Journalof MarineResearch, 56, 329–347, 1998

Deep water properties, velocities, anddynamics over ocean trenches

byGregory C. Johnson 1

ABSTRACT Observationsof water properties and deep currents over several trenches in the PaciŽ c Ocean centralbasins give consistent evidence for recent ventilation of water below the trench sills and cyclonicsense of circulationover the trenches. A dynamicalargument for this pattern is advanced. First,a reviewof previousanalyses of hydrographicdata shows that the trenches are well ventilated bydensebottom water, that within the trenches this bottom water generally spreads away from its source,and that a cyclonicsense of circulationis suggested over some trenches. Then, this cyclonic senseof circulationover the trenches is further documented using deep current meter and  oatdata. Finally,bathymetry is used to motivatea simpledynamical framework for  owover trenches. If the trenchsides are sufficiently steep and the trench is sufficiently removed from the equator to ensure a regionof closed geostrophic contours, then any upwelling over that region will drive a strongdeep cyclonicrecirculation in theweakly-stratiŽ ed abyssthrough vortex stretching. The magnitude of this recirculationis limitedby bottom drag. Ageostrophic  owin a bottomEkman layer into the trench balancesthe water upwelled over the trench. The cyclonic recirculation is muchstronger than the upwelling-driven owpredicted across blocked geostrophic contours by the linear planetary geostrophicbalance.

1.Introduction Theclassical theoretical framework for thethermohaline circulation of the abyssal oceanassumes localized sinking at high latitudes forced by buoyancy loss from air-sea exchange.This sinking is balancedby widespreadupwelling at lowerlatitudes that in turn countersthe effects of downwarddiffusion of buoyancy from thesurface (Stommel and Arons,1960). If upwellingincreases with distance from thesea  oorand bathymetry is sufficientlygentle to avoidregions of closedgeostrophic contours, the planetary geostro- phicbalance dictates overall poleward interior  ows.With a boundarycondition of nonet owinto the eastern edge of each basin, the interior  owis fed from deepwestern- boundarycurrents. These dynamics result in recirculation regions near the poles where interior owfeeds deep westward- owing boundary currents at poleward walls. The deep western-boundarycurrents near these recirculations sometimes  owbacktoward the high latitudesources. Predictions of locations and strengths of deep boundary currents have

1.PaciŽ c MarineEnvironmental Laboratory, NOAA, 7600Sand Point Way, N.E. (Bldg. 3), Seattle, Washington,98115-0070, U.S.A. 329 330 Journalof MarineResearch [56, 2 beenconŽ rmed by observationsin locations throughout the W orldOcean (W arren,1981). Manyvariations on thisframework havebeen investigated, and a smallsample are given below.Interior zonal jets have been observed and modeled  owingaway from aneastern deep-watersource (W arren,1982) and toward an eastern deep-water sink (W arrenand Speer,1991; Speer et al., 1995).The distortion of thecirculation by gentlebathymetry has beendiscussed (W arrenand Owens, 1985). Abyssal spin-up and nonuniform interior upwellingin uences have been modeled (Kawase, 1987).Effects of a fullynonlinear continuityequation (Speer andMcCartney, 1992) have also been investigated. Thefocus of thiswork is abyssalcirculation over deep trenches, speciŽ cally along the westernand northern margins of thePaciŽ c Oceancentral basins. The simple Stommel- Aronsframework mustbe modiŽed substantially here because steep bathymetry results in regionsof closed geostrophic contours over the trenches, a situationpredisposed to strong recirculations(W elander,1969). Theoretically, a densebottom water source introduced intoa stratiŽed rotating deep basin shaped more like a bowlthan a boxcan drive an anticyclonicinterior circulation. This tendency, coined the hypsometric effect, results from decreasingvertical velocity with decreasing depth owing to the increasing area of the basin 1 1 withdecreasing depth (Rhines and MacCready, 1989). However, 1- 2 and 2- 2 layer numericalmodels as well as analytical results demonstrate that in situations where stratiŽcation is weak, upwelling over closed geostrophic contours is associated with a strongcyclonic recirculation tangent to the contours. The results are similar for elevatedor depressedtopography in sink-driven experiments with prescribed uniform upwelling (Strauband Rhines, 1990) and in source-driven basin-Ž lling experiments (Kawase and Straub,1991; Kawase, 1993a,b).The upwelling within the region of closed geostrophic contoursresults directly in vortex stretching that drives a strongcyclonic recirculation, limitedonly by bottom drag. A bottomEkman layer associated with this drag transports mass intothe region normal to the closed contours. If thecirculation is in steady-state, the bottomEkman transport balances the mass lostto upwellingwithin the region. Inthe following, Ž rst aliteraturereview shows several inferences about this deep  ow from hydrographicdata. W aterproperties below the trench sills reveal that bottom water thereis not stagnant. That is to say,each series of trenchesis activelyventilated by bottom water.In addition, water propertiesin some locations suggest  owpatterns.In the PaciŽ c, theinferences from thewater properties are that the bottom water in these trenches is spreadrelatively rapidly away from itssouthern source and often that a cyclonicsense of circulationis evident.These two inferences are not contradictorysince the southernbottom watersignature can be carriedrapidly away from itssource on one branch of thecyclonic circulationaround the trench. Next, velocity measurements are used to document a cyclonicsense of circulation over several trenches. Finally, the trench bathymetry is shown toresult in closedgeostrophic contours, and this fact is usedto placethe observations in a theoreticalframework. 1998] Johnson:Deep circulation over ocean trenches 331

