Frontogenesis, Subduction, and Cross-Front Exchange at Upper Ocean Fronts

Home , Downwelling, Front (oceanography)

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. C2, PAGES 2543-2557, FEBRUARY 15, 1995

Frontogenesis, subduction, and cross-front exchange at upper ocean fronts

Michael A. Spall Department of PhysicalOceanography, Woods Hole OceanographicInstitution, Woods Hole, Massachusetts

Abstract. The subduction of water at upper ocean fronts driven by internal instabilities is investigated.A simpleanalytic model which assumesconservation of potential densityand potential vorticity is used to characterizethe expectedstructure of subductedparcels as a function of the surface layer depth and the length scale of the parcel. Parcels subducted from a deep surfacelayer will be characterizedby anomalouslylow potential vorticity and anticycloniccirculation, while shallowsurface layers result in subductedparcels with high potential vorticity and cycloniccirculation. A nonlinear isopycnalprimitive equation model is used to demonstratehow baroclinicinstability and the resulting frontogenesisforce the subductionof parcelsbelow and acrossthe front. Frontogenesisgenerates vertical velocities of 0(30 m d-•) and ageostrophiccross front flowsof 3 to 5 cm s-•. The subductionis achievedby the deep ageostrophicflow which carries water from the surface layer below and acrossthe front. The subductedparcels quickly developa circulation through balanced adjustment, anticyclonicfor deep surfacelayers and cyclonicfor shallow surfacelayers. The characteristics of parcels subducted in winter conditions closely resemble a class of eddies called submesoscale coherent vortices. The horizontal and vertical scales of the vortices are determined by the frontogenetic mechanism and the depth of the surface layer. The total permanentsubduction rate is estimatedto be 20 m yr-• for frontal subductiondriven by frontogenesis,although local (and temporary)subduction can be muchlarger. The subducted anticyclonic vortices are often coupled to upper ocean cyclonic vortices, thus forminga baroclinicdipole that propagatesat approximately3.5 cm s-• and is capableof transporting the anomalouswater propertiesfar from the region of formation. Similarities with observationsin the North Atlantic Subtropical ConvergenceZone and near the Gulf Stream are discussed.

1. Introduction ter through subductioncan significantlyinfluence the biologicalcycle [Strass, 1992]. The processby which water is transferred from the The physicsof oceanicsubduction are not well known. mixed layer into the stratified interior of the ocean is It is believedto be at leastpartially controlledby the generally referred to as subduction. This processis be- large-scalevariations in atmosphericwind stresscurl lieved to be important to the physicsof both the oceans and net buoyancyflux (see, for example,Marshall et and the atmosphere. The properties of the main ther- al. [1993,and references therein]). The generalpattern mocline in the ocean are to a large degree set when the of westerlies at midlatitudes and trade winds at low water parcels were last in contact with the atmosphere. latitudes sets up a convergentEkman transport with Dynamical properties, such as potential vorticity, den- implied downwellingat the regionof the subtropical sity, and temperature, play an important role in de- convergence zone where the wind stress curl is a maxi- termining the large-scalecirculation and stratification mum. This vertical velocitycontributes at leastpart of within the main thermocline. The absorption of chemi- the massflux from the mixed layer into the permanent cals from the atmosphereby the ocean dependsstrongly thermocline. The surfaceof the permanentthermocline on the subductionprocess and may play a key role in is not horizontal, however, and a horizontal flow from a the globalclimate system.In addition, biologicalactiv- regionof a deepmixed layer into a regionof a shallow ity is particularly large in the near-surfacelayers, and mixed layer also transfersmass from the mixed layer the exchangeof nutrients and biologicallyactive mat- into the permanent thermocline. Simple calculations indicate that, on large scales,this mechanismcan be of the sameorder of magnitudeas Ekmanpumping [Mar- Copyright 1995 by the American GeophysicalUnion. shall et al., 1993]. Paper number 94JC02860. Upper ocean fronts are also thought to be places 0148-0227/95/94JC-02860505.00 where subduction might occur becausethey are re-

2543 2544 SPALL: FRONTAL SUBDUCTION gions where deep isopycnalshave large vertical excur- This paper is outlined as follows. A simple analytical sions and often outcrop into the surface mixed layer. solution that providessome guidelines for the structure Surface-intensifiedfrontal regions are found in many and circulation of parcels exchangedacross a potential places throughout the world's oceans. Some are per- vorticity gradient is presentedin section2. In section3 manent, large-scalefeatures of the general circulation, a nonlinear primitive equation model is applied to the such as the Gulf Stream, Kuroshio, and the Antarctic problem of frontal subduction for two distinct initial Circumpolar Current. Other fronts are intermittent in conditions. The subduction mechanism and its rela- nature where they may exist for timescalesof weeks tionship to submesoscalecoherent vortices are discussed to months and then break down, such as those found in section 4, and final conclusionsare presentedin sec- in regions of Ekman convergencelike the Subtropical tion 5. ConvergenceZone (STCZ) in the North Atlantic and Pacific. Strong frontal regionsare often observedalong the periphery of larger-scale mesoscaleeddies in the 2. A Simple Model for Subducted North Atlantic STCZ between22øN and 32øN [Halli- Parcels well et al., 1991]. Simplescaling estimates by Follows and Marshall [1994]that are basedon the ageostrophic A simple model is developedto describe the struc- axial circulation associatedwith frontogenesissuggest ture of parcels that are transferred across a localized that subduction driven by frontal processesmay be potential vorticity gradient. The model is developed as large as that due to the large-scaleEkman conver- and discussedwithin the context of frontal subduction, gence. (Similar ideas are applied to exchangein the however, the underlying dynamics are relevant to the atmospherictropopause by Followsand Austin [1992].) more general class of problems. Frontal regionsoften Pollard [1986]found parcelsof low potential vorticity mark a transition between different water masses and water below the mixed layer on the warm side of one havean associatedchange in stratification(or potential of these fronts whose temperature and salinity charac- vorticity) acrossthe front. This is particularlytrue for teristics suggestedthat it originated upstream in the isopycnallayers that outcrop in the frontal region. The mixed layer on the cold side of the front. We focus here thicknessof the surface layer is strongly influencedby on this subclassof fronts which are largely confinedto local atmosphericforcing, however;once subducted be- the upper few hundred meters, although many of the re- low warmer surfacelayer waters, the water is no longer sults presentedhere are relevant in a generalway to the directly forced by the atmosphere and approximately broader class of surface-intensifiedfronts. The present conservesquantities such as heat and potential vorticity. focusis motivated by their abundanceand the relatively A consequenceof this is that the depth of the surface high-resolutiondata setswhich have beencollected near layer on the cold side of the front is generally different these fronts (such as the Frontal Air-Sea Interaction from the thickness of the same isopycnal layer below Experiment(FASINEX); see Weller [1991], Pollard and the surface on the warm side of the front. In the vicin- Regier[1992] (hereinafter referred to as PR92), and the ity of mixed layer fronts this transition can take place data reportedby Voorhisand Bruce[1982] (hereinafter overhorizontal scales of O(10 km). If a columnof wa- referredto as VB82)). ter is transferred from the surfacelayer to the stratified The relative influences of internal frontal processes interior, its thicknesswill be anomalousrelative to the and external atmosphericforcing on frontal subduction ambient stratification. A schematic of such a subducted are not known. The evolution of actual upper ocean water parcelis shownin Figure I for the situationwhere frontsis likelyto be influencedby surface•rcing (wind the surfacelayer is thickerthan the sameisopycnal layer and buoyancy),turbulent mixing in the mixed layer, in the stratified interior. This situation is typical of and large-scaleflows in addition to the front's own in- fronts observed in the North Atlantic STCZ in winter. trinsic time dependence.In the presentstudy the mech- If the parcel conservespotential vorticity as it is carried anisms inherent in the internaT instability of the front acrossthe front, the thermal wind relation requiresthat are isolated from these other complicating factors in the subductedparcel be squashedand spreadlaterally order to obtain a clearer understandingof this underly- as it developsa horizontal circulationand negativerel- ing component.This is justified by the scalinganalysis ative vorticity. of Followsand Marshall [1994],by the relativelyshort The model consistsof three isopycnal layers, as in- timescales of baroclinic instability and the associated dicated in Figure 1. The thicknessof the surfacelayer frontogenesisthat are O(1 week), and by the consis- on the cold side of the front is hm, the thickness of tency betweenthe resultspresented here and variousob- the same isopycnallayer in the interior is hi, and the servations. It is expectedthat these resultswill remain thicknessof the subducted parcel is h. The horizontal relevant to the more generalsystem, and investigations scaleof the subductedparcel is L, and g• is the reduced into the influencesof atmosphericforcing and an active gravity(assumed to be constantbetween layers I and 2 mixed layer will be the subjectof a later study. Many is- and layers2 and 3). Layer 3 is assumedfor simplicity suesaddressed here are alsorelevant to the more general to be infinitely thick and motionless.The frontal width problem of mass exchangeacross a potential vorticity and the depth of the surfacelayer on the warm side of gradient. the front are not important, althoughit is assumedthat SPALL: FRONTAL SUBDUCTION 2545

