies in the mean heat ␶␶x y ¯ux and vertical turbulent kinetic pro®les found ␩ ϭ , ␰ ϭϪ at z ϭ 0 and within the upper quarter of the mixed layer, may be due ␳␯0 ␷ ␳␯0 ␷ to the lack of large-scale temperature and salinity struc- → → tures in the numerical simulations, and an omission of ␩, ␰ 0asz Ϫϱ. their interaction with wind stress. (10) One possible mechanism for the generation of the vertical temperature variance detected by both the hy- Solutions to (9), given (10) and assuming ␶ y ϭ 0, are

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC SEPTEMBER 2002 STRANEO ET AL. 2613

FIG. 9. Laminar Ekman solution in terms of vorticity [cf. (11)] for an easterly wind stress of 0.1 N mϪ2.

␶ x z ␰ ϭϪ ez/␦ sin and E ␳␯ ␦ FIG. 10. Schematic representation of the four basic numerical ex- 0 ␷ ΂΃ periments. Initial density distribution is in solid black and mean ¯ow direction is shown as black circles. Wind stress is shown above ver- ␶ x z z/␦ tical section in the gray circle, and the direction of ␩E ϭ e cos , (11) VE is indicated by the gray arrow. ␳␯0 ␷ ΂΃ ␦ where ␦ ϭ ͙2␯␷ / f is the Ekman layer depth. Thus, in the vorticity framework, the laminar Ekman balance equates the tilting terms in the vorticity equation i®cation is constant (N ϭ 3 ϫ 10Ϫ4 sϪ1). For nowind, (representing the generation of one horizontal vorticity destab and stab, density decreases linearly to the north component due to the tilting of the planetary vorticity at a rate of 0.001 kg mϪ3/km, and the ¯ow is westward vector by the other) with the vertical viscous terms. and surface intensi®ed. These parameters are typical of Given this, (10) and (11) illustrate how an easterly wind wintertime conditions in the interior of the Labrador stress is a source of meridional vorticity at the ocean's Sea, as discussed in SKR. Except where noted, a wind surface that, through the tilting of planetary vorticity stress of 0.1 N mϪ2 is applied uniformly over the interior vector, generates negative zonal vorticity within the Ek- of the model domain, rapidly decaying to zero at the man layer. Fig. 9. lateral boundaries. It is applied simultaneously with the surface buoyancy ¯ux. Due to the lateral boundaries b. Nonhydrostatic model there is both a baroclinic and barotropic ``wind in a channel'' response. However, the barotropic ¯ow does Baroclinicity is the other factor that contributes to the not affect the vertical structures, which are the focus evolution of zonal vorticity ␰, as seen in the last equation here, and the baroclinic response is con®ned to a few of (4). The term by represents the generation of vorticity kilometers of the lateral boundaries. To avoid such due to a horizontal density gradient. The last two terms boundary effects, results are shown for the central por- on the right-hand side of (4) represent the dilution of tion of the domain only. It is important to recognize vorticity due to mixing. We now use the nonhydrostatic that in the interior the horizontal density gradients are model to investigate the effects of baroclinicity and typically an order of magnitude smaller than in the wind together. boundary current region. Hence the wind-transported We present results from four different experiments buoyancy is negligible with respect to the surface buoy- (see Fig. 10): an initially horizontally homogeneous ancy removal. ocean subject to a wind stress, nobcl; a weak baroclinic ¯ow with no wind, nowind; the same baroclinic ¯ow with a destabilizing wind, destab; and stabilizing wind, 1) VORTICITY BALANCE IN THE CONVECTIVE CELLS stab. The stabilizing (destabilizing) wind scenario refers to the case of an Ekman transport of buoyancy across In all the experiments a convective cell develops as the baroclinic front, which increases (decreases) the ver- a localized downward displacement of isopycnals within tical stability. In all four experiments convection is driv- the surface thermal boundary layer. This localized dis- en by the same surface buoyancy loss of 2 ϫ 10Ϫ7 m 2 placement, associated with the sinking of dense ¯uid, sϪ3 applied for 3 days to an ocean whose vertical strat- generates vorticity of opposite sign on the two sides of