Figure1. Deep trenches at the western and northern edges of the PaciŽ c Oceancentral basins revealedby theGEBCO 7000-misobath (IOC, IHO, andBODC, 1994).The labeled boxed areas correspondto individual panels of Figure5, and contain the trenches extensively discussed, (a) TheKermadec and T ongaTrenches, (b) the southern end of the Mariana Trench, (c) the Izu-Ogasawara,Japan, and Kuril Kamchatka Trenches, and (d)the Aleutian Trench.

2.Deep waterproperties ThePaciŽ c Oceanis ringed around much of its margins by deep trenches (Fig. 1). SigniŽcant trenches are found elsewhere in the W orldOcean. However, readily available long-termdeep current measurements over trenches are all found at the western and northernedges of the PaciŽ c Oceancentral basins. For thesake of brevity, only water propertiesin this region will be discussedin detail. No bottom water forms intheNorth PaciŽc Ocean;instead it entersthe PaciŽc Oceancentral basins in a deepwestern-boundary currentfrom thesouth. The following literature review starts closest to thisbottom water source,with water properties of theKermadec Trench, moves clockwise around the PaciŽ c Ocean,and ends with the water properties of theAleutianTrench, farthest from thesource. ZonaltranspaciŽ c hydrographicsections at 32.5 and 28S (Whitworth et al., 1996; Warren,1973) cross the Kermadec Trench. The sections show that the water belowthe sill isabout as cold (in potential temperature), fresh, dense, oxygen-rich, and silica-poor as bottomwater justto the east. These properties are characteristics that distinguish the more recentlyventilated modiŽ ed Antarctic Bottom W aterfrom theless recently ventilated 332 Journalof MarineResearch [56, 2 modiŽed NorthAtlantic Deep W ater.These water masses are the two main components of theCircumpolar Deep W aterthat ventilates the deep PaciŽ c Ocean,with the former being dominantin the bottom water of thesouthern hemisphere, and the latter being dominant in thebottom water of thenorthern hemisphere. Properties below the trench sill distinguish waterthere as strongly southern in origin. This conclusion is not surprising, since the trenchis coincident with the northward- owing deep western-boundary current banked againstthe Kermadec Island Arc (Whitworth et al., 1996;W arren,1973). The oxygen-rich natureof thewater belowthe sill clearly shows that water thereis not stagnant. This water mustbe sufficiently ventilated to maintain this characteristic in the face of biological consumption.In addition, a troughin theisotherms immediately over the trench is visible tovarying degrees in thefourzonal sections near 32.5S and the single zonal section at 28S. Assuminggeostrophy and a referencevelocity of zero somewhat above the trough, this persistentfeature is consistentwith a bottom-intensiŽed cyclonic sense of circulation over thetrench, as notedby Whitworth et al. (1996). Farthernorth, a zonaltranspaciŽ c sectionacross the north end of theMariana Trench at 24N(Roemmich et al., 1991)shows that the water belowthe trench still is relativelycold, salty,dense, oxygen-rich, and silica-poor .Asectionnear the saddle point of the Izu- Ogasawaraand Japan Trenches at 35N (Kenyon, 1983) also shows these tendencies. In the NorthPaciŽ c Ocean,these tendencies distinguish more newly arrived Circumpolar Deep Waterbelow from theolder PaciŽ c DeepW aterabove. By this latitude the modiŽ ed North AtlanticDeep W atercomponent of Circumpolar Deep W ateris dominant in the bottom water,which is why the distinguishing salinity and silica criteria for southernorigin bottom waterchange from southto north. At bothlatitudes, water of more extreme southern characteristicsis found offshore. However, the relatively oxygen-rich and silica-poor natureof water below the trench sills again argues for relativelyrecent ventilation with southernbottom water. Neither section has station spacing adequate to revealnear-bottom isothermde ections over the trenches. Inzonal sections across the Kuril Kamchatka Trench at 42and47N, and a meridional sectionacross the AleutianTrench at 152W(T alley et al., 1991),local water propertiesare mostextreme in theirsouthern characteristics below the trench sills. Data from fourshort meridionalsections across the Aleutian Trench at 165E, 175E, and 175W ,discussed previouslyfollowing similar lines of inquiry (W arrenand Owens, 1985; 1988), also supportthis hypothesis. The role of these trenches in spreading bottom water poleward alongthe western boundary and eastward along the northern boundary of the North PaciŽ c Oceanhas been discussed (Talley et al., 1991;Talley and Joyce, 1992). A mapof dissolved silicaon anear-bottompotential isopycnal in the North PaciŽ c Ocean(T alleyand Joyce, 1992)clearly shows a tongueof silica-poor(and oxygen-rich) water. This tongue spreads polewardover the trench along the western boundary and then eastward over the equatorwardside of thetrench along the northern boundary. In addition, the northern and westernboundary sections in this region show a narrowband of highsilica at theboundary onthe inshore side of the trench, implying southward and westward  ow,respectively 1998] Johnson:Deep circulation over ocean trenches 333