upper ocean front v- -•- + • + 4Rg'•r.r (2) where R is the radius of curvature and r is the radial direction. The relative vorticity is given by

(•v v (3) subducted parcel The coupledset of (1), (2), and (3) determinesthe thickness of the isopycnal layer and the circulation ve- Figure 1. Schematicof the upper ocean front, three locity of the subducted parcel as a function of radius. isopycnallayer configuration.The surfacelayer depth is h,•, the thicknessof this isopycnallayer in the stratified Layered approximations to these equations have been interior is hi, the thicknessof the subductedparcel is solvedfor by Flicrl [1979] (hereinafterreferred to as h, and the radius of subductedparcel is L. F79), Ikcda [1982],and McWilliams[1988]. Following the procedure of F79, these equations may be combined to form a second-orderpartial differential equation for the thicknessof the upperlayer is O(h,.•) and sufficient the velocity v as to prevent outcropping of parcels that are subducted Oe 10v 1 v v • across the front. We assumethat the subductedparcel originated from Or2 t v = 0, (4) the cold side of the front in the surface layer with no rel- whereLd -- (g'hm)X/2/fis theinternal deformation ra- ative vorticity and that potential density and isopycnal dius. The thicknessof the parcel may then be calculated potential vorticity q are conservedas the parcel is sub- from the velocity as ducted below the front. It is, of course,straightforward to modify the potential vorticity to reflect a nonzero initial relative vorticity. The conservationof potential h-h 1+7+7 . vorticity may be expressedas The boundary conditions to be satisfied are v - 0 f fq-• at r = 0, h = hi at r = L, where L is the radius of q- hm= h ' (1) the vortex. Equations(4) and (5) are solvedusing a fourth-order Runge-Kutta method by integrating from The planetaryvorticity is f (constant),and ( is the rel- the center of the vortex out to the radius where h -- hi. ative vorticity calculated within an isopycnallayer. By The potentialvorticity of the vortex(or f/h.•) and the using the isopycnalrelative vorticity, we are able to in- thicknessat the center of the vortex are initially spec- corporate the twisting terms, which convert horizontal ified. The solution then gives the radius of the vortex vorticity into vertical vorticity, implicitly into the con- (or equivalentlythe Burger number) and the velocity servation relation. PR92 have found that these terms profile. The condition that h = hi at r = L differs from may be important in the vicinity of such upper ocean the vanishinglayer thicknesscondition required by F79. fronts. This results in a continuous layer thickness, but a dis- For the present analysiswe will adopt the somewhat continuouspotential vorticity profile at the edge of the conservativedefinition of a subductedparcel as one that vortex. This is consistent with the idea that the wa- is carried below the surface layer and away from the ter within the vortex originated on the other side of front. The physical motivation for this definition is the front and is thus not constrained(nor expected) that such parcels are the most likely to be observedin to have the same potentiM vorticity as the surrounding and to impact the general circulation. This approach water. It will be shown that this permits a much wider also allows us to obtain an analytic solution, by assum- range of both anticyclonicand cyclonicsolutions than ing that the subductedparcels are characterizedby a found in the vanishinglayer thicknessmodels of F79, vortex of radius L. Much of the following analysis is McWilliams [1988],and Killwomb[1983]. qualitatively valid for more general parcel shapes and The thicknessof a subducted parcel at the center h0 for parcelswhich remain dynamically influencedby the is shownin Figure 2a • a function of the surfacelayer front. The mechanismby which the parcel is subducted depthh• andthe Burgernumber (B = g'h•hi/f•L•). is not known or specifiedat this point; however,it will All thicknesseshave now been nondimensionalized by be shownin the following sectionthat frontal instabil- the interior layer thickness hi. Parcels with an anoma- ity and frontogenesiscan forceparcels to crossthe front lous surfacelayer depth (h• • 1) will developa cir- and become subducted in a manner consistent with this culationonce subducted according to (2). The result- simple model. ing generation of relative vorticity requiresa changein The velocity within an isopycnal layer is related to thickness in order to conservepotential vorticity as re- the layer thicknessthrough the gradient wind relation quired by (1). For h• > 1 the subductedparcel will as have negative relative vorticity and must thus experi- 2546 SPALL: FRONTAL SUBDUCTION

(o) 10• The thickness anomaly of the anticyclonesis very smallas the radiusbecomes small (B >_O(1)) because the maximum slope of the interface is limited by the gradientwind relation. Killworth[1983] showed that for vanishing layer thicknessoutside the vortex the radius _o• 100 of thevortex cannot be less than 2(2g•h•)•/2/f (where h• is now the dimensionallayer thicknessat the vortex center),which means the Burgernumber of the parcel (basedon the parcel thickness) B = g•h•/f2L• < 0.125. This constraintmay be generalizedfor a Burger number i i i i iii i • i definedwith the surfacelayer thicknessand allowingfor 100 10 • a nonzero layer thickness outside the vortex to be Burger number B h,•

