Near-surface horizontal convergence and dispersion near the tidal-mixing front on Northeastern Georges Bank

Deep-Sea Research II 48 (2001) 311}339

Near-surface horizontal convergence and dispersion near the tidal-mixing front on Northeastern Georges Bank夽 Kenneth F. Drinkwater*, John W. Loder Fisheries and Oceans Division, Ocean Sciences Division, Bedford Institute of Oceanography, P.O. Box 1006, Dartmouth, Nova Scotia, Canada B2Y 4A2 Received 25 November 1998; received in revised form 8 November 1999; accepted 22 December 1999

Abstract Horizontal dispersion and convergence are evaluated from near-surface drifter data collected during the summer and autumn of 1988 and summer of 1989 in the vicinity of the tidal-mixing front on northeastern Georges Bank. The e!ective horizontal di!usivity coe$cient, K , estimated from the relative motion of the  drifters over the duration of the cluster tracking, increases as the cluster length scale, with a range from approximately !100 to 450 m s\ for length scales of approximately 5 to 58 km. At length scales(20 km, the magnitude of K is near zero with many negative estimates, indicative of convergence. At length scales  '20 km, K increases in magnitude and scatter. Above 30 km length scales, K is typically between   200}400 m s\. The dispersion as a function of length scale is compared to published estimates using apparent di!usivities, which are adjusted for the "nite size of the drifter cluster at release. Georges Bank shows lower apparent di!usivities at length scales(20 km and higher ones at scales '20 km. The latter are believed to be principally due to the large horizontal gradients in the seasonal #ow "eld, although other processes perhaps associated with the large tidal currents may also contribute. At the shorter length scales, the low dispersion is due to convergent processes. Examples of convergence at di!erent locations and under di!erent wind and strati"cation conditions are presented. Convergence near the tidal-mixing front tends to occur under light wind conditions and was observed in both seasons and in both years. During two intense southwestward windstorms, drifters also converged in the Bank's vertically well-mixed zone, apparently due to a combination of spatially varying Ekman depth and topographic e!ects.  2000 Elsevier Science Ltd. All rights reserved.

1. Introduction Strong tidal and non-tidal currents in shallow shelf regions such as Georges Bank provide the potential for enhanced overall horizontal dispersion rates while at the same time o!ering the 夽

Paper published in December 2000. * Corresponding author. Fax: 1-902-426-6927. E-mail addresses: [email protected] (K.F. Drinkwater), [email protected] (J.W. Loder). 0967-0645/01/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 4 5 ( 0 0 ) 0 0 0 8 4 - 9