(Warrenand Owens, 1985; 1988; Talley et al., 1991;T alleyand Joyce,1992). Finally, close examinationof theseven individual sections across the trenches reported in thesestudies revealsslight troughs in isotherms directly over the trenches, again consistent with a bottom-intensiŽed cyclonic sense of circulationover the trenches. However, with the weak shearsand minimal water-property guidance in these abyssal regions, the inference of geostrophic owdirection from thermalwind is perilously dependent on the assumed referencevelocities. Insummary, existing studies show that water below the sills of these trenches always has relatively,and sometimes extreme, southern water properties, suggesting that the trenches arewell ventilated with bottom water of southernorigin. Previous analysis of hydrographic datasuggest decreasingly southern bottom water propertiesbelow the deep trench sills withincreasing clockwise distance from thesource in the southwest corner (progressing northwardalong the western boundary and then eastward along the northern boundary). Furthermore,evidence from theliterature shows that the Kuril Kamchatka and Aleutian trenchesrapidly spread bottom water away from thesouthern source. Studies detail how thedeep silica distribution also suggests that there is acyclonicsense of circulationover andwithinthese trenches. Finally, published vertical sections show that deep isotherms just abovethe trenches are suggestive of a bottom-intensiŽed cyclonic sense of circulation.

3.Deep velocities Here datafrom sixdeep current meter arrays and one deep deployment of  oatsare discussedand shown to provide more evidence for acyclonicsense of circulation over deepocean trenches, greatly augmenting the information from water-propertyand density distributions.Most of these trenches are the same ones on the western and northern marginsof the PaciŽ c Oceancentral basins discussed in the previous section. These measurementsare reviewed working from southto northalong the western boundary and thenfrom westto east along the northern boundary, as before.Current directions here are reportedas °T,indegreesclockwise from north.For example,90° T signiŽes eastward ow. Recently,a currentmeter array was deployedacross the Kermadec Trench at 32.5Sto quantifythe transport of thedeep western-boundary current there. These data have been analyzedand discussed at somelength (Whitworth et al., 1996).A deepcyclonic sense of circulationis evident over the trench, superimposed on theequatorward  owofthedeep western-boundarycurrent. T wentymoorings were deployedover 22 monthsfrom 178.753W to168.225W ,withcurrent meters at nominal depths of 2500, 4000, and 6000 m (or near-bottomwhere the bottom is shallower than 6000 m). Sevenmoorings west of 177W arelocated over the steep sides of thetrench and the adjacenteastern  ankof theKermadec IslandArc. Theaxis of the observed mean currents in this region (weighted by record length),is near27° T. The isobaths, for boththe trench and the island-arc eastern  ank,have roughlythe same orientation. V erticalproŽ les of themean velocity rotated in thisdirection (Fig.2) show a strong(exceeding 9 cms 2 1)positive(nominally equatorward)  owalong isobathsbanked against the island arc eastern  ank.This feature is the core of the deep 334 Journalof MarineResearch [56, 2