ß B< 8(h0-1)' (6) (b) • o• where h0 is the nondimensional thickness of the parcel at the center. This relation is the same as Kill- worth's when the parcel thicknessis large comparedto the layer thickness outside the vortex, recoveringthe • 100 previous constraint on the minimum radius of anticyclones. However, anticyclonesof smaller radius are per- mitted when the thicknessof the isopycnallayer outside the vortex does not vanish. This smaller scale is consistent with the range of Burger numbers commonlyob- 10 -1 servedin submesoscalecoherent vortices [McWilliams, 10-• 100 10 • 1985].The thicknessanomaly (and circulation)can be quite large for B < 1, especiallyso for vortices with Burger number B very low potentialvorticity (large h,•). In this regime Figure 2. Solutionfor structureof subductedparcel as the lines of constant parcel thicknesshave a slope of a function of initial surface layer depth and the Burger OhmlOB= 8(h0- 1), as seenin Figure2a. number,(a) parcelthickness (solid lines h0 > 1, con- The relative vorticity at the center of the subducted tour interval is 1; dashed lines h0 < 1, contour interval parcel(scaled by f) is shownin Figure2b as a function is 0.1), and (b) parcelrelative vorticity (solid lines pos- of the surfacelayer depth and the Burger number. Con- itive, dashednegative, contour interval is 0.25). servation of potential vorticity requires that all parcels subducted from a surface layer with a depth greater encecompr•ession, while for hm < 1 the parcelwill have than the internal layer thickness develop anticyclonic vorticity to compensatefor vortex compression,while positive vorticity and undergo stretching during sub- all parcels subducted from shallow surface layers de- duction. The amount of compressionor stretching in velop cyclonic vorticity. For a surface layer that is just the final state is balanced by the offsetting generation the same thickness as the interior isopycnal layer, the of relative vorticity. As expected, if the surface layer subducted parcel can have no relative vorticity. As the is initially deeper than the interior layer thickness,the subductedparcel will alsobe thicker than the surround- surfacelayer becomesincreasingly deeper (shallower) than the internal layer thickness, the vorticity of the ing fluid and thinner than the initial surfacelayer depth (1 < h0 < hm). If the surfacelayer is the samethick- subductedparcel becomesincreasingly negative (pos- nessas the interior, the subductedparcels must also be itive). The gradientwind relation limits the anticyclonic vorticity to be greater than -1, however,cyclones of the samethickness (hm = h0 = 1). A thin surface are not subject to this constraint and can developvery layer resultsin local anomaliesthat are thinner than the large relative vorticity. The relative vorticity increases surroundingsand thicker than the initial surfacelayer with increasingBurger number (as the horizontallength depth (hm < h0 < 1). The Burgernumber is inversely scaledecreases) and with increasingthickness anomaly. proportional to the horizontal length scale. The sub- In the limit of small Burger number the anticyclone ducted parcelsmaintain a larger portion of their initial thicknessh0 -* h,•(1- 2B) and the relativevorticity surface layer thicknessas the horizontal scalesbecome • -, -2B becomedependent only on the Burger num- larger (B decreases),while parcelsof smallhorizontal scale must have a thickness that is closer to the ambi- ber of the parcel. ent thickness. Note that we have made no assumptions 3. Frontogenesis and Subduction about the volume of the subducted parcels. The volume is not constantin Figure 2a; it increaseswith increasing The simple model discussedin the previoussection h,• and with decreasingB. did not specify the means by which parcelsmight be SPALL: FRONTAL SUBDUCTION 2547