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possibility of reduced dispersion rates in some areas (e.g. near-surface convergence in frontal zones). Indeed, earlier studies suggest the Bank is a highly dispersive environment, e.g. surface drifter studies have indicated horizontal di!usivities of order 100}1000 ms\ on scales of order 50 km (EG&G, 1979; Flagg et al., 1982), and a heat budget has indicated di!usivities of 150}380 m s\ for the central Bank in summer (Loder et al., 1982). Growing understanding of shear dispersion and chaotic stirring in energetic and spatially complex #ow "elds (e.g. Zimmerman, 1986; Ridderinkhof and Zimmerman, 1992; Ridderinkhof and Loder, 1994; Hannah et al., 1998a; Xu et al., 2000) point to several physical mechanisms for e!ective horizontal dispersion associated with the strong horizontal and vertical current shears on the Bank. On the other hand, the seasonal tidal-mixing front on Georges Bank (e.g. Flagg, 1987; Horne et al., 1989; Loder et al., 1993) provides the potential for near-surface convergence zones over the Bank's #anks from spring through autumn. Idealized (steady state) circulation models suggest that vertical mixing can reduce the along-frontal geostrophic jet in tidal-mixing fronts, resulting in an unbalanced pressure gradient that drives cross-frontal #ow including near-surface convergence (James, 1978; Garrett and Loder, 1981). More realistic 3-d circulation models (e.g. Naimie et al., 1994; Chen et al., 1995; Naimie, 1996; Chen and Beardsley, 1998) have con"rmed the importance of both frontal and tidally recti"ed circulation to the seasonally varying gyre on Georges Bank, and indicate the occurrence of some surface convergence. However, these models together with recent observational studies (e.g. Loder et al., 1992a) also indicate strong tidal variability and complex cross-frontal residual #ows in the frontal zone, such that the actual spatial and temporal structure of the cross-frontal #ows on Georges Bank remains uncertain. Direct measurements of surface convergence in tidal-mixing fronts historically have been elusive, although the observed concentration of debris, biological material and predators (e.g. LeFevre, 1986; Schneider et al., 1987) provides strong indirect evidence for its occurrence. Pingree et al. (1974) were among the "rst to report direct observations of convergence. Radio-tracked drifters drogued at 5 m and placed approximately 600 m on either side of a surface front between the Guernsey and Jersey Islands in the English Channel converged at the front within 4 h of deployment, and remained together for 3 h until recovery. In contrast, Simpson et al. (1978) observed highly variable currents near a surface front in the Irish Sea, with no evidence of convergence, and attributed the complex #ow patterns to the presence of frontal instabilities and eddies. At a tidal-mixing front o! Yorkshire in the United Kingdom, convergence was observed from maps of surface currents obtained with high-frequency radar (Matthews et al., 1993) and from a shipmounted acoustic Doppler pro"ler (ADCP) operating for 24 h (Lwiza et al., 1991). The former indicated moderate (0.14 m s\) along-front geostrophic #ow accompanied by convergent transverse currents of 0.02 m s\ near the front, but only in 4 out of the 20 days of measurements and under spring tide conditions. Di!erences in the structure and intensity of tidal-mixing fronts between regions, and temporal variability associated with the seasonal and tidal-modulation cycles, winds and other in#uences limit the representativeness of these observations for fronts in general. It is clear that additional measurements are required to establish the nature and persistence of convergence at tidal-mixing fronts, and the implications for dispersion rates. In this paper we describe drifter measurements taken in the vicinity of the tidal-mixing front on the Northeast Peak of Georges Bank. A total of 17 clusters, each containing 2}11 near-surface drifters, were released and tracked for one to several days during the summer and autumn of 1988 and the summer of 1989 (Drinkwater et al., 1992).

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Fig. 1. The study area on the northern #ank of Georges Bank showing the 1988 current meter sites (labelled 1}6).

The goals of the study were to: (i) determine the near-surface horizontal dispersion characteristics over northeastern Georges Bank, (ii) measure the rates of any surface convergence in the vicinity of the tidal-mixing front, and (iii) determine the spatial scales and temporal persistence of any convergence zones.

2. Study area 2.1. Setting Georges Bank is located on the outer edge of the continental shelf at the mouth of the energetic Gulf of Maine-Bay of Fundy tidal system (Fig. 1). Over the central part of the Bank, the waters are vertically mixed throughout the year, primarily due to strong ('1 m s\) semidiurnal tidal currents (Bigelow, 1927; Garrett et al., 1978; Horne et al., 1996). From spring to autumn, a tidal-mixing front separates the mixed area from the strati"ed waters over the Bank's sides (Flagg, 1987). The front is most intense along the Bank's northern #ank where there is steep sloping topography. In the present study area on the northeastern section of the Bank, the depth increases gently to the east and steeply to the north at the Bank edge (Fig. 1). The currents in this area are dominated by the rotary tidal currents superimposed upon an eastward residual drift that is part of the Georges Bank anticyclonic gyre (e.g. Butman et al., 1982; Horne et al., 1989). 2.2. Frontal study Our drifter tracking was part of a suite of physical and biological oceanographic measurements taken during the 1988}89 Georges Bank Frontal Study (Loder et al., 1992b, 1993; Perry et al.,