Figure2. V erticalproŽ les of velocity components [cm s 2 1,positivevalues shaded] parallel (left panel)and perpendicular (right panel) to the axis, 27° T ,ofmean velocity vectors over the KermadecTrench from a currentmeter array along 32.5S (Whitworth et al., 1996).The data are objectivelymapped assuming a Gaussiancovariance with correlation lengths of 1750 m inthe verticaland 28 kminthehorizontal and an error-to-signalenergy of 0.01.The correlation lengths usedare roughly the mean instrument spacings in the region and the error-to-signal energy is unrealisticallylow ,socontours are faithfulat and between current meters (black dots), but should beregardedwith care outside array limits. V erticalexaggeration is 100:1. The 5-minute resolution ETOPO5 bathymetryis used. See Figure 5a formooring locations and Figure 1 fortrench location. 1998] Johnson:Deep circulation over ocean trenches 335 western-boundarycurrent, consisting of CircumpolarDeep W ater(Whitworth et al., 1996). Offshore andshallower (around 2500 m), aweaker(exceeding 2 cms 2 1)negative(nomi- nallypoleward) return  owofPaciŽc DeepW ateris found (Whitworth et al., 1996). Most relevantto the point at hand,at deeper levels (4000 m andnear-bottom) the  owremains nominallyequatorward over the west side of the trench, but switches to a weaker(just exceeding2 cms 2 1)negative(nominally poleward)  owoverthe east side of thetrench. Thispattern is consistent with the geostrophic velocities implied by the isotherm trough immediatelyover the trench (Whitworth et al., 1996).The velocities perpendicular to the weightedmean current axis (Fig. 2) areeverywhere small and less organized, as mightbe expectedfor thecomponent roughly perpendicular to theisobaths. Dataare available from asmallbut useful current meter array at thesouthwestend of the MarianaTrench that also provide evidence for acyclonicsense of circulation there. Statisticsfor thesecurrent meter records are available on theW orld-Wide-Webhome page for theDivision of Physical Oceanography in the Ocean Research Institute at the Universityof Tokyo(h ttp://dpo.ori.u-tokyo.ac.jp:81/). Threecurrent meter moorings, each withtwo current meters, were deployedacross the southwest end of the trench. Here the trenchaxis is orientedroughly east-west, and the mooring line crosses it nominallyalong 142.6E(see Fig.5b for mooringlocations). Deployments started in July1995 with record lengthsfrom 370to 441days, and an averagelength of 424days. Mooring latitudes range from 10.998to 11.600N and instrument depths range from 6095to 9860m. The (record lengthweighted) mean velocity vectors for bothcurrent meters at eachmooring are very closelyaligned with the isobaths, and again the  ow(not shown) is cyclonic in sense aroundthe trench axis. On the north side of thetrench, over the 6960-m isobath, the owis nominallywestward with a magnitudeof 1.3cm s 2 1.At thecenter of thetrench, over the 10286-misobath, the velocity magnitude is a minimumat 0.1cm s 2 1.Onthe south side of thetrench, over the 6520-m isobath, the  owisnominallyeastward with a magnitudeof 0.5 cm s2 1. Thenext useful current meter array is at the north end of the Izu-Ogasawara Trench. Thesevelocity data provide excellent evidence of thecyclonic sense of deepcirculation overthe trench. Again, statistics are available at http:/ /dpo.ori.u-tokyo.ac.jp:81/.Thefocus hereis on 30 current meter records nominally along 34N, longer than 100 days, with deploymentsstarting as early as November 1987 and as late as May 1995. The record lengthsrange from 266to 536 days, with an average of 401days. Their longitudes range from 141.170to 142.547E and their depths range from 3830to 8961m. The bathymetry hereis more complicated than at the array over the Kermadec Trench, with a lessuniform orientationof the trench walls. However, the moorings are roughly clustered at six locations,and the deep velocities are similar for mostdepths and deployments at each location.Therefore, the (record-length weighted) mean velocity vectors at each location aresimply presented over the bathymetry (Fig. 3). The mean directions are very closely alignedwith the isobaths, and again the sense of circulationis cyclonicaround the trench axis.On the west side of the trench the  owis nominally equatorward with magnitudes of 336 Journalof MarineResearch [56, 2

Figure3. Mean deep current vectors over GEBCO bathymetry(IOC, IHO, andBODC, 1994).The Japancoast (thin lines), and isobaths at 1-km intervals (thickest line at 1 kmtothinnest line at 9km)are shown. Data from moorings along 34N (available on the World-Wide-Web home page forthe Division of Physical Oceanography in the Ocean Research Institute at the University of Tokyo,http:/ /dpo.ori.u-tokyo.ac.jp:81/)nearthe north end of the Izu-Ogasawara Trench are recordsexceeding 100 days. All are below 3800 m. Data near 36N (Hallock and Teague, 1996) are between2000 and 4200 m atthe south end of the Japan Trench. V ectorsare averaged at each location(record length weighted) from instruments within these depth intervals. Data near 1900 and4900 m attheeastern location near 36N are excluded for reasons discussed in the text, so the vectorthere is representative of 2900 m only.See Figure 5c for average mooring locations and Figure1 fortrench locations.

3.6,4.6, and 2.4 cm s 2 1,roughlyover the 4500, 6000, and 9000-m isobaths, respectively. At thecenter of thetrench the velocity magnitude is a minimumat 0.8 cm s 2 1, nominally equatorward.On the east side of the trench the magnitude is 3.0 and 12.8 cm s 2 1, but nominallypoleward, roughly over the 9000 and 6000-m isobaths, respectively. A few more deepcurrent meter records (again from http://dpo.ori.u-tokyo.ac.jp:81/)tothe south (near 33and29N) also show nominally equatorward  owofsimilar magnitudes on thewestside ofthetrench roughly over the 5000-m isobath, but these data are not shown here. At around36N isanother deep current meter array at thewesternboundary spanning the JapanTrench near its southwestern end (Hallock and T eague,1996) as well as RAFOS 1998] Johnson:Deep circulation over ocean trenches 337