subducted below the front, nor did the solution deter- ducted. Wang [1993]has modeledthe developmentof mine the length scaleof the subductedparcels. It is ex- frontogenesisand parceldownwelling in the vicinity of pectedthat the verticalvelocities will have to be large an oceanfront and found verticalvelocities as large as in order for parcelsto be adiabatically subductednear 80 m d-•. Thissuggested that subductionwas taking fronts becausethe isopycnalsurfaces are very steep. place, althoughthe model integrationswere not long In addition, we anticipate that someageostrophic flow enoughto determine the amount or structure of any component will be required to transfer parcels across fluid parcelswhich might have been permanentlysub- the isobars that are coincident with the front. It is now ductedacross the front. Samalsonand Chapman [1995] demonstratedthat frontogenesiscan provide a mecha- have modeledthe large-amplitudebehavior of an up- nism for this parcel subduction and scale selection. per oceanfront similar to caseA belowusing a spectral Becausethe theory of frontogenesisis well described primitive equation model. They find similar vertical ve- in the literature(see, for example,Hoskins [1982]), only locities and plumesof low potential vorticity to those a brief review of the mechanism will be included here. reported here. Frontogenesisrefers to the rapid developmentof strong horizontalgradients in densityfrom a preexistingweak 3.1. An Isopycnal Primitive Equation Model of densitygradient. If a confluentlarge-scale flow field ex- Frontal Subduction ists, it will act to increasethe horizontaldensity gradi- An isopycnalprimitive equation model is now usedto ent over a portion of the front. The confluentflow might test whether, under certain circumstances,frontal in- be supplied by a large-scalegeostrophic flow field or stability and frontogenesismight lead to parcel subduc- by finite amplitudebaroclinic wave development along tion, and whether the simple model introduced in the a preexistingfront. As parcels are carried along the previous sectionis a useful predictor of the structure of front into the region of confluentflow, they must expe- such parcels. We expect primitive equationphysics to rience an acceleration in order to remain in cross-front be necessaryto capture the nonlinearaspects of fronto- geostrophicbalance. This accelerationis compensated genesisthat are important to the developmentof large for by an ageostrophicvelocity accordingto the semi- Rossbynumber featuresand large vertical velocitiesan- geostrophicmomentum balance as ticipated to be important in frontal subduction. The Dug isopycnalconfiguration allows for adiabatic evolutionof f - Dr' (7) the flow becausecross-isopycnal mixing is not necessary where va is the ageostrophiccross-front flow and ug for computationalstability. As indicatedin section2, it is the geostrophicalong-front flow. Thus for an upper is expectedthat this will be important to the final state oceangeostrophic flow that is acceleratingdownstream, of the subductedparcels if potential vorticity is con- an ageostrophicflow developsdirected from the anticy- served. It is recognizedthat in the real ocean,parcels clonic(warm, assumingnorthern hemisphere) side to may not conservetheir potential vorticity, particularly the cyclonic(cold) sideof the front. As the jet acceler- in the vicinity of the surfacelayers, and that the solu- ates, cyclonic vorticity is increasedon the cyclonicside tions discussedhere and in the previoussection are most of the front and anticyclonicvorticity is increasedon the relevant to the ideal limit. I believe that the conserva- anticyclonicside of the front. Conservationof potential tive model is the appropriate place to start becauseof vorticity requires that the horizontal flow be convergent the clarity and understandingthat conservationprinci- on the coldside of the front (downwelling)and divergent ples bring to the problem. The results presentedhere on the warm sideof the front (upwelling).Mass conser- will also provide a basisfor understandingthe role of vation closesthis vertical cell through an ageostrophic nonconservativeprocesses in more complex models in flow from the cold side to the warm side in the subsur- the future. face layer below the front. A schematic of the familiar The model equations. The model used is the ageostrophiccirculation in the vicinity of the front is isopycnalprimitive equation model describedby Black shownin Figure3 (similarsketches are givenby Hoskins andBoudra [1986]. The modelsolves the horizontalmo- [1982],Bleck at al. [1988],and PR92). The deepcross- mentum equations and the continuity equation within front ageostrophicflow will tend to carry parcelsfrom each layer. The layer-integratedhorizontal momentum the surfacelayer below and acrossthe front, suggesting equations are written as that the parcel may become at least temporarily sub- cyclonic•,•_.• onticyclonic 0---•-+ V-- - (• + f)k x v + ond I comoression = +(Ap)-•V ß(AApVv) + (v* - v)/7 (8) downwellingstrelrcaingv •x.l • •nd where v - (u, v) is the horizontalvelocity vector, p tlinq is the pressure, k is the vertical unit vector, ( = Figure 3. Schematicof ageostrophicvelocity resulting Ov/Ox- Ou/Oy is the relativevorticity, M - gz + pa is from frontogenesisnear an upper oceanfront. the Montgomery potential, a is the specificvolume of 2548 SP•LL: FRONTALSUBDUCTION the layer(constant), Ap is the pressurethickness of the anomalies of the three isopycnal layers are taken to be layer, and A is an eddy viscosity coefficient. An addi- 25.7, 26.0, and 26.3 kg m-a, givinga reducedgravity tional term has been added to the standard momentum g• - 0.003 m•' s-x. The body forceterms are imple- equations that relaxes v toward a specified value v* mented between y = 0 and y = 60 km with a restoring with time constant7. This forcing term is nonzeroonly timescale7- 3 days. over a small downstream extent of the model domain Two caseswill be reported here, one with a deep sur- and is used to investigatethe influenceof a maintained face layer and one with a shallowsurface layer, as shown baroclinic inflow of the jet. Featureswhich are advected schematicallyin Figure 4. The deep surfacelayer case into this regionfrom upstream(periodic boundary con- (caseA) usedparameter values of fix= 100m, ti•.= 0 m, ditions)are slowlysuppressed toward the inflowstruc- and D•. = 125 m. In this case the cold surface layer is ture specified by v*. The results presented here are 125 m deep and the thicknessof this same isopycnal qualitatively unchangedwithout this forcingterm; how- layer away from the front on the warm side is 25 m, a ever, after longtimes (greater than 50 days)the front factorof 5 less.The shallowsurface layer case (case B) becomesmore diffuse and convolutedand a larger vol- used values of fix = 75 m, tb. = 150 m, D•. = 200 m. ume of water becomessubducted away from the surface The shallow cold surface layer is 50 m deep, while the (seesection 4). thicknessof this layer away from the front on the warm The continuity equationis representedas a prognostic side is 125 m, a factor of 2.5 more. The cross-front equation for the layer thickness Ap, scale is taken to be 1 = 16 km in both runs. Instability and meander developmentare initiated by introducing OAp Ap* - Ap a superpositionof small-amplitude(1 km) meandersbe- + v. - . tween 75 km and 300 km wavelength. The maximum depth of the model domain is 300 m. Additional runs A restoring term similar to that in the momentumequa- have been carried out with an initially motionlessfourth tions is included in the continuity equation to force layerbetween 300 m and 1000m depthwith •r0= 27.3 the layer thickness toward a specified value that is in that are qualitatively the same as those discussedhere, geostrophicbalance with v*. so it is not believedthat the shallow model domain sig- Initial conditions. The initial conditions reflect nificantly influencesthe results. Turbulent mixing along a preexisting frontal region that is composedof three isopycnalsurfaces is parameterizedby a Laplacian vis- isopycnal layers. The front is sufficientlystrong that cositywith a coefficientof A = 5 m•' s-x. Thereis no the uppermostlayer outcropsin the frontal region, ex- cross-isopycnaldiffusion or stressbetween layers. The posing the secondlayer to the atmosphereon the cold model has been made as inviscid as possible,within nu- sideof the front (indicatedschematically in Figure1). merical stability constraints,in order to use potential The initial interfacedepths are definedby the following vorticity conservationas a guide to the interpretation functions: of the results. While the real ocean may include com- px = fixtanh [2(x- xo)/1], (10) plex mixing and diabatic effectsthat are very poorly understood,it is felt that for such a process-oriented 1 study the conceptualadvantages of the adiabatic, in- p•.- D•.+ •5•.(tanh [2(x- xo)/1]- 1), viscid limit outweigh the loss of simplicity that must where p• is the depth of interface k, 5• is the changein accompanythe inclusionof more complexmixing pa- the depth of layer k acrossthe front, D• is the depth of rameterizations. interface 2 away from the front on the warm side, 1 is The deepsurface layer front caseis similar in param- the horizontal scale of the front, and x0 is the position eter space to the fronts in the North Atlantic STCZ of the front. For x < x0 the interface between layers studiedby VB82, Pollard[1986], Eriksen et al. [1991], I and 2 outcrops and px is set to zero. These interface PR92, $amelson[1993], and $amelsonand Chapman depths also define the forcing ter• Ap* and v*, with a [1995].It is stressedhere that the presentcalculations motionlessdeep layer. We do not incorporate or study the processeswhich are responsible for the initial formation of the front or the depth of the surface layers but merely initialize the model with a structure which t2.5 m •00m ! is consistent with the fronts observed in the STCZ. The body force term may be thought of • a crude par•e- terization of the actual external forcingwhich maintains the observed fronts in the ocean. The model domain is 300 km by 300 km with a hor- deep mixed layer sh(•llowmixed I(•yer izontal grid resolution of 2 km. The boundary conditions are free slip at x - 0 and x - 300 km and periodic Figure 4. Schematicof model initial conditionsfor in the y direction. The Coriolis parameter is taken to (a) caseA, the deepsurface layer, and (b) caseB, the be f = 10-4 s-x and constant.The potentialdensity shallow surface layer. SPALL: FRONTAL SUBDUCTION 2549 are not intended to be a prediction of any particular ob- this compression,each of the subducted parcels has de- served frontal variability. We seek to understand how veloped anticyclonic vorticity, as indicated in Plate l d. the internal dynamicsof frontal instabilities might lead While the amplitude varieswithin the vortices,a typical to the subduction of parcels from the near surface be- valueof the relativevorticity (scaled by f) is -0.4. This low the front and to characterizethis processfrom two is sufficiently large that we expect the cyclostrophic extreme initial conditions,one with a deep surfacelayer force terms to be important in the gradient wind bal- and one with a shallow surface layer. ance. The anticyclonic vorticity and a subsurfacemaximum in velocity emphasize that these parcels are not 3.2. Case A: A Deep Surface Layer simply rings that have pinched off from the frontal in- This experiment is configured to approximate the stability in a manner consistentwith Gulf Stream ring fronts found in the North Atlantic STCZ in winter, as formation events. In fact, these subsurfacevorticies ap- studied in the Frontal Air-Sea Interaction Experiment pear often to be formed in connectionwith surface in- (FASINEX) [Weller,1991, and references therein]. The tensifiedcold corerings, as discussedfurther in the next early evolution of the deep surface layer front is con- section. sistent with what is expected based on linear stability The structure and amplitude of the subductedparcels theory. The small initial perturbations along the front is quite consistent with the results presented in sec- grow in amplitude through baroclinic instability; that tion 2. The nondimensionalsurface layer depth (parcel is, the perturbations are gaining energy from the po- thicknessbefore subduction) is hm - 5, and the sub- tential energy representedby the slopingisopycnals at ducted parcels have a nondimensionalheight h • 3.1 the front. The dominant wavelengththat emergesfrom and a relative vorticity at the core of approximately the random perturbations is of the order of 60 km, con- ( - -0.4. The diameter of the subducted parcels is sistent with the linearly most unstable mode and the approximately 25 km, giving a Burger number B - observationsof VB82. See $amelson[1993] for a dis- g•hmhi/f2L2 - 0.24. The uniformpotential vorticity cussionof the linear stability analysis of a similar up- solution discussed in section 2 predicts a nondimen- per oceanfront and $amelsonand Chapman[1995] for a sional height of the subducted parcel as h = 2.9 and numerical study of the nonlinear evolution of this most the relative vorticity as ( = -0.42, close to that seen unstable mode. The potential vorticity within layer 2 in Plate l d. This indicates that the structure of the is shown in Plate la after 8 days of integration. The parcels after subduction is not dependent on the de- deep surface layer is characterized by low q, while the tails of the subduction process,provided that potential stratified interior has high q due to its relatively thin vorticity is conservedduring the process. The gradi- layer thickness. The growing instabilities are evident ent wind balance is a good approximation to the final all along the front. The initial relative vorticity within dynamical balance of the vortices. layer 2 is very small, consistentwith the assumptions 3.3. Case B: A Shallow Surface Layer made in the analytic model in section 2. The front is still evidenton day 24 (Plate lb) as a The early development of the shallow surface layer sharpgradient in potentialvorticity, although its path is front (not shown)is similarto that for the deepsurface quite convoluted. Many small-scale features are found layer front. The development of baroclinic instability near the front, includinglong filaments, small cyclones and baroclinic waves introduces perturbations to the and anticyclones,and larger patchesof anomalousvor- front that develop cyclonic and anticyclonic vorticity. ticity. Severalregions of low q water have separatedon The timescale of the instability is shorter than for the the stratified side of the front. The cores of the vor- deep surface layer front because the vertical shear of tices have conservedtheir potential vorticity, although the velocityis approximately50% stronger(maximum in somecases, water characteristicof the frontal region initial velocityis 50 cm s-1) as the interfacebetween (intermediateq) has alsobeen carriedaway from the layer 2 and 3 now shallowsto 50 m on the cyclonicside front. The isolated vortices are approximately 25 km of the front. The cyclonic side of the front is now char- in diameter with a very sharp front in potential vortic- acterized by high q in layer 2, while the anticyclonic ity separating them from the ambient fluid, consistent side of the front has relatively low q. The frontal insta- with the assumptionsmade in section 2. The event that bility draws filaments of high q into the low q region, formed the vortex near x = 200 km, y = 75 km will be analogousto the processfound in the deepsurface layer discussed in detail in the next section. case. Once into the thicker low q water, the subducted As the parcels are carried across the front into the plumes are stretched vertically and develop strong cy- region of increasedstratification, they are also carried clonic vorticity. downbelow the warmersurface layer (subducted)and After 18 days of integration the unstable meanders compressed,as anticipated by the simple theory pre- have produced severalsmall, cyclonicfeatures of high q sented in section 2. The thicknessof layer 2 is shown in on the low q sideof the front (not shown).The coresof Plate lc on day 24. Each of the low q parcels has been anomalous vorticity are much smaller than the anticy- compressedfrom its initial thickness of 125 rn in the clonicfeatures producedin run A, approximately 8 km surface layer to approximately 80 m. Consistent with in diameter. This decrease in horizontal scale of the 2550 SPALL: FRONTAL SUBDUCTION