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC 2614 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32

FIG. 11. Snapshots of the zonal relative vorticity for convective cells under different conditions (positive is solid. negative is dotted, contour interval is 2 ϫ 10Ϫ4 sϪ1). ``Reference'' indicates the experiment with no wind and no initial baroclinicity. the dense core via the baroclinic term.2 This vorticity and, in our zonally invariant scenario of rolls, are char- is responsible for the broader and slower re- acterized by a positive and a negative vorticity lobe on gions surrounding the sinking. Thus, in the absence of either side of the sinking core. For the sake of com- any background spatial inhomogeneities or wind stress, parison with the four experiments described above we convective cells are symmetric about the vertical axis, show the typical signature of plumes in a scenario with no wind and no initial horizontal strati®cation (Fig. 11). 2 The source of the baroclinicity in this case is the localized sinking The addition of a wind stress implies, as argued of dense ¯uid, which is distinct from the baroclinicity resulting from above, the generation of a surface boundary layer of a large-scale horizontal density gradient. vorticity. For example, an easterly wind stress, as is

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC SEPTEMBER 2002 STRANEO ET AL. 2615 applied in nobcl, is a source of negative zonal vorticity pro®les of the meridional velocity, perpendicular both in the Ekman layer (Fig. 9). Our experiments show how to the wind and to the baroclinic ¯ow, are shown in Fig. this surface layer of negative vorticity is continuously 12 for the four scenarios. In each case the laminar Ek- depleted as convective cells transfer vorticity from the man solution for the meridional velocity3 is shown as boundary layer into the interior via vertical advection. well. No secondary circulation develops in the no-wind This wind-generated vorticity advected out of the Ek- and no-baroclinicity case (not shown). The model ve- man layer, in turn, causes the plumes to become ver- locity pro®les shown are obtained by averaging both in tically sheared (Fig. 11). Hence, of the two upwelling space, over the interior 30 km of the domain, and in lobes surrounding the central sinking core, the one time, over one day, during active convection. The av- whose sign is the same as that generated by wind tends eraging is necessary both to remove the plume vari- to dominate (Fig. 11). A parcel initially located at the ability and, more importantly, the inertial oscillations surface will ®rst be advected northward within the Ek- that are generated during convection. The amplitudes man layer but, once entrained by sinking ¯uid and ad- are reduced as a result of this averaging but retain their vected vertically out of the boundary layer, will move vertical structure. southward. While driving a similar vertical asymmetry Wind alone acting over an overturning ocean, nobcl, in the plumes, this mechanism is essentially different drives a laminar Ekman-type solution in the top layer from that of slantwise convection described in SKR. In and a weaker, broader return ¯ow at depth within the the latter case the tilting of plumes occurs as a result convective layer (Fig. 12) due to the vertical advection of the baroclinic term due to the background horizontal of wind-generated vorticity. In the absence of wind, but strati®cation and the net effect is for ¯uid to sink and in the presence of a horizontal strati®cation, nowind, the spread toward the lighter ¯uid (Fig. 11). When wind secondary circulation is the thermally direct one that is and background lateral strati®cation are both present, typical of slantwise convection (Fig. 12; see also SKR). the two effectsÐbaroclinicity and advection of surface Coupling of the baroclinic and wind effects generates vorticityÐcouple. In the stabilizing case these two vor- a two-layer thermally direct circulation in stab (Fig. 12) ticity producing terms are of the same sign resulting in and a three-layer circulation (thermally indirect above strongly sheared plumes (Fig. 11). In the destabilizing thermally direct) in destab (Fig. 12). In both cases the case the two terms are of opposite sign, and the two surfacemost ¯ow is con®ned to the Ekman layer. The mechanisms are in competition. In the latter scenario decreasing importance of wind effects away from the for typical interior Labrador Sea parameters, this surface is evident in the direct circulation below the amounts to quasi-vertical plumes (though not vertically indirect one in the destabilizing case. A series of ex- uniform properties, see below). periments with varying wind intensity reveal how the It is important to realize that the magnitude of these cross-over point between the thermally indirect and the two terms will, in general, vary with depth. For the thermally direct circulation becomes deeper with in- background baroclinic term, the variation is dependent creasing wind speed (not shown). on any changes of