oatsdeployed along the array at 3000m. These data are mostly consistent with a cyclonic senseof deep circulation over the Japan Trench (Fig. 3). The current meter data have been usedto document evidence of a weak,1.3 and 1.6 cm s 2 1,nominallyequatorward, deep western-boundarycurrent below 2000 m overthe 3300 and 4600-m isobaths on the west sideof the trench (Hallock and T eague,1996). These authors have also summarized variousother current meter records farther to the northeast at similar depths that show similarnominally equatorward velocities on the west side of the trench. The mean  ow directionsare all strongly aligned along isobaths, as inthe previous examples. On the east sideof thetrench a stronger,5.2 cm s 2 1,nominallypoleward  owexistsnear 2900 m over the6400-m isobath (Hallock and T eague,1996). Near 4900m arelativelystrong, 3.2 cm s2 1 owis found toward 318° T .Thislocation is veryclose to Kashima 1 Guyot, whichrises to around 3500 m, so the  owat 4900 m maybe heavily in uenced by this seamountand is not included in Figure 3. Measurements near 1900 m reportan even stronger,8.2 cm s 2 1,nominallypoleward, 65° T ow,inaccord with expectations, but it maybe sufficiently shallow to be unrepresentativeof theabyss, so it is alsonot included in Figure3. Neutrallybuoyant RAFOS oatsdeployed at a nominaldepth of 3000m during currentmeter operations all show nominally poleward  owontheeast side of thetrench and,with the exception of the oatdeployed farthest west, weaker nominally equatorward owonthewest side of thetrench (S. C.Riser,personal communication, 1997). Deepcurrent meter data over the Kuril Kamchatka Trench come from arecent deploymentof nine moorings ranging in position along a linefrom 36.40N,146.11E to 42.30Nto 150.23E (W .B.Owens andB. A.Warren,personal communication, 1997). Y et again,the available current meter records are consistent with a deepcyclonic sense of circulationover the trench, with westward  owonitspoleward side and eastward  owon itsequatorward side. Current meters were deployedat nominal depths of 2000,3000, and 4000m for alengthof 744 to 758 days, with one exception of a 379-dayrecord. The northwesternmooring is located roughly over the 4000-m isobath on the poleward side of thetrench axis. The magnitude of themean velocity at 2000and 3000 m isonly0.2 and 0.5 cm s2 1,butthere is a4.3cm s 2 1 owtoward259° T, nominally westward and roughly parallelto the isobaths, at 4000 m (see Fig.5c for mooringlocations). The nextmooring to thesoutheastis located between the 7000and 6500-m isobaths just on the equatorward side ofthetrench axis. This mooring has an extra instrument at anominaldepth of 5500m and theexceptionally short record at 3000 m. The  owdirections and magnitudes at this mooringare similar at alldepths, and the record-length average is 8.1cm s 2 1 toward59° T, nominallyeastward, again roughly parallel to the trench axis. Finally,another current meter array was occupiedover the AleutianTrench along 175W (Warrenand Owens, 1985; 1988). Since only two moorings are located over the trench, a cyclonicsense of circulation around the trench is only suggested by these data. This circulationmay be shifted poleward of thetrench axis because there is eastward  owover theaxis. Five moorings were deployedover a fourteen-monthperiod from 45.972to 50.990N,with current meters at nominal depths of 2000, 3000, and 4500 m. The three 338 Journalof MarineResearch [56, 2

Figure4. V erticalproŽ les of velocity components [cm s 2 1,positivevalues shaded] oriented perpendicular(left panel) and parallel (right panel) to the axis, 77° T ,ofthemean velocity vectors overthe Aleutian Trench from a deepcurrent meter array along 175W (W arrenand Owens, 1985; 1988).The data are objectively mapped assuming a Gaussiancovariance with correlation lengths of1250m inthevertical and 145 km inthehorizontal and an error-to-signalenergy of 0.01. The correlationlengths used are roughly the mean instrument spacings in theregion and the error-to- signalenergy is unrealistically low ,socontoursare faithful at and between current meters (black dots),but should be regardedwith care outside array limits. V erticalexaggeration is 100:1. The 5-minuteresolution ETOPO5 bathymetryis used. See Figure 5d for mooring locations and Figure1 fortrench location. mooringsnorth of 49Nare located over the steep topography of thetrench and the rise just tothe south. The axis of the observed mean currents in this region (weighted by record length),is near 77° T. The isobaths, for boththe trench and the rise just to thesouth, have roughlythe same orientation. V erticalproŽ les of the mean velocity rotated in this direction (Fig.4) show a moderate(exceeding 3 cms 2 1)negative,nominally westward,  owalong isobathson thepoleward side of the trench, banked against the Aleutian Island Arc. This owis the expected deep northern-boundary current (W arrenand Owens, 1985; 1988). Over thetrench and on its equatorward  ankis a slightlyweaker (exceeding 2 cms 2 1) positive,nominally eastward, return deep  owpreviouslywithout interpretation (W arren andOwens, 1985; 1988). The velocities perpendicular to the mean current axis (Fig. 4) are againeverywhere small and less organized, as might be expected for thecomponent roughlyperpendicular to theisobaths. Insummary, available velocity measurements from long-termdeep current meters and oatsover the Kermadec, Mariana, Izu-Ogasawara, Japan, Kuril Kamchatka, and Aleutian Trenchesare nearly all consistent with cyclonic gyres of atleast a few cms 2 1 magnitude aroundthe trenches. These direct measurements are consistent with the inferences about thevelocity Ž eldfrom hydrographicproperty distributions and geostrophic shear in the 1998] Johnson:Deep circulation over ocean trenches 339 studiesreviewed in the previous section. The measurements interpreted here to imply cyclonicgyres above the trenches could also imply unconnected current-countercurrent pairsaligned with the trench axes, but the theoretical framework advancedbelow argues againstthis possibility.