(o) 2.1 2.8 3.5 4.2 0.7 1.4 2.1 2.8 300 • • • • • • • • • i 300 • • • ! ! I I

250 250

200 200

150 150

100 100

5O 5O

O • o 50 100 150 200 250 300 o 50 100 150 200 250 300

(c) (d) 10.0 30.0 50.0 70.0 90.0 110.0 130.0 -0.8 -0.4 0.0 0.4 0.8 ,.•00 I ! I I I I ,jI I I I I ! I .__1! I I I I I I I ! ! I 250 250 -

200 200 -

150

100 ,._ 5O 1005O 0 0-1 I ! I I I !'i'lI I I ! 0 50 100 150 200 250300 0 50 100 150 200 250 300

Plate 1. Potential vorticity in isopycnallayer 2 for caseA with a deepsurface layer. (a) Early meander developmenton day 8 showinginitial protrusionof low potential vorticity water into the stratifiedinterior. (b) Later stageon day 24, whereseveral patches of low potentialvorticity water have crossedunder the front and are becomingisolated from the front. (c) Layer thickness and (d) relativevorticity of isopycnallayer 2 on day 24. Note that subductedlow potential vorticity parcelshave been compressedand have negativerelative vorticity.

core comparedto run A is largely becausethe parcels of 0.4, the predicted thicknessof the subductedparcels get stretchedvertically when they are subducted(with from section2 is h = 0.81 (101.25 m) with a relative a compensatinghorizontal contraction) instead of com- vorticity of ( = 1.0, which is in closeagreement to that pressionwith horizontal spreading. Much of the cy- found in the primitive equation model results. This ex- clonic circulation is composedof intermediate q water ample demonstratesthat the qualitative behavior pre- from beneath the front. The core characteristics of the dicted by the simple model is reproducedhere and em- cyclonesare well predicted by the adjustmentto gra- phasizesthe importance of the cross-frontpotential vor- dient wind balance in section 2. For a parcel radius ticity gradient for the adjustment processand senseof of 4 km and a surface layer nondimensionalthickness circulation in the subducted parcels. SPALL' FRONTAL SUBDUCTION 2551