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1993). In addition to the drifters, the physical oceanographic program included moored current and hydrographic measurements at six sites in the frontal zone in 1988 and one in 1989 (Loder and Pettipas, 1991; see Fig. 1 for the location of the mooring sites); hydrographic surveys using CTD (Conductivity}Temperature}Depth) pro"lers and a CTD on an undulating towed BATFISH (Loder et al., 1992a); and small-scale turbulence estimates from microstructure pro"les (Oakey and Pettipas, 1992; Yoshida and Oakey, 1996). The motivation was to develop an improved description and understanding of circulation and mixing in the frontal zone, for use both in estimating the fate and impacts of discharges from oil and gas exploration on the Bank and identifying environmental in#uences on plankton and larval distributions and abundance.

2.3. Frontal structure and seasonal evolution The frontal system on northeastern Georges Bank is actually a hybrid of a tidal-mixing front and a shelf (bank)-edge front due to the di!erent salinities of the waters on and o! the Bank (Loder et al., 1993). The tidal-mixing front generally lies between the 60 and 80 m isobaths and is oriented roughly east}west in the western sector of our study area (near 673W) but bends to the southeast on the Northeast Peak. Its cross}bank position varies seasonally, with an on-bank advance in spring and summer, and an o!-bank retreat in the autumn (Loder et al., 1993). On the main mooring line across the Bank's northern edge (Fig. 1), the amplitudes of the seasonal and fortnightly/monthly displacements are 10}20 km, comparable to the 10}15 km tidal excursions. The evolution of the frontal structure during the 1988 drifter studies is illustrated by the cross-bank temperature and current distributions from current meters on the main mooring line (Fig. 2; see Loder and Pettipas, 1991 for details). A persistent gradient in near-bottom temperature is apparent between mooring sites 2 and 4, with intensi"cation and on-bank advance of the strati"cation through the summer (note that the near-surface region is not fully represented since the upper current meters were generally 11 m or more below the surface). The along-bank residual currents (Fig. 2; Loder and Pettipas, 1991) also show remarkable persistency with a general strengthening and broadening through the summer, and peak currents in the near-surface region at the edge of the Bank exceeding 0.4 m s\ in late August. The only notable exceptions to this persistence in June}October 1988 were current reversals during two intense storms in early October (see subsection on the 7}10 October drifter experiment). As a result of the tidal-mixing front (and the 60}80 isobaths) turning southeastward away from the Bank edge, the residual #ow on the Bank plateau weakens and spreads on-bank as one proceeds east in the study area. This spreading, as well as the persistence of the residual current pattern, is clearly apparent in the areal distribution of the monthly mean currents from the moored measurements (Fig. 3). The cross-bank spreading of the residual current results in a cross-bank divergence that should provide a tendency for increased north}south separation of drifters on the 30-km scale of the moored array (the extent to which the near-surface frontal-scale #ow is divergent in a 2-d horizontal sense is unclear however.) An alternative view of this spreading is the multiple summertime recirculation pathways found by Limeburner and Beardsley (1996) over the eastern end of the Bank in near-surface drifter studies. In addition to the tidal and subtidal hydrographic and current variations in the frontal zone on northeastern Georges Bank, there are also signi"cant in#uences from large-amplitude internal

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Fig. 2. Low-pass "ltered temperatures and currents during 1988 derived from the current meter data. The velocity contours are the along-bank #ows (positive to the east, out of the page). The near surface (11 m) cross-bank #ows are designated by arrows. The instrument positions, from mooring sites 1}4 in Fig. 1, are indicated by dots in the temperature panels.

waves (Loder et al., 1992a; Brickman and Loder, 1993). An internal hydraulic jump forms at the Bank edge during o!-bank tidal #ow and subsequently evolves into a pair of soliton-like depressions that move on-bank into the frontal zone. These depressions and associated high-frequency internal waves can often be detected visually as a series of surface slicks and apparent convergent lines. The waves break at, or prior to reaching, the tidally mixed waters and contribute to both vertical mixing (Brickman and Loder, 1993) and surface drift (Loder et al., 1992a) in the frontal zone. Together with tidal advection, the internal waves result in a strong coupling between the tidal-mixing front and the processes at the Bank edge.