4.Theoretical framework For allof the trenchesdiscussed in the previoustwo sections, the bathymetry unambigu- ouslyresults in regions of closed planetary geostrophic, or f/h,contours.Here f is the local Coriolisparameter and h isthe total thickness of the water column. Regional plots presentedfor theKermadec and Tonga Trenches (Fig. 5a); the southern portion of the MarianaTrench (Fig. 5b); the Izu-Ogasawara, Japan, and Kuril Kamchatka Trenches (Fig.5c); and the Aleutian Trench (Fig. 5d) conŽ rm thisassertion (see Fig.1 for Fig.5 panellocations). In some studies h isdeŽned as thethickness of somedeep layer beneath anarbitraryisobath or isopycnal(Kawase andStraub, 1991; Kawase, 1993a,b).DeŽ ning h asthetotal water-column thickness is amorestringent test for closedgeostrophic contours. If athinnerabyssal layer alone were tofeel the in uence of theisobaths, the regions of closedcontours over the trenches would be largerthan those shown. At anyrate, linearized planetarygeostrophic theory requires blocked geostrophic contours, so it isnotapplicable wherecontours are closed. Hence, the trenches are special dynamical regions, as discussed below. Numericalsimulations of Žnite-depthabyssal layers under inŽ nitely deep resting surface layershave shown that over regions with closed geostrophic contours upwelling results directlyin vortex stretching that drives a cyclonicrecirculation around these contours (Strauband Rhines, 1990; Kawase andStraub, 1991; Kawase, 1993a,b).Unlike eddy- driven ows,which have a directiondependent on the contour gradient, these recircula- tionsare cyclonic in sense over both hills and trenches that result in regions of closed geostrophiccontours, since they are driven by upwelling-induced vortex stretching. These experimentscannot reach a steadystate because they rely on prescribed upwelling or a supplyof mass tothe abyssal layer for forcingand do not include vertical mixing. However,the abyssal upwelling or mass sourcecan be keptsmall so the net abyssal layer thicknesschanges very slowly. The vortex stretching interior to agivenclosed geostrophic contourowing to theupwelling is balancedby the bottom drag along that contour, so the velocitieswithin the regions of closed geostrophic contours reach a nearlysteady balance. For asimilardynamic balance to holdover the trenches, the mechanics must be along thefollowing lines: A netupwelling over the trench is balanced by verticaldiffusion at the topof theabyss. This upwelling maintains relatively low pressure just over the trench. In theabyss,where stratiŽ cation is weakand  ownearlybarotropic, conservation of potential vorticitytends to prevent water from owingacross geostrophic contours and eliminating thepressure gradient, so water recirculates cyclonically around the trench in geostrophic balance.Restated, the upwelling results in vortexstretching, driving a cyclonicrecircula- tionaround the trench. W atercan cross geostrophic contours in abottomEkman layer or 340 Journalof MarineResearch [56, 2

Figure5. Absolute magnitude of planetary geostrophic, or f/h,contours[at 2 3 102 9 m2 1 s2 1 intervals]where f isthe local Coriolis parameter and h thetotal water depth, plotted for three differenttrench systems, (a) the Kermadec and TongaTrenches [from 0.6 to 1.6 3 102 8 m2 1 s2 1] withmooring locations for Figure 1 ( 1 ’s);(b) the southern portion of the Mariana Trench [from 0.2 to 1.2 3 102 8 m2 1 s2 1]withthe three mooring locations ( 1 ’s);(c) the Izu-Ogasawara, Japan, andKuril Kamchatka Trenches [from 0.8 to 1.8 3 102 8 m2 1 s2 1]withaverage locations for Figure3 andthe two moorings over the Kuril Kamchatka Trench ( 1 ’s);and (d) the Aleutian Trenchwith mooring locations for Figure 4 ( 1 ’s)[from1.6 to 2.6 3 102 8 m2 1 s2 1].The5-minute resolutionETOPO5 bathymetryis used. Some of thecontours over each trench (lightest regions) areclosed. The white regions are land masses. See Figure 1 forlocation of eachpanel. 1998] Johnson:Deep circulation over ocean trenches 341

Fig.5. (Continued) wheresmall-scale topographic relief allows ageostrophic  ow,sothe cyclonic recircula- tionis sufficiently strong such that the bottom ageostrophic transport into the trench balancesthe mass lostto upwelling. Restated, the magnitude of the upwelling-driven cyclonicrecirculation is limitedby bottomdrag. After ventilatingthe trench ageostrophi- callynear the bottom, water slowly spirals upward as it upwells and recirculates cyclonicallyaround the trench. Moreinsight into the dynamical balance can be obtained by manipulating reduced- gravity, f-plane,shallow-water equations for anabyssallayer. In addition to thegeostrophic balance,the momentum equation includes time-dependence, advection and a simple Rayleighterm, R 5 (2vf )1/2h2 1,thatmultiplies the horizontal velocity u. This term parameterizesfriction as a bottomdrag resulting from interiorspin-down by vertical velocityat thetop of the bottom Ekman layer. Here verticaleddy viscosity is v,theCoriolis parameteris f,andthe abyssal layer thickness is h.Thecontinuity equation is fully nonlinear,retaining time-dependence and including a sourceterm w withthe dimensionsof velocityto represent upwelling at the top of the abyss. Manipulation of themomentumand continuityequation gives a potentialvorticity equation w z q 1 u ·= q 5 q 2 R , (1) t h h wherethe potential vorticity q 5 ( f 1 z )/h,andthe relative vorticity z 5 = 3 u. 342 Journalof MarineResearch [56, 2