4. Discussion dicated in the potential vorticity field upstream of the trough. A downwardvelocity of 30 m d-• is found in The discussionis focused on the development and the trough and an upward velocity 30 m d-• is found dynamics of case A, the deep surface layer, for several in the crest where the front is advectedinto the low q reasons. The shallow surface layer is more represen- water. This stretching and upwelling is a result of the tative of conditions in summer, when the upper ocean changein ambient layer thicknessand drives a strong is strongly stratified due to seasonalwarming. Parcels cyclonic circulation near x - 155 km, y - 75 km, as that are subducted at a front in summer will probably indicated by the geostrophiccomponent of the total ve- not be carried out of the seasonal thermocline and are locity in Plate 2c. This strong cyclone is consistent likely to be reentrained into the surface layer in the fol- with the linear stability predictionsof Samelson[1993], lowing winter. Thus while suchparcels might be formed the observations of PR92, and the model results of and be relevant to the structure of the seasonal ther- Wang[1993] and Samelsonand Chapman[1995]. This mocline, their influence on the general circulation away strong cyclonic circulation is advecting low q water un- from the upper surface layer is likely to be small. In der the front and high q water out from under the front. addition, the fronts observedin the STCZ are generally Note the beginning developmentof an anticycloniccir- found in winter, when the surface layer is deep relative culation along the edge of the cyclonic meander near to the interior stratification. x - 170 km, y = 70 km. The ageostrophicvelocity is shown superimposedon the potential vorticity field 4.1. The Subduction Mechanism in Plate 2d. There is an ageostrophicflow of approximately 3-4 cm s-• acrossthe potentialvorticity front The analysis focuses on the event that formed the in the same region where anticyclonic vorticity is ob- anticyclone seen at x - 200 km and y - 75 km on served in the geostrophicflow. This cross-frontflow is day 24 (Plate lb), althoughthe processis foundto be the deep signature of frontogenesisindicated schemat- common to all of the subduction events. Long time ically in Figure 3. The ageostrophicflow in the tight integrations(100 days)indicate that the sameprocess cyclone at x = 155 km, y = 75 km is in opposite direc- continuesto work at later times, when the front is quite tion to the geostrophicflow, while that along the anti- convoluted, but the picture is much clearer for the ini- cyclonic edge of the developingmeander is in the same tial set of formations because of the initially smooth direction as the geostrophicflow. This is as expected front and quiescent ambient water. The early develop- by the gradient wind relation becausethe geostrophic ment of the meander that formed the vortex is typical balance overestimates the flow in cyclonesand underes- of a baroclinic wave disturbanceon a meanderingfront. timates the flow in anticyclones. The horizontal velocity is shown superimposed on the The ageostrophicvelocity advects low q water across potential vorticity in layer 2 on day 8 in Plate 2a. The the potential vorticity front into the high q stratified initial conditions had zero velocity in layer 2 and a max- interior. The low q water adjusts to the stratified in- imum surfacevelocity of 35 cm s-•. The development terior accordingto the gradientwind relation(2). As of a cyclonic/anticyclonicvortex pair is evident. This indicated by the discussion in section 2, this requires situation produces a confluent flow near x - 160 km, that the low q parcel develop anticyclonic relative vor- y - 55 km, where the flow advectsthe low q (thick ticity; the early stages of this development are evident isopycnallayer) toward the regionof highq (thin isopyc- in Plate 2c. This adjustment takes place quickly, so nal layer). This causesan increasein the horizontalgra- the subducted water is developing anticyclonic vortic- dientof layerthickness (one may think of layerthickness ity even as it is still being carried acrossthe front by the as a proxyfor potentialtemperature) and is conducive ageostrophicflow. Thus the meander developsa dipole to the nonlinear frontogenesismechanism discussed pre- with cyclonic vorticity driven by stretching and anti- viously. cyclonic vorticity as the low q water is carried across The downstream velocity in the upper layer must in- the front and adjusts to the ambient stratification. The crease in the region of compressedlayer thickness in dipole pair propagatesinto the high q region, pulling accordance with the thermal wind relation. As indi- plumes of low q away from the front as seen in Plate 3a catedby (7), a cross-streamageostrophic velocity must and eventually separatesfrom the front in the high q re- balance the geostrophicdownstream acceleration in the gion. The cyclonic vorticity in layer 2 is suppressedby upper ocean. The resulting convergencein the upper the compressionof the water column, leavingmostly the layer leads to a downwellingon the cyclonicside of the anticycloneof low q subductedinto the regionof high q. front and, through potential vorticity conservation,the After the parcel has separated from the front, it is ap- development of cyclonic vorticity. The vertical veloc- proximately 25 km in diameter and nearly axisymmetric ity at the interface between layers 2 and 3 is shown in (Plate lb). By day 40 the dipolepair has propagated the vicinity of the developingmeander on day 12, su- well awayfrom the front (Plate 3b), travelingapproxi- perimposed on the potential vorticity in Plate 2b. The mately 3.5 cm s-x until it encountersthe boundaryof confluenceof the layer thicknessand, through thermal the model domain. The adjusted state in layer 2 shows wind, the acceleration of the upper ocean flow, are in- that the anticyclone is dominant over the cyclone in 2552 SPALL: FRONTAL SUBDUCTION

(o) (b) i 1.0 2.0 3.0 4.0 0.0 1 .o 2.0 5.0 4.0 80 ,,_[,•u,,'•.,- ,, .:.,:,._:-- 9O 7O

8O 6O

7O 5O

6O ! 40

140 150 160 170 140 150 160 170 10.0 cm s -1

90 -• •- •'-' ''. •,,''''' ' 90 • -'"- --L'• ,',,-' •ll • •, , • ,,, 8O

6O .... . 60 , •

140 150 160 170 140 150 160 170 ; 10.0 cm s-• ---* 2.5 cm s-1

Plate 2. Details of the subductionmechanism for a subregionof caseA (deepsurface layer). Various componentsof the velocity field are shownsuperimposed on the potential vorticity within isopycnallayer 2. (a) Horizonalvelocity on day8, (b) verticalvelocity on day 12 (contourinterval is 10 m d-•, dashedlines indicatedownwelling), (c) geostrophiccomponent of the horizontal velocityon day 12, and (d) ageostrophiccomponent of the horizontalvelocity on day 12.

the deep layer. The maximum geostrophicvelocity in potential vorticity) and developedits positiverelative layer 2 is approximately20 cm s-1 and the maximum vorticity as a result of stretching as it was carried away ageostrophicvelocity is approximately5 cm s-1 in the from the front. The water with anticyclonic vorticity in same direction as the geostrophic velocity, consistent the upper layer did not originate within the front. It with the gradient wind balance. has the same low potential vorticity as the surrounding The cycloneis dominant in the upper layer, although fluid in layer i and developsnegative relative vorticity there is still some anticyclonic circulation over the deep as a result of compressiondue to the deep anticyclone anticyclone,as shownin Plate 3c on day 40 (the con- raising the interface between layers i and 2. It is this touredfield is nowlayer thickness). This cycloniccircu- dipolar pairing of the baroclinic vortices that gives rise lation is similar to the more traditional cold ring pinch- to a self-propelling vortex pair that can rapidly carry off eventsthat are generally associatedwith vortex for- heat, salt, and other water properties away from the mation at fronts. The water in layer i with cyclonic front. Hogg and Stornrnel[1985] termed such vortex vorticity originatedwithin the frontal zone(it has high pairs hetons because of their ability to transport heat. SPALL- FRONTAL SUBDUCTION 2553

(b) r--r -- 45.0 60.0 75.0 90.0 105.0

120 ======

-i: ...... " "-'•>x-%,."•..,, : :'". , ß 100 ';"" ...... " " " •z •• • •'•.• k•//• •' '

60 140 150 160 170 180 190 230 250 270 290 -1 -1 velocity ---> 10.0 cm s velocity > 20.0 cm s

120

250 250 270 290 -1 velocity --• 20.0 cm s Plate 3. (a) Geostrophicvelocity superimposed onthe potentialvorticity in isopycnallayer 2 onday 18, (b) totalvelocity with potential vorticity in layer2 onday 40, and (c) totalvelocity with layer thicknessin layer 1 on day 40.

