JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. C10, PAGES 25,705-25,721, NOVEMBER 15, 1996 Localized convectionin rotating stratified fluid J. A. Whitehead Department of Physical Oceanography,Woods Hole OceanographicInstitution, Woods Hole, Massachussetts J. Marshall Department of Earth, Atmospheric and Planetary Science,Massachusetts Institute of Technology, Cambridge, Massachusetts G. E. Hufford Woods Hole OceanographicInstitution, MassachusettsInstitute of Technology Joint Program, Cambridge, Massachusetts Abstract. We study the convectiveoverturning of a rotating stratified fluid in the laboratory. Convection is induced from the surface of a salt-stratified fluid by the introduction of salty fluid over a circular area. The external parameters are buoyancy forcing of strength, B0, applied over a circular area of radius R•, the rotation rate as measuredby f, ambient stratification N, and the depth H. The experimentsare motivated by physical scaling argumentswhich attempt to predict the length and velocity scalesof the convectivechimney as it adjusts under gravity and rotation and breaks up through baroclinic instability. The scalesof interest include the number, size, and typical speedsof the fragmentsof the brokenchimney, the final depth of penetrationof the convectivemixed layer, and the total volume of convectivelyproduced water. These scalesare tested against the laboratory experiments and found to be appropriate. In this idealized problem we have found the depth of penetration dependsonly on the size and strength of the forcing and the ambient stratification encountered by the convection event; it does not depend explicitly on rotation. The implications of the work to deep water formation in the Labrador Sea and elsewhere are discussed. Finally, the study has relevance to the role and representation of baroclinic eddies in large-scale circulation of the ocean. Introduction Chapman,1995]; or, in the openocean, by deepconvec- tion events which are manifested as a very deep mixed That deep water in the oceansis cold, and the deep- layerinduced by wintertimebuoyancy loss [Storereel, el est water is the coldest, has been known since the al., 1971]. The latter processis the focusof this study. 18th century [Ellis, 1751], althoughsalinity can com- Deep ocean convectionis apparently only found in re- plicate this simplepicture [Veronis,1972]. In general, gionsthat are preconditionedregions, where gyre-scale the oceans are stably stratified everywhere, except in and mesoscale circulation have weakened the ambient top and bottom mixed layers; even polar oceans are stratificationsufficiently for rapid cooling/evaporation/ stably stratified in spite of the fact that the coldest freezingto producevery deep mixed layersduring pe- water is created there and sinks downward to spread riods of maximum coolingin winter. During the for- out to temperate and tropical latitudes. Thus surface mation of the deep mixed layer, water moves vertically cooling/evaporation/iceformation do not frequentlydi- with velocitiesof 2-10 cm s-1 within the deepmixed rectly produce water that is denser than the deep- layer [Storereelel al., 1971;Schott and Leaman,1991]. est water in the region. Instead, in polar oceans the The vertical movement is both upward and downward dense water "makes its way" downward by two differ- and is recorded episodicallyby current meters; these in- ent routes: by flowing downward as density currents dividual convectioncells have becomeknown as plumes, along the continentalslope from areasof origin in shal- and they act to efficiently "mix" the layer. The mixed low seas[see e.g., Nansen,1906], [Gawarkiewiczand layer depth increasesfrom h,undredsof metersto possi- bly thousandsof meters over the period of a few days. After and possiblyduring the latter stagesof the deep Copyright1996 by the AmericanGeophysical Uifion. mixed layer formation, the entire volume of mixed-layer Papernumber 96JC02322. fluid sinks by spreading laterally at its base and con- 0148-0227/96/96JC-02322509.00 tracting laterally at the surface. Simultaneously, the 25,705 25,706 WHITEHEAD ET AL.: CONVECTION IN ROTATING STRATIFIED FLUID sides of the deep mixed layer develop geostrophiced- Numericalstudies by Jonesand Marshall [1993]have dies which augment this sinking. also supported the scalingstested by Maxworthy and Many theoretical, numerical, and laboratory model- Narimousa[1991, 1994] in the laboratory.Using nonhy- ing studies have clarified the dynamics of such deep drostatic models,they focusedon both the production ocean convectionevents. Killworth [1976]; Crdponel of the small-scaleconvection cells and the emergenceof al. [1989],and Madecel al., [1991],for example,focused the larger aggregatescale in which lumps of cold wa- upon