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Fig. 3. The mean horizontal currents by month in the 10}25 m and mid-depth (34}43 m) layers. Smoothed versions of the 60, 100 and 200 m isobaths are also included.

3. Lagrangian methodology 3.1. Drift buoys and release strategy We used two types of drifting buoys in our study. The accurate surface tracker (AST) is an undrogued, surface buoy (top 1 m) positioned at 1}6 h intervals using the ARGOS satellite system (Fig. 4A; Dempsey, 1988). No positions were obtained between approximately 2 : 00 and 7 : 00 UT

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Fig. 4. The (A) ARGOS and (B) LORAN-C buoys used in the study and (C) the drogue con"guration for the LORAN-C buoy.

(Universal Time) because the satellite's orbital swath path did not overlap with the study region. ARGOS classi"es the accuracy of each buoy position depending upon the number of satellite messages received, the duration of the satellite pass, the minimum angle between the satellite orbit and the buoy, and the stability and consistency of the message received by the satellite. From this information, the latitudes and longitudes are categorized to lie within either 150, 350 or 1000 m of their true values 68% of the time (designated as quality 3, 2 or 1, respectively). Over 80% of the data were of quality 2 with the remainder divided nearly equally between quality 1 and 3. LORAN-C buoys also were used. These receive LORAN-C information, store it internally, and transmit it on VHF frequencies back to the research vessel. A detailed description of the buoy and its performance is given in Woodward et al. (1991). The buoy consists of a cylindrical hull approximately 1.5 m in length and a high-density foam ring for #oatation (Fig. 4B). A 1-m diameter, 5-m long holey sock drogue centered at 10 m was attached to the buoy on most occasions (Fig. 4C). Positions were obtained every 30 min and the transmitted LORAN-C data were logged on board the ship. The transmission range of the buoys was 30}50 km. Upon recovery of the buoy, the

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internal memory containing the LORAN-C position information was transferred to a computer, edited and the latitudes and longitudes were calculated. The absolute accuracy of the LORAN-C positions is estimated at 250 m (Canadian Coast Guard, 1988) with a repeatability of 25}50 m (Crawford, 1988; Mackas et al., 1989). Tests performed on land near the Bedford Institute con"rmed these "gures with the repeatability close to 25 m. Buoy clusters were released during four cruises, one in each of July, August and October 1988, and July 1989. During the summer of 1988, only ARGOS buoys were available, but on later cruises both types of buoys were deployed. All clusters were released 10}20 km upstream (west) of the current meters (Fig. 1) so that they would typically drift through the array. The buoys were generally deployed in a line or box con"guration across the tidal front although the strong tidal currents (1 m s\) and "nite deployment times (several hours) often resulted in an irregularly shaped cluster at the time of the "rst common "x for all buoys (considered to be the time of the cluster release). Vertical temperature and salinity pro"les were taken at most buoy release and recovery sites using a Guildline digital CTD. During July and October 1988, hydrographic data also were collected in the vicinity of the buoys with the BATFISH. Of the 17 clusters of drift buoys deployed (Drinkwater et al., 1992), 10 included LORAN-C buoys. Cluster sizes ranged from 2 to 5 ARGOS buoys and 3 to 9 LORAN-C buoys with an average of 3 and 6, respectively. The tracking varied between 1 and 5 days. Winds every 3 h were available from a meteorological buoy moored approximately 100 km south of the study site. In addition, wind speed and direction were recorded every 2}4 h from the ship's anemometer. The wind direction conforms to the oceanographic convention, i.e. the direction is that towards which the wind is blowing. 3.2. Data treatment and analysis The positions of the satellite-tracked buoys were obtained from the ARGOS data archives and edited to remove bad data. Velocities were calculated and additional positions eliminated if the magnitude of the resultant velocities exceeded 1.5 m s\. Where possible, the ARGOS positions were further checked through comparison of the velocities with those determined from the LORAN-C buoys. Approximately 3% of the ARGOS data were thus eliminated, with the majority of those being of quality 1. LORAN-C positions were determined from time di!erences (TDs) to the nearest 0.01 ls in the arrival of a series of radio wave pulses sent from a master and one or more secondary stations. Processing of the LORAN-C data included application of the Additional Secondary Factor (ASF) obtained from the Canadian Coast Guard (1988). The ASF compensates for local conditions because the LORAN-C radio waves travel at di!erent speeds over land and water. The data were also corrected for cycle selection errors commonly referred to as lane jumps (see Drinkwater et al., 1992, for details). Velocities were calculated from the edited drifter positions using successive "xes. In the absence of storm winds, the buoys released on the northern #ank of Georges Bank tended to move eastward to southeastward, consistent with the historical circulation pattern. Tidal currents inferred from the buoy trajectories reached speeds of over 1 m s\ on the Bank, whereas those o! the northern edge were about 0.2 m s\. Residual currents were relatively weak ((0.1 m s\) in the mixed waters (vertical density di!erences, *p , of (0.1 between 50 m and the R surface), increased (0.15}0.2 m s\) near the boundary between mixed and strati"ed waters