the horizontal strati®cation with It is conceivable that the secondary circulations depth. In our experiments this term is set to be spatially shown above are capable of creating vertical structure uniform. The wind term, on the other hand, decays away in an ocean that previously had none or very little. To from the surface as the vertically advected vorticity is show this we introduced a passive tracer in the model, diluted by mixing. Hence in our simulations, the vertical whose distribution can effectively show the cumulative advection term tends to dominate in the upper portion effect of the secondary circulation. The tracer concen- of the convective layer, while the baroclinic term be- tration is initially vertically homogeneous but linearly comes more relevant in the lower portion. We can es- increasing toward the north. We plot pro®les of tracer timate the relative importance of the two terms by com- concentration anomaly that are averaged over the in- paring their magnitude at the surface: terior 30 km of the domain. In all of the runs with wind we show results for three different stress magnitudes: wind f ␶/␳␯ 3 ϫ 10Ϫ7 ϭ 0 ␷ ϭ 30, 0.05, 0.1, and 0.2 N mϪ2. In the absence of a horizontal ഠ Ϫ8 baroclinicity By 10 strati®cation the tracer anomaly distribution is solely where the magnitude of the wind term is estimated via due to tracer transport within the Ekman layer and sub- the wind stress condition. Thus, close to the surface, the sequent vertical mixing of this anomaly within the con- wind stress tends to dominate the vorticity evolution vective layer. The net effect is a quasi-vertically ho- and is more effective in deforming plumes than a hor- mogeneous anomaly of tracer concentration within the izontal density gradient. mixed layer (Fig. 13). An increase or decrease in the wind stress simply enhances or decreases the anomaly. For the slantwise convection case, the thermally direct 2) SECONDARY CIRCULATION circulation results in a decrease (increase) in tracer con- One of the effects of tilted plumes is the generation of a secondary circulation in the plane perpendicular to 3 This can be derived from (11) by assuming that the velocity tends → the direction of the mean current or mean wind. Vertical to zero as z Ϫϱ, and that uz ϭ ␶/␳0␯␷ and ␷ z ϭ 0 at the surface.

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC 2616 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32

FIG. 12. Horizontally and temporally averaged pro®les of the meridional velocity (solid) during convection for the four basic experiments. Overlaid is the laminar Ekman solution (dashed). centration in the upper (lower) half of the convective cillations generated by the plumes, our model proved layer (Fig. 13). This shows how vertical structure can to be an inadequate tool for exploring how these effects be created via slantwise effects alone. The effect of wind could be parameterized. Finally, because of the two- can further enhance the creation of vertical structure dimensional assumption used in our simulations, it is through the strongly sheared cells in the stabilizing case impossible for us to predict how three dimensional pro- (Fig. 13) or the more complex vertical structure of the cesses, such as plume±plume interactions, may affect ¯ow in the destabilizing case (Fig. 13). the vertical momentum and tracer concentration struc- These simulations demonstrate that, under the action tures observed here. In general we expect the real ocean of baroclinicity and wind, convective plumes do not to be more turbulent than our relatively viscous model, simply vertically homogenize quantities such as mo- and the effect of the smaller scales on the dynamics mentum or a passive tracer. This represents a dramatic described here must be investigated with more sophis- departure from the often-used assumption that proper- ticated models. If, however, wind effects tend to deform ties tend to be vertically uniform within mixed layers. plumes into roll-like structures, as observed in the LES Parameterization of these effects, then, cannot be easily simulations of Harcourt (1999), the two-dimensional re- achieved by simply increasing the magnitude of the ver- sults presented here should indeed apply. tical mixing over the depth of the convective layer. In- stead, one might require a vertically varying eddy dif- 5. Conclusions fusivity, as well as one that evolves in time as the con- vective layer deepens. We were unable to diagnose such This study has addressed the role of wind in con- an effective eddy diffusivity using this model. This is vection in strongly and weakly baroclinic ¯ows, a prob- in part due to the nonstationarity of the problem, given lem that ®nds a natural application in the Labrador Sea the continuously evolving convective layer, but also to boundary current system and interior. In the ®rst part the large degree of variability present in our simulations. of the paper we showed, using simple Ekman dynamics, Because of the limited domain, and of the inertial os- that the advection of buoyancy due to wind can be