In somecases a clear dipolaf structuredoes not develop els of Robinsonet al. [1988] and Spall and Robinson from the model meanders and these subducted anticy- [1990]associated with coldring formation events. The clonesdo not propagateaway from the front. They horizontal scaleof the anticyclonesin their resultswas are eventuallyteentrained by the meanderingfront and largerthan that foundhere, consistent with the larger pulledback across (i.e., only temporarilysubducted). deformation radius associated with the Gulf Stream The presenceof a large-scaleflow may alsoserve to ad- front(approximately 35 km) comparedwith the inter- vect subductedparcels away from the front and avoid nal deformationradius for the presentupper oceanfront reentrainment,although/• is likely to becomeimportant (approximately6 km). Wood[1989] also formed deep to the large-scalepropagation of thesefeatures. anticyclonesfrom a primitiveequation model of the Analogousdipolaf structures were found in the quasi- Gulf Stream and interpreted the senseof circulation geostrophicand primitiveequation Gulf Streammod- throughconservation of potentialvorticity. Samelson 2554 SPALL: FRONTAL SUBDUCTION and Chapman[1995] find a plume formationsimilar in avoid arbitrary definitions of "low" potential vorticity the early stagesto that discussedhere and the forma- water and also to account for subducted water after it tion of a small anticyclone,although they do not find has mixed with the ambient water. This estimate in- a strong dipole, nor does the anticyclonefully separate cludesboth the temporary and permanently subducted from the front in their model. This differenceis pos- waters, although the cutoff of 10 m only influencesthe sibly due to either (1) the presenceof cross-isopycnalestimate of the temporary subductionrate becausethe diffusionin their modelor (2) their more continuously permanently subductedwater is all much deeper than stratified vertical representation(spectral decomposi- this depth, typically at depthsbetween 80 m and 150 m. tion) versusthe low-resolutionisopycnal representation The volume of permanently subductedwater is calcu- used here. This is speculationonly, however,and fur- lated by performingthe integral within layer 2 only at ther study is required to understand these differences. positionsgreater than x - 200 km, which was chosen to be outside the meander envelopeof the front. The 4.2. The Subduction Rate subduction rate is then calculated by dividing the to- A simple estimate of the volume of low potential vor- tal volume of subducted low potential vorticity water ticity water advected acrossthe front by frontogenesis by the time of integration and the surfacearea of the is now obtained. The maximum velocity in layer I in- modeldomain (9 x 10xø m•), assumingthat the density creasesfrom approximately40 cm s-x at the crestof of suchfronts in the oceanis one per width of the model the developingmeander to approximately50 cm s-x at domain. the trough as a result of the convergentlayer thickness. The total and permanent subductionrates are given This accelerationof 10 cm s-x takesplace over about in Figure 5 as a function of time for a 100-dayintegra- 10 km or in about0.2 days(following a parcelfrom crest tion. The temporary subductionrate is quite large, be- to trough),giving an acceleration rate of 5x 10-6 m s-2. tween100 m yr-x and200 m yr-x anddecreases steadily Togetherwith a Coriolisparameter of f - 10-4 s-x, after day 10. The permanent subduction rate begins this requires an average ageostrophiccross-front ve- to increaseon day 10, as the first vorticies are carried locity of 5 cm s-x from (7). Let the volumeof the beyond x - 200 km and after day 25 remains nearly subductedparcel be approximatedas vol - 2•r1•5/3, constantat 20 m yr-x. This indicatesthat the volume where I is the radius of the subducted parcel and 5 is of subducted water increases at a uniform rate and that its thickness. This estimate assumesthat the height the subduction mechanism continues to work even after is given by the uniform potential vorticity solution as the initially uniformfront is stronglyconvoluted (for ex- h(r) - h[1- (r/l)•]. If this ageostrophicflux occurs ample,see Plate I for day24). The sizeof the subducted acrossthe same length scale I along the front, then the parcelslater in the calculation are approximatelytwo time required for the ageostrophicvelocity to flux the times larger than thoseformed early in the calculation vortexmass is estimatedto be t - 2•rl/3va, whereva is becausethe meander wavelength increaseswith time, the ageostrophicvelocity. For a radius of I - 10 km and although their characteristicsand the formation mech- an ageostrophicvelocity of 5 cms-x, thisgives a forma- anism appear to be similar. The same calculation was tion time of 5 days. This is consistentwith the timescale carried out for a model run without the ad hoc body of the modeled and observedfrontogenesis events for force term in the momentum and continuity equations. which the ageostrophicvelocity persists. This run gives a higher permanent subduction rate of Keeping in mind the idealized nature of the model, an approximately40 m yr-x that is nearlyuniform after estimate of the annual subduction rate from the surface 50 days. This higher rate is due to the continual relax- layer into the stratified interior driven by frontal instabilities is now made. The total volume of subducted water V is calculated in layer 2 as V= f qhdA-q2 f h dA (11) 200 - qx - q2 where q is the potential vorticity, h is the thicknessof layer 2, and the area integral is taken over all of layer 2 lOO - where the interface between layer i and layer 2 is deeper than 10 m. It is assumedthat all of the water in layer 2 is composedof only two typesof water, that whichorig- inated on the cold side of the front with potential vor- 0 ticity qx and that which originated on the warm side of lOO the front with potential vorticity q•. This will give an 0 2o 40 60 80 upper bound estimate to the subductionrate because time (deys) water that originatedbeneath the front with intermedi- Figure 5. Subduction rate for caseA; dashedline is ate potential vorticity will contributeto the total sub- total subduction rate, solid line is the permanent subduction volume. This approach is taken in order to duction rate. SPALL: FRONTAL SUBDUCTION 2555 ation of the isopycnal slope at the front as a result of The properties of parcels subducted by frontogene- baroclinic instability. The addition of the forcing term sis at a deep surface layer front are quite similar to restores the baroclinicity of the front and inhibits the the category of vortices termed submesoscalecoherent coveringover of water due to the slumpingisopycnals. vortices(SCVs) by McWilliams[1985]. Their charac- This result suggeststhat the inclusionof the processes teristic properties may be summarized as follows. They responsiblefor the initial formation of the front would generally have a small vertical scalewith a middepth ve- probably reduce the total permanent subduction,com- locity maximum. Their horizontal scalesare less than pared with the unforcedcase, by continuallypulling the the first deformation radius with a horizontal structure isopycnalson the cold side of the front up toward the of a singleextremum in the geopotential.They tend to surface. be nearly symmetric in the vertical and axisymmetric This subduction rate is less than but of the same in the horizontal. Nearly all observedSCVs are anticy- order of magnitude as that due to the convergenceof clonic with a relative low in the potential vorticity at the large-scaleEkman transport and variationsin the their center. Although it is clear that many SCVs are surface layer depth, which is typically 50-100 m yr -1 of a subsurfaceorigin (e.g., meddies),the propertiesof at midlatitudesin the subtropicalgyre [Marshallet al., others appear to have their origins in the winter mixed 1993]. The presentestimate is quite closeto the scaling layer [Lindstromand Taft, 1986]. This diversitywould est,imate of Follows and Marshall[1994] (25m yr -•) and seem to suggestthat more than one generationmech- slightlyless than the numericalcalculations of $amelson anismexists. McWilliams [1985]discusses several pos- and Chapman[1995] (37.5 m yr-x for the samefrontal sibilities and favors strong diapycnal mixing events on densityas assumedhere) for frontal subduction.There small spatial scalesand the resulting balanced adjust- are also other differenceswith the previous estimates, ment, although the processesthat control the mixing suchas the strengthof the frontalregion (Samelson and and determine the horizontal and vertical scales of the Chapmanhad a strongerfront), ambientstratification, anomalous water have not been described. model formulation, and time of integration. The low potential vorticity of SCVs suggeststhat diapycnal mixing is important in setting the initial po- 4.3. Relationship to Observations in the STCZ, tentiM vorticity of the water parcels. The surface layer Submesoscale Coherent Vortices, and Deep An- is a likely place to search for sources due to diapyc- ticyclones nal mixing