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(*p "0.1}0.8), and were maximum (0.25}0.35 m s\) over the northern side of the Bank in highly R strati"ed waters (*p '1). These currents are in good agreement with the moored measurements R (Figs. 2 and 3).

4. Horizontal dispersion rates In the case of discrete particles such as a cluster of drifters, dispersion refers to the rate at which the cluster spreads out from a combination of advective and di!usive processes. In a horizontally uniform mean #ow "eld, a cluster would be carried undisturbed by the mean #ow (advected) while smaller eddies or turbulent motions act to pull the cluster apart (di!usion). However, if there are horizontal gradients in the mean #ow on the scale of the cluster size, they will deform the cluster thereby contributing to its dispersion. Since the ocean consists of a more or less continuous spectrum of motion, its partitioning into advective and di!usive processes is often not straight forward and depends upon the scale of di!usion one is interested in. While di!usion is sometimes used synonymously with dispersion, they are only equivalent if there is no spatial variation in the mean velocity "eld. 4.1. Ewective dispersion First we estimate a bulk measure of the overall dispersion rate from the Georges Bank drifter data that includes both the e!ects of turbulent di!usion and the horizontal shears in the mean #ow. An e!ective horizontal di!usivity coe$cient (K ) can be de"ned in terms of the time rate of change  of the spread of the cluster, which in discrete form is 1 *(p) . K "  4 *t

(1)

For a cluster of n (*3) drifting buoys, the mean square displacement p is 1 L p" (x#y), (2) G G n G where x and y are the horizontal displacements of the ith drifter from the cluster centroid. The G G length scale (l) of the cluster is taken as l"3p.

(3)

K was estimated from Eq. (1) for each full cluster of drifters and for subsets in some cases. All  contained 3 or more buoys. The use of selected subsets of drifters allowed additional estimates of K over both smaller spatial scales, such as in the immediate vicinity of the tidal front, and longer  time scales, in cases where technical problems resulted in the early termination of data from one or more of the buoys. We chose to analyze 7 subsets of the LORAN-C buoys in addition to the 10 full clusters of LORAN-C buoys and 11 clusters of ARGOS buoys. The two buoy types were analyzed separately because of the di!erences in accuracy and sampling frequencies of the position estimates, and because the LORAN-C buoys were usually drogued while the ARGOS buoys were not. In

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Fig. 5. K as a function of the average length scale. The left panel shows the results from the full range of length scales  encountered during our study and the right panel is expanded for length scales (20 km.

