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The in Uence of the Ambient Ow on the Spreading of Convected Water

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The in Uence of the Ambient Ow on the Spreading of Convected Water Journalof MarineResearch, 56, 107–139, 1998 The inuence ofthe ambient ow onthe spreading ofconvected water masses bySonya Legg 1,2 andJohn Marshall 3 ABSTRACT Weinvestigatethe in uence of a cyclonicvortical owonthelateral spreading of newlymixed uidgenerated through localized deep convection. Localized open ocean deep convection often occurswithin such a cyclonicgyre circulation, since the associated upwardly domed isopycnals and weakerstrati cation locally precondition the ocean for deeper convection. In theabsence of ambient ow,localizedconvection has been shown to result in stronglateral uxesof buoyancygenerated by baroclinicinstability, sufficient to offset the local surface buoyancy loss and limit the density anomalyof theconvectively generated water mass. Herewe examine the consequences of acyclonicambient owonthisbaroclinic instability and lateralmixing. T oisolatethe in uence of thecirculation on this later stage of localized convection, weparameterize the convective mixing by the introduction of baroclinic point vortices (‘ ‘hetons’’) in atwo-layerquasi-geostrophic model, and prescribe the initial owbyapatchof constantpotential vorticity.Linear stability analysis of the combined system of pre-existing cyclonic vortex and convectivelygenerated baroclinic vortex indicates scenarios in which the pre-existing cyclonic circulationcan modify the baroclinic instability. Numerical experiments with the two-layer QG modelshow that the effectiveness of the lateral heat uxescan be stronglydiminished by the action ofthepre-existing circulation, thereby increasing the density anomaly of theconvected water mass. 1.Introduction Inseveral recent studies of localized open ocean deep convection (Legg and Marshall, 1993;Send and Marshall, 1995; Visbeck et al., 1996; Ivey et al., 1995;Coates et al., 1995; Brickman,1995; Legg et al., 1996)it has become clear that baroclinic instability of the localizedconvection site leads to signi cant lateral uxesof buoyancy as uidis transportedaway from andinto the convectingsite by niteamplitude eddies. These lateral uxesmay be largeenough to completely offset the surface forcing. A statisticallysteady statemay result, in which the density anomaly of theoverturned uidceases to increase, andthe deepening of themixed layer is halted. If thelateral uxesachieved by baroclinic instabilitywere inany way rendered less effective, different water-mass propertieswould result. 1.Institute for Geophysics and Planetary Physics, University of California,Los Angeles, California, 90024; U.S.A. 2.Present address: Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, 02543,U.S.A. 3.Department ofEarth, Atmospheric and Planetary Sciences, MIT,Cambridge,Massachusetts, 02139,U.S.A. 107 108 Journalof MarineResearch [56, 1 Previousstudies of localizedconvection have considered a convectingregion within a volumeof eitherin nite extent (Legg and Marshall, 1993; Legg et al., 1996)or conned by thenumerical domain (Jones and Marshall, 1993) or laboratory apparatus (Coates et al., 1995;Brickman, 1995). Most of these studies assume a quiescentinitial ow(although Ivey et al. (1995)considered a preconditioning owdriven by arotatingdisc). Observa- tions,however, reveal that convection often occurs within a localgyre circulation (Killworth,1983). This may be associatedwith (i) localtopographic features such as the Rhonefan in the northwest Mediterranean (Swallow and Caston, 1973; Hogg, 1973) or MaudRise in theW eddellSea (Gordon, 1978; Alverson and Owens, 1996), (ii) winter-time intensication of the wind-driven circulation (Pinardi and Navarra, 1993) or (iii)localized coolingsuch as that generated by winds blowing off theice-sheet in the Labrador Sea (Clarkeand Gascard, 1983; Seung, 1987) or a combinationof all three processes. A cyclonicshear is associated with doming of isopycnalsup tothesurface and provides one ofthe‘ ‘preconditioning’’ factorsnecessary for deepconvection events. Since the eddies generatedby baroclinic instability carry uidout of the convecting region and into the ambientcirculation, the spreadingphase of deep-waterformation should not be considered inisolation from thebackground ow.Recentobservations in the Labrador Sea (Peter Rhines,personal communication, 1997) show signi cant barotropic eddy activity occur- ringat thetime of deepconvection, further motivating an investigation of thein uence of barotropic owontheconvection and spreading. Severalrecent studies have begun to examine the preconditioning of the ocean for locallydeeper convection by the ambient circulation, including the owtrapped over topography(Alverson and Owens, 1996; Madec et al., 1996),isolated geostrophic eddies (Legg