generation of a large-scaleflow while parameter- ter cluster together. Legg and Marshall [1993]found izing the convectivescale. The dynamicsof adjustment that the lumps of densewater tended to pair up with with the surroundingstratified fluid and the production correspondinggyres of cyclonicsurface fluid to produce of eddies along the region dividing the cooled and un- "beton" pairs, which movethe densefluid laterally from cooled fluid were topics of interest. The cooling was the place of origin. regarded as a distinct event with the lateral adjust- Helfrich and Battisti [1991]studied the flow created ment processeshappening concurrently. Linear theory by a steady point buoyancysource in a rotating strat- of rotating Rayleigh-Bdnard convectionsummarized in ified flow. Helfrich [1994] conducteda similar study the work by Chandrasekhar[1961] was employed to ad- of flow createdby impulsivesources (called thermals). dress the dynamics of the plumes. Davey and White- Scaling considerationswere developedfor velocity and head[1981], for example,showed that convectioncells length scales and successfullycompared with labora- wider than an appropriately defined Rossby radius of tory experiments. An important result in both studies deformation(gApH/po)•/2/f would not grow, where g is that fluid would accumulate at a terminal depth until is accelerationfrom gravity, Ap/p is the proportionof the beton mechanismproduced eddy pairs that would vertical densityvariation (but an adversedensity gra- remove the fluid. dient, with densestwater on the surface),H is depth The present study considersflow created by an ex- of the fluid layer, and f is the Coriolis parameter. Fer- tended but confinedbuoyancy source in rotating, strat- nando et al. [1991] and Bubnovand Golitsyn[1990], ified fluid. It can be considered to be an extension of used scalingarguments to explore the nonlinear regime, Maxworthyand Narimousa[1991, 1994]with stratifica- determined the region of parameter space where rota- tion added. Or, it can be consideredto be an extension tion was dominant, and produced information about the of Helfrich and Battisti [1991]with finite buoyancysize length and velocity scaleswithin that region. Fernando, added. Laboratoryexperiments (in section3) will test et al., [1991]identified the length scale scalings(outlined in section2). trot- (Bolf3)•/•' (1) DynamicalConsiderations suchthat the critical depth, found experimentally to be Nondimensional Numbers 12.7/rot, is the boundary layer thicknessbeyond which rotation becomes important in steady convection. The When an unstratified fluid of total depth H is forced significanceof/rot is that for distancesgreater than/rot to convect by uniform surface cooling in the presence the effectsof rotation are important whereasfor smaller of rotation f, there is only one nondimensional com- distancesrotation is not. Typically, in the ocean, /rot bination of the main external parameters B0, f, and is about 100 m. Here B0 is buoyancy flux defined for H heatingor coolingas B0 = gc,H!/pcp, whereg is ac- , X/Bo/f3 trot celerationof gravity, c• is the coefficientof thermal ex- R0= H = H' (4) pansion,H! is the heat flux per unit area, p is den- which will be called the natural Rossbynumber R3 sity, and cp is specificheat, respectively.For salt flux, (its physicalsignificance is reviewedin Marshallet al., Bo = g/•Fs, where/• is the salt coefficientof expansion [1994]).Here/rot = v/Boll 3 canbe consideredto be a and Fs is the volume flux of salt. Maxworthy and Na- measure of the vertical scale to which convectionpene- rimousa[1991, 1994] presentedevidence in supportof trates in an unstratified fluid during an inertial period. the importance of/rot and introduced the associateddi- If R• is large, then the convectionwill be limited by the mensionless "natural" Rossby number defined in terms oceandepth beforeit feelsthe effectsof rotation;if R• is of external parameters small, then the convectionwill come under geostrophic controlbefore encountering the bottom. Briefly,R• is = (2) large in the atmosphereand small in the ocean. Only in oceanicregions which experiencedeep convection can In addition, a new length scale,a radius of deformation, R3 get small enoughfor rotation to be important. In the ocean,typical values for f, B0, and H are f • 10-4 s-•, B0 • 10-7 m2 s-3 (correspondingto a heatloss of was found to determine the diameter of groups of • 2000W m-2), andH • 1000-4000m, givingan R• individual thermals that aggregatedon the bottom in in the range.0.08-0.4 so rotation cannot be neglected closed cells. in the ocean. In the laboratory experiments presented WHITEHEAD ET AL.: CONVECTION IN ROTATING STRATIFIED FLUID 25,707 here R• rangesfrom 0.04 to 0.41, and in our numerical made up of many aggregates.Some parts of