addition to estimating K over the total tracking time, we also determined K using time   di!erences (*t) containing an integer number of 25-h periods in order to minimize possible variations arising due to the semi-diurnal and diurnal tides. Thus, for example, if a LORAN-C cluster was tracked for 64 h, K was estimated for periods of 0}64, 0}25, 25}50, and 0}50 h after  release. For the ARGOS buoys that are sampled at irregular times, the closest time intervals to integer number of 25-h periods were used. Plots of K as a function of length scale are shown in Fig. 5. The length scale was taken as the  average of l at the beginning and end of the time period used. The general pattern of the relationship is similar for both buoy types and independent of the time period chosen. At length scales below 10 km, K is near zero. Approximately half of the estimates are negative, signifying  convergence of the cluster. Between length scales of 10}20 km, the range increases (between!37 and 82 m s\) but the mean remains low (10 m s\). While the majority of the estimates are positive, there were still a large number of negative K 's. At scales between 20 and 30 km there is  a steep rise in K accompanied by increasing scatter. Although the range of K extends from !100   to 450 m s\ beyond length scales of 30 km, most values lay between 200 and 400 m s\. The latter fall within the range found in other energetic tidal regimes (100}1000 m s\; Zimmerman, 1986) and estimated for central Georges Bank from heat budget considerations (150}380 m s\; Loder et al., 1982). Our values however, are less than those of EG&G (1979) for the northern #ank of the Bank. They reported K ranged from 150}1000 m s\ with a mean of around 500 m s\ for  length scales of 20}60 km. Note that the negative values found at the longer length scales were due to temporary convergence over a 25-h period. 4.2. Comparison with Okubo+s dispersion estimates Okubo (1971, 1974) published dispersion rates in the open ocean and coastal environments based principally upon dye studies. The dye is generally released at a point source while the initial patch size for drifter releases is typically much larger. Assuming dispersion is a function of length scale, dispersion rates estimated from point source dye releases should, therefore, be lower at a given length scale than those obtained from drifter studies (EG&G, 1979). Smith (1989) noted the

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need to account for the virtual origin associated with the initial distribution of a cluster of buoys in order to make a valid comparison between drifter and dye study results and proposed using a modi"ed version of (1), i.e. p , (4) K " 4(t #t)  where t is the hypothetical time required for the cluster to grow from a point source to the  dimensions of the drifter cluster at the time of release, and p is the mean square displacement at t, the time since release. Thus, (t #t) is the di!usion time of the cluster from a point source. We refer  to K as the apparent horizontal di!usivity following Okubo (1971) and Smith (1989), in order to distinguish it from the e!ective di!usivity (K ) estimated from the measured spreading rate of the  cluster. On the basis of similarity theory of turbulence, Okubo (1974) argued that the area of a patch should increase as t and the apparent di!usivities should obey a 4/3-power law, i.e. p"c et 

(5)

and K "c el, (6)  where c and c are numerical constants, e is the rate of energy dissipation, t is the time from the   point source release, and l is the length scale of the patch. Using dye and #oat dispersion data, Okubo (1974) found that Eq. (5) applied locally over particular time scales with di!erences in the "t occurring at around half a day and 5 days. Similar results occurred in "tting Eq. (6) with changes at length scales of approximately 1 and 20 km. These di!erences were attributed to e being relatively constant within, but di!ering between, the tidal (time scales from 1 h up to 1/2 day), inertial (time scales from 1/2 day to several days) and subinertial (time scales greater than several days) spectral ranges. We estimated t from Eq. (5) using the measured p at the time of release and Okubo's (1974)  estimate of c e for the inertial subrange of 5.4;10\ in mks units. The corresponding value of e is  similar to the upper-ocean values (order 10\ m s\) computed from microstructure measurements along the Georges Bank mooring line (Loder et al., 1993). Knowing t , we then calculated  K for each cluster or subset of drifters from Eq. (4). The apparent di!usivities for the ARGOS and for the LORAN-C drifters based on the full tracking duration are provided in Tables 1 and 2, respectively. Corresponding K and K values  are strongly coupled with the latter exceeding the former at higher values, as expected (Fig. 6). At smaller values, however, K 'K . This is because of the observed convergence. K is negative   under such circumstances but K is by de"nition always positive since it is referenced to a point source. Estimates of K based on the Georges Bank drifters are plotted as a function of l (Fig. 7) in C order to compare with Okubo (1974). His values are given by Eq. (6). Estimates of c e for the  inertial and sub-inertial ranges were obtained from Fig. 7 in Okubo (1974). Georges Bank dispersion shows a steeper rate of increase, with lower di!usivities than predicted at length scales smaller than approximately 15}20 km and higher di!usivities at length scales '20 km. For the LORAN-C and ARGOS buoys, K varied as l  and l , respectively; however, after taking