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC SEPTEMBER 2002 STRANEO ET AL. 2617

FIG. 13. Vertical pro®les of tracer concentration anomaly (horizontally averaged) for the four basic experiments. When wind is applied, results from three different magnitudes of wind stress are shown: ␶ (inNmϪ2) ϭ 0.1 (solid), 0.2 (dashed), 0.05 (dash±dot). The zero line is shown for reference. roughly one-third the size of the surface buoyancy ¯ux namics of convective mixing in the presence of weak in the strongly strati®ed baroclinic Labrador Current. baroclinicity and windÐapplicable to the interior Lab- Therefore, wind effects should not be neglected when rador Sea. This process leads to asymmetric develop- considering convection in such a ¯ow. Furthermore, in ment and deformation of the convective plumes. The agreement with the slantwise convection scenario of plumes remove wind-generated vorticity from the sur- SKR, we ®nd that the baroclinicity of the Labrador Cur- face Ekman layer and advect it to deeper depths, which rent results in a deeper and denser convective layer com- explains both the resulting plume distortion and the sec- pared to the one-dimensional mixing prediction. The ondary circulation that develops. This in turn gives rise combined effects of wind and baroclinicity suggest that to a pattern of mixing within the convective layer that intermediate convection can occur within the baroclinic generates vertical structure, as was demonstrated using portion of the Labrador Current, resulting in densities a passive tracer. The resulting vertical gradients contra- within the upper LSW range, which may even reach the dict the classic idea of convection as a means of ver- classic LSW range. While the speci®cs of our analysis tically homogenizing the ocean, which is in line with are pertinent to the baroclinic Labrador Current, the recent observations from the Labrador Sea. mechanisms discussed here can be generalized to any This study has shown, for two different oceanic re- baroclinic boundary current subject to large surface gimes, that convective mixing cannot be decoupled from buoyancy ¯ux and wind stress. In light of the results of the larger scales. It has also highlighted the shortcom- Spall and Pickart (2001), who argue that the net sinking ings of simple one-dimensional mixing schemes in a of dense ¯uid within the meridional overturning cir- baroclinic ¯ow ®eld. This suggests that parameteriza- culation mostly occurs at boundaries, we speculate that tions of convective processes need to be veri®ed against wind-facilitated convection in boundary currents may nonhydrostatic experiments in scenarios that are differ- be a sizable fraction of the total dense water mass ¯ux. ent from the idealized horizontally homogeneous sce- In the second part of the paper we addressed the dy- narios within which they were developed. Because of