Fig.5. (Continued)

FollowingPedlosky (1987), a simplebalance is obtained by multiplication of (1) by h followedby integrationover a region, Ac ,boundedby aclosedgeostrophic contour, Cc , w f dA 5 Ru · dl. (2) e e Ac h r Cc

Thearea integral of theupwelling drives vortex stretching that is balancedby bottomdrag oncirculationaround the closed geostrophic contour. In deriving (2) upwellingis assumed tobe balanced by vertical diffusion, so that the system is in steady-state and the time-dependencevanishes. The vertical advective-diffusive balance at the top of theabyss 1998] Johnson:Deep circulation over ocean trenches 343

Fig.5. (Continued) coupledwith the Ekman layer at thebottom allows application of the divergence theorem, souponintegration the advective term also vanishes. The upwelling term in (1) remainsas anareaintegral in (2), with a simpliŽcation resulting from theassumption of smallRossby number so z f.Thefrictional curl term in (1) reducesto a lineintegral in (2) after ½ integrationand the application of Stoke’s theorem. Thisdynamical balance can be appliedto thevelocity data over the trenches to getan estimateof the magnitude of the necessary upwelling. For example,using the 5-minute resolutionETOPO5 bathymetry,the Izu-Ogasawara Trench is enclosedby f/h 5 1.15 3 102 8 m2 1 s2 1,boundingan area of 7.2 3 1010 m2 (roughly980 km in the meridional directionby 73kminthezonal direction) with a pathintegral of length2.3 3 106 m. The deepvelocity tangent to thisgeostrophic contour over the Izu-Ogasawara Trench is roughly 0.03 m s2 1.Thearea-averaged value of f/h insidethis geostrophic contour is 0.99 3 102 8 m2 1 s2 1;andthe mean value of ( f )1/2h2 1 alongthe path is 1.3 3 102 6 s2 1/2 m2 1. The leastwell constrained parameter is n ,whichcould conceivably range from 1 3 102 5 to 1 3 102 2 m2 s2 1.Abyssalviscosity estimates are sorely lacking, so this range is based on a rangefor microstructure-basedestimates of abyssaldiffusion (Polzin et al., 1997)assum- ingaPrandtlnumber between one and twenty. Fortunately, this parameter is undera square root,so the three-decade variability is reduced to a factorof thirty.These parameters yield upwellingvelocities from 4.0 3 102 7 to 1.3 3 102 5 m s2 1,arangeroughly three to one hundredtimes one estimated interior value for theabyss (Stommel and Arons, 1960). Whilethe present estimates are large, they fall well within the range of abyssal mass budgetsfor sillover ows, such as a recentone made north of the Samoan Passage (Roemmich et al., 1996).The net volume transport of bottom water ageostrophically ventilatingthe trench required to feedthe upwelling over it isreasonable. It ranges from 0.03 3 106 to 0.9 3 106 m3 s2 1,atmost a tenthof the net in ow of Circumpolar Deep Waterinto the North PaciŽ c Ocean(Johnson and Toole, 1993). W erethe effective vertical eddyviscosity and therefore the deep upwelling near the upper limits over most trenches, thena signiŽcant fraction of Circumpolar Deep W atercould be cycled through these trenchesas it moves around the PaciŽ c Ocean. 344 Journalof MarineResearch [56, 2