events becausemixing is much stronger in The modeled formation mechanism is consistent with the boundary layer than it is in the ocean interior. several aspects of the observationsin the STCZ. Hori- Boundary mixing is also an important element in the zontal and vertical ageostrophicflows of similar struc- subsurfacesource proposed by D'Asaro [1988]. The ture and amplitude to those produced by the model present mechanism does not require that the mixing were found by VB82 and PR92, with upwelling and take place on the submesoscalescales of the vortices, flow toward the front from the warm side in the up- rather it is assumed to take place on the atmospheric per ocean and a correspondingdownwelling and flow synoptic scale, which is much larger than the oceanic below the front from the cold side. VB82 described a cross-frontal scale. The scale of the SCVs is selected processof cold water sinking adjacent to the front and through the frontogenesismechanism acting at upper across the front in a subsurfacelayer. These investi- ocean fronts, which, for the small-scale fronts of the gators concludedthat frontogenesiswas taking place; STCZ, forces an ageostrophicflow on scalesmuch less however, they did not directly observeany deep flow to than the first deformation radius of the main thermo- crossthe front. The low potential vorticity filament ob- cline stratification. The large vertical velocity that is servedunder the front by Pollard [1986]suggests that coincidentwith the frontogenesisforces the parcelsout subduction can pull water below the front while con- of the surface layer and into the permanent thermocline. serving its potential vorticity, although the separation Large-scaleflows or the dipole pairing would then pre- of blobs of this water was not observed. The data set sumably carry the relatively stable vortices away from of P R92 partially samples a parcel of low potential vor- the sourceregion. The dynamicsof the adjusted SCVs ticity water below the surface well away from the front is the same as that previously proposedby Mc Williams with relative vorticity of approximately-0.4 f and hor- [1988]and Ikeda [1982],namely that of balancedadjust- izontal scaleof approximately10-20 km. The salinity ment to an anomalous patch of low potential vorticity of the blob is much lower than the ambient water and water. similar to the salinity in the mixed layer on the cold side Similarities are also noted with larger-scaledeep an- of the front, suggestingthat it might have been formed ticyclonesfound near the Gulf Streamin models[Spall there in a manner consistent with the present model and Robinson,1990; Robinson et al., 1988]and observa- results. Several features of the plume formation, cy- tions [Richardson,1993; Bane et al., 1989]. Richardson clonic, and anticyclonicvortices are also strikingly sim- finds evidence of many deep anticyclonesto the south ilar to observationsin the vicinity of shelf break fronts of the Gulf Stream near 700 m that are approximately reportedby Garvineet al. [1988],although estimates of as strong as cyclonesat this depth. He notes, how- the vertical circulation in this area were not available. ever, that very few anticyclonesare observedin surface 2556 SPALL: FRONTAL SUBDUCTION drifters, suggestinga subsurfacemaximum in velocity. tion rates are typically much larger, between 100 and Bane et al. [1989] documentone suchanticyclone and 200 m yr-1. The internalprocesses of frontogenesis find a radius of 150-200 km with deep maximum swirl and subduction are very important to the local dynam- velocitiesof greaterthan 50 cm s-1 at 900 m depth ics of upper oceanfronts and contributesignificantly to and surfacevelocities approximately 25 cm s-1. This their local variability. They are also likely to be very increased horizontal scale of the anticyclones is consis- important to the local biologicalactivity and exchange tent with the scale found in the models of Robinson betweenthe propertiesof the turbulent mixed layer and et al. [1988]and $pall and Robinson[1990] and as ex- the permanent thermocline. pected for the larger deformation radius and meander The structure of parcelssubducted from a deep sur- scale in the vicinity of the Gulf Stream compared with face layer closely resembles a class of vortices called the fronts of the STCZ. Richardson[1993] also doc- submesoscale coherent vortices. Their characteristic uments the apparent formation of a deep anticyclone features(small horizontal scales, subsurface maximum, from the upstream side of a meander as a cold ring was anticyclonicvorticity) are consistentwith the subduc- formed. This is just the time and location that the tion mechanism discussed here. The volume of the vor- frontogenesismechanism proposed here forms the deep tices is determined by the space and timescales of the anticyclones. frontogenesis,typically producing anticyclonicvortices of approximately 25 km in diameter over timescales of 5. Conclusions I week. The vertical scale of the vortices is determined by the depth of the surface layer, relative to the sub- The processof subduction from the upper ocean be- surface stratification. Parcels that are subducted in late low and across a preexisting upper ocean front in the winter would be the most likely to be observed in the absenceof surface forcing has been investigatedusing permanent thermocline becausetheir signal would be both a simple analytic model and an isopycnalprimitive large and they would most easily escapereentrainment equation model. The fronts studied here are roughly into the deepeningmixed layer in the followingwinter. modeled after the surface-intensified fronts observed in This suggeststhat those submesoscalevortices whose the Subtropical Convergence Zone of the North At- temperature and salinity characteristics identify their lantic, although many of the conclusionsmay be rel- origin in the winter mixed layer may have been formed evant to a wider variety of fronts and to the general through frontal subduction. Similarities with deep an- problem of mass exchange across a potential vortic- ticyclones observed south of the Gulf Stream are also ity gradient. It has been shown that baroclinic wave noted. growth along the front can trigger regionsof frontogenesis,which are characterizedby periodsof large vertical Acknowledgments. Supportfor this workwas provided velocitiesof 0(30 m d-1) and cross-frontageostrophic by the Office of Naval Researchgrants N00014-90-J-1490 flowsof 3-5 cm s-1, consistentwith observationsand and N00014-93-1-0572.I would like to thankRoger Samel- son and Dave Chapmanfor helpfuland interestingdiscus- previous models. The downwellingon the cold side of sionsand also for sharingtheir preliminaryresults. Peter the front pulls water down and below the front, at least Killworthmade helpful suggestions regarding the analytic temporarily subductingit from the oceansurface. Only modelsin section2. Commentsand criticisms by two anony- that portion of the anomalous water that is carried mous reviewers also led to an improved presentationof the across the front by the ageostrophicdeep circulation results. This is contribution 8733 from the Woods Hole can be permanently subducted, however, and the re- OceanographicInstitution. mainder of the plume returns to the cold side of the front. The subducted water has anomalous potential References vorticity, relative to the ambient fluid, and develops a circulation through balanced adjustment to the gradi- Bane, J. M., L. M. O'Keefe, and D. R. Watts, Mesoscale ent wind relation, consistent with the analytic model. eddies and submesoscale,coherent vortices: Their ex- Deep anticyclonic circulations are often formed in con- istencenear and interactionswith the Gulf Stream, in nection with the more traditional surface-intensifiedcy- Mesoscale/SynopticCoherent Structures in Geophysical clonic cold core rings as a dipole pair that quickly prop- Turbulence,edited by J. Nihoul and B. Jamart, pp. 501- agates away from the front, carrying with it anomalous 518, Elsevier, New York, 1989. water properties from the opposite side of the front. Bleck, R., and D. Boudra, Wind-drivenspin-up in eddy- A total subductionrate driven by frontogenesisof ap- resolvingocean models formulated in isopycnicand iso- proximately20 m yr-1 is estimated.This is somewhat baric coordinates,J. Geophys.Res., 91, 7611-7621,1986. Bleck, R., R. Onken, and J. D. Woods, A two-dimensional lessthan estimates of subductiondue to large-scalevari- model of mesoscalefrontogenesis in the ocean, Q. J. R. ations in atmospheric forcing, which are typically 50- Meteorol. $oc., 11•, 347-371, 1988. 100 m yr-1. The presentestimate is rough,however, D'Asaro, E., Generation of submesoscalevortices: A new given the uncertainties in the number of fronts in the mechanism,J. Geophys.Res., 93, 6685-6693, 1988. ocean, the neglect of external forcing, and the absence Eriksen,C. C., R. A. Weller, D. L. Rudnick,R. T. Pollard, of an active mixed layer. Temporary(or local) subduc- and L. A. Regier, Ocean frontal variability in the Frontal SPALL' FRONTAL SUBDUCTION 2557

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