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC 2618 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 the simpli®cations made, we are not able to address how Schott, and D. Farmer, 1999: Observing deep convection in the the dynamics described here can modify, or be modi®ed Labrador Sea during winter 1994±95. J. Phys. Oceanogr., 29, 2065±2098. by, three-dimensional processes such as vortex±vortex Pickart, R. S., and D. J. Torres, 1998: Wintertime hydrography of the interaction and by baroclinic instability. This needs to Labrador Sea during active convection. Eos, Trans. Amer. Geo- be addressed with more complex models. phys. Union, 79, OS174. ÐÐ, W. M. Smethie Jr., J. R. N. Lazier, E. P.Jones, and W. J. Jenkins, 1996: Eddies of newly formed upper Labrador Sea Water. J. Acknowledgments. FS would like to thank the School Geophys. Res., 101 (C9), 20 711±20 726. of Oceanography of the University of Washington, Seat- ÐÐ, M. A. Spall, and J. R. Lazier, 1997: Mid-depth ventilation in tle, and R. W. Sternberg, in particular, for support while the western boundary current system of the sub-polar gyre. completing a portion of this work. RP was funded under Deep-Sea Res., 44, 1025±1054. Contract N00014-97-1-0043 from the Of®ce of Naval ÐÐ, R. A. Clarke, and D. Torres, 2002: Hydrography of the Labrador Sea during active convection. J. Phys. Oceanogr., 32, 428±457. Research. Renfrew, I., G. W. K. Moore, P. S. Guest, and K. Bumke, 2002: A comparison of surface-layer and surface turbulent-¯ux obser- vations over the Labrador Sea with ECMWF analyses and NCEP REFERENCES reanalyses. J. Phys. Oceanogr., 32, 383±400. Rhines, P. B., and J. R. N. Lazier, 1995: A 13-year record of con- Haine, T. W. N., and J. Marshall, 1998: Gravitational, symmetric, and vection and climate change in the deep Labrador Sea. Atlantic baroclinic instability of the ocean mixed layer. J. Phys. Ocean- Climate Change Program: Proceedings of the PI's Meeting, A. ogr., 28, 634±658. M. Wilburn, Ed., University Corporation for Atmospheric Re- Harcourt, R. R., 1999: Numerical simulation of deep convection and search, 57±64. the response of drifters in the Labrador Sea. Ph.D. thesis, Uni- Schott, F., M. Visbeck, U. Send, J. Fischer, L. Stramma, and Y. De- versity of California, Santa Cruz, 367 pp. saubies, 1996: Observations of deep convection in the Gulf of ÐÐ, E. Steffen, R. W. Garwood Jr., and E. A. D'Asaro, 2002: Fully Lions, northern Mediterranean, during the winter of 1991/92. J. Lagrangian ¯oats in Labrador Sea Deep Convection: Comparison Phys. Oceanogr., 26, 505±524. of numerical and experimental results. J. Phys. Oceanogr., 32, Spall, M. A., and R. S. Pickart, 2001: Where does dense water sink? 493±510. A subpolar gyre example. J. Phys. Oceanogr., 31, 810±826. Lab Sea Group, 1998: The Labrador Sea Deep Convection Experi- Steffen, E., and E. D'Asaro, 2002: Deep convection in the Labrador ment. Bull. Amer. Meteor. Soc., 79, 2033±2058. Sea as observed by Lagrangian Floats. J. Phys. Oceanogr., 32, Lazier, J. R. N., and D. G. Wright, 1993: Annual velocity variations 475±492. in the Labrador Current. J. Phys. Oceanogr., 23, 659±678. Straneo, F., and M. Kawase, 1999: Comparisons of localized con- Lavender, K., R. E. Davis, and W. B. Owens, 2000: Mid-depth re- vection due to localized forcing and to preconditioning. J. Phys. circulation observed in the interior Labrador and Irminger Seas Oceanogr., 29, 55±68. by direct velocity measurements. Nature, 407, 66±69. ÐÐ, ÐÐ, and S. Riser, 2002: Idealized models of slantwise con- Lilly, J. M., P. B. Rhines, M. Visbeck, R. Davis, J. R. N. Lazier, F. vection in a baroclinic ¯ow. J. Phys. Oceanogr., 32, 558±572.

Unauthenticated | Downloaded 09/24/21 12:10 PM UTC