5.Discussion Theobserved deep cyclonic sense of circulation over the trenches is consistentwith a theoreticalframework predictingcyclonic recirculations driven by upwellingover regions ofclosed geostrophic contours. Of course,without other evidence, these recirculations couldbe driven by eddy potential-vorticity  uxesresulting from currentmeandering, waves,and other time-dependent phenomena in theupper ocean (Haidvogel and Rhines, 1983).In fact, the eddy driving does not have to occur over the entire trench, since such forcingover just a smallregion of theclosed geostrophic contours has beenshown to drive recirculationgyres (Thompson, 1995). Since most of thetrenches discussed are overlaid somewhereby a near-surfaceboundary current or boundary current extension, this mechanismcannot be discounted as a potentialdriving mechanism for thecyclonic recirculationsover the trenches. However, the relatively oxygen-rich and (in most locations)silica-poor character of waterbelow the trenchsills argues that the trenchesmust berelativelyvigorously ventilated by bottomwater, which must upwell over the trenches, mostlikely driving the cyclonic recirculations there. Thisdiscussion of course begs the question of what forces the cyclonic recirculation. Thesimple vertical advective-diffusive balance posited for thedeep ocean (Munk, 1966), whereupwelling of cold water from belowbalances diffusion of heat from above,may dominateand allow a densitygradient along the trench axis. Alternatively, the water atthe trenchbottom may be warmedmostly from belowby geothermal heating, allowing it to upwelland be replaced by colder, denser, source water. The relative sizes of geothermal heatingfrom belowand vertical diffusion of heatout of theabyssal layer above the trench canbe compared. There are few heat owmeasurementswithin trenches, but the values around0.050 W m 2 2 intheJapan Trench (Y amanoand Uyeda, 1989) are similar to the25 measurementscharacterized as being within PaciŽ c Oceantrenches with depths greater than5000 m reportedby Pollack et al. (1993).The diffusive  uxof heat from aboveis 6 2 3 2 4 2 1 given by k r cpu z, where r cp , 4 3 10 J m °C, and u z , 1 3 10 °C m for abovethe trenchsills. For thetwo quantities to be of comparable magnitude requires a vertical diffusivity k of 1 3 102 4 m2 s2 1,certainlyplausible for anabyssal value over steep topography(Polzin et al., 1997).With the large uncertainty in k and u z,itis difficult to speculatewhich effect might dominate. Manylong trenches exist, but no moreof which we areaware havelong-term velocity measurementsover them. In the PaciŽ c Ocean,the Philippine and Middle America Trenchesare both signiŽ cant trenches with closed geostrophic contours. These trenches are locatedin marginalbasins, and may not have sufficient bottom water ventilationto drive a strongcyclonic recirculation. However, maps of bottom water propertiesincluding dissolvedoxygen and silica do suggest that neither is totallystagnant (Mantyla and Reid, 1983).The Peru Chile Trench is probablylong enough to belocallyventilated by bottom waterat the southern end, supporting overall deep upwelling. This supposition is supported byastudyof theabyssal  owinthe region suggesting the Peru Chile trench is aprimary 1998] Johnson:Deep circulation over ocean trenches 345 sourceof bottom water inow for thePeru and Panama Basins (Lonsdale, 1976). The fact thatthis trench is adjacent to aneasternboundary may not have a largeeffect on thenature ofthe recirculation, except on how it is fed with dense water. However, the trench intersectsthe equator, meaning the geostrophic contours are not closed. Thus, there should onlybe adeection of thenormal planetary geostrophic  owwarpedby the topography, notnearly as strong as the cyclonic recirculations (Kawase, 1993a).In the Atlantic Ocean, alongtrench that might have a cyclonicrecirculation similar to those discussed previously istheSouth Sandwich Trench. In the Indian Ocean, the Java Trench, which intersects the equatorand sits on aneasternboundary, is probablydynamically similar to thePeru Chile Trenchin thePaciŽ c Ocean. Itwould be interestingto quantifythe strengths of upwellingand recirculation around a deeptrench. The recirculation strength in the trenches may dwarf thesize of the net along-trench owandupwelling, as suggestedby thetheoretical framework advancedin theprevious section. In addition, the presence of deep western-boundary currents fre- quentlyconfounds matters. These factors would make it difficultto sufficientlyinstrument atrenchwith current meters to diagnose the recirculation, net  ow,andupwelling. Careful hydrographicmeasurements do reveal water-property contrasts and geothermal shear. However,the small signals, the potential for aliasingowing to thesynoptic nature of the measurements,and the difficultyin determiningreference velocities all mean that diagnos- ingan accurate absolute horizontal circulation much less upwelling over the trenches with hydrographicdata alone is virtually impossible. Deep  oatmeasurements would be difficultbecause side walls present problems below trench sills and above trench sills the oatsmight wander away from thenarrowtrenches. One possibility for quantifyingthe net owandupwelling strength is adeliberatetracer release experiment. The path length of closedgeostrophic contours and the magnitude of the deep cyclonic velocity for the Izu-OgasawaraTrench (if thevelocity measurements at the north end are typical) suggest anadvective time-scale of two years for owto cycle around the trench, a periodthat makesit amenableto sucha technique.For therange of verticalvelocity estimated in the discussion,a riseof between 30 and 1000 m wouldbe expected in one circuit of the hypothesizedspirals described by deep water parcels over the trench. The horizontal and verticalmovement and spreadingof a tracerpatch released below the trenchsill on oneside ofthetrench could be usedto diagnose the deep circulation and upwelling there.

Acknowledgments. Thiswork was funded by the NOAA Officeof Global Programs through the Climateand Global Change Program and the NASA PhysicalOceanography Program. The work wouldnot have been possible without the current meter and  oatdata collected, some of it quite recently,and kindly provided prior to publication by W orthD. Nowlin,Jr., W .BrechnerOwens, StephenC. Riser,Keisuke T aira,Bruce A. Warren,and Thomas Whitworth, III. Theirefforts are gratefullyacknowledged. LuAnne Thompson helped with theoretical considerations. The comments ofBruce W arrenand an anonymous referee greatly improved the manuscript. This is PMEL contributionnumber 1909. 346 Journalof MarineResearch [56, 2

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Received: 6October,1997; revised: 6January,1998.