et al., 1998),and wind-driven barotropic gyres (Madec et al., 1996).All of these studiesshow that in additionto inuencing the localization of convection,the ambient ow mayalso in uence the spreading of the convected uid.Alversonand Owens (1996)show thatbaroclinic instability may be replaced by mean owadvection in the presence of a uniform ow,while Madec et al. (1996)suggest that a barotropicgyre circulation may suppressbaroclinic instability of theconvecting area. In this study we examinein detailthe inuences of ambient gyre owsassociated with the preconditioning and wind-driven circulationon the development of baroclinic instability. W einvestigatein particular the possibilitythat this pre-existing circulation can affect the rate at which convected water subsequentlyspreads away from theformation region, and the efficiency with which baroclinicinstability draws buoyancyinto the convecting patch. Thein uence of barotropic owon baroclinic instability has been examined in the contextof atmospheric baroclinic life cycles, where a ‘‘barotropicgovernor’ ’ (James, 1987)can suppress the eddy activity. In contrast to thesezonal atmospheric ows,in the oceanicconvection context both baroclinic and barotropic ows arelocalized within eddiesor gyres, where the spatial scale of thelocalization can in uence the stability. Weusea highlyidealized model to capturebaroclinic instability and its modi cation by theambient circulation: a pointvortex ‘ heton’model of the convecting process, embedded 1998] Leggand Marshall: In uence of ambient ow 109 withina contour-dynamicalrepresentation of thepre-existing circulation. The point-vortex modelwas introducedby Leggand Marshall (1993) (hereafter LM), and its efficiency and applicabilityin the study of the properties of thespreading phase of convection demon- stratedby Legg et al. (1996)(hereafter LJV). Theadvantages of this Lagrangian formulationinclude its low cost, and the absence of boundariesor viscousprocesses. W e regardthe results of hetonmodel experiments as providing a usefulguide ranging across parameterspace which can be investigated further by other (more expensive)numerical modelscontaining more complete physics. Throughthe combination of linear stability analyses (a varianton the results of Flierl (1988)and Nakamura (1993)) and numerical experiments using the heton model, we nd thatthe addition of an ambient circulation comprising a vortexwith a strongbarotropic componentcan suppress the baroclinicinstability of theconvected region. The suppression oftheinstability is aconsequenceof thechange in the absolute vorticity of theconvective region,and along with it, stronger angular momentum constraints on the instability process.Associated with the reductionin instability, the lateral spreading of theoverturned uidis diminished, as are the lateral uxesof buoyancydrawn into the convecting region from theperiphery. W econcludethat the properties of themixed water willbe alteredby thepresence of abarotropicswirl, with a smallervolume of denserwater beinggenerated. InSection 2 we briey reviewthe properties of theheton model of the spreading phase ofoceanconvection from LMandLJV ,andoutline the potential vorticity representation of thepreconditioned ow.After adiscussionof thepredictions for stabilityof theconvected regiondeduced from lineartheory in Section3, numerical experiments using the Lagran- gianquasi-geostrophic two-layer point vortex/ contourdynamics model are described in Section4, andthe implications for deep-waterformation discussed in Section5. 2.A pointvortex model of the convectionregion Thelocalized convective mixing due to buoyancyforcing at the ocean surface leads to thegeneration of adensityanomaly in theconvected region, which under the in uence of rotationand gravity relaxes to a stateof geostrophic adjustment, with a baroclinicrim currentassociated with the regionof dense uid.The baroclinicstructure of thisgeostrophi- callyadjusted state can be representedmost simply in atwo-layerquasi-geostrophic model witha cyclonic owinthe upper layer and an anticyclonic owinthe lower layer. The ongoingforcing serves to transform the density of the uidfrom thatof theupper layer to thatof the lower layer, thereby raising the interface between the layers in the forcing region.Prognostic equations in the quasi-geostrophic representation are given in terms of potentialvorticity, which contain information on the velocity eldsin addition to the densityanomaly. W emakea furtherdiscretization by representing the potential vorticity eldin terms of an ensemble of point vortices. Since the potential vorticity anomaly associatedwith a densityanomaly is baroclinic(the surface density anomaly is replaced by apotentialvorticity anomaly placed beneath an isothermal surface as described by Bretherton(1966) and elucidated further in LM),the point vortex representation
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