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Table 1 Estimates of the horizontal eddy di!usivities on Georges Bank from ARGOS drifters Tracking period M/D/Y

No. of Buoys

l (km) l (km) t(h)  

t (h) 

K  (m s\)

K (m s\)

K $SD V (m s\)

K $SD W (m s\)

Aug. 23}26/88 Aug. 27}28/88 Aug. 29}31/88 Sep30}Oct2/88 Oct. 3}6/88 Oct. 7}10/88 Oct. 11}12/88 Oct. 13/88 Oct. 14}16/88 Jul. 14}19/89 Jul. 24}26/89

4 4 4 3 3 4 4 4 3 3 4

28 19 28 17 11 10 23 14 6 31 28

150 118 152 107 80 78 134 95 57 163 152

379 61 326 265 3 !7 224 !16 !2 392 172

120 33 109 90 7 2 66 12 2 186 69

116$81 31$32 90$82 * * 4$5 23$28 10$8 * * *

59$42 32$21 64$48 * * 5$4 64$39 22$14 * * *

55 26 53 42 12 6 37 13 6 81 42

46 35 48 43 65 85 30 11 38 111 42

The length scales of the cluster at the release (l ) and end (l ) of the tracking are based upon the measured mean-square   displacements, p; t is the duration of the cluster tracking; t is hypothetical time from a point source to the cluster size at  release and was estimated from Eq. (5); the e!ective horizontal di!usivity, K , is derived from Eq. (1); the apparent  horizontal di!usivity, K , is derived from Eq. (4); and K , K are the anisotropic di!usivities in the east}west and V W north}south directions, respectively, estimated from (8) with c"0.1.

Table 2 Estimates of the horizontal eddy di!usivities on Georges Bank from LORAN-C buoys. See Table 1 for description of the variables Tracking period M/D/Y

No. of Buoys

l (km) l (km) t(h)  

t (h) 

K  (m s\)

K (m s\)

K $SD V (m s\)

K $SD W (m s\)

Oct. 1}2/88 Oct. 3}6/88

3 6 4 5 3 4 4 3 9 8 5 7 4 6 5 6 4

10 15 14 19 20 14 11 7 24 25 28 17 11 21 18 28 13

117 92 84 122 101 241 101 70 188 217 206 129 106 140 180 242 114

82 !20 !14 13 !16 641 58 7 199 219 78 51 36 82 164 409 25

28 12 8 20 9 184 19 6 68 89 57 27 18 34 64 126 18

* 16$7 11$8 13$12 * 19$14 13$7 * 83$37 82$37 69$43 28$11 4$22 39$25 37$25 61$36 10$9

* 36$11 14$11 34$15 * 65$77 10$7 * 61$19 58$23 29$18 30$19 3$2 70$39 75$52 150$82 10$11

Oct. 7}10/88 Oct. 11}12/88 Oct. 13/88 Oct. 14}16/88 Jul. 14}20/89

Jul. 20}21/89 Jul. 24}26/89 Jul. 27}29/89

19 13 12 20 15 56 15 9 39 48 44 22 16 25 34 57 18

26 16 34 41 83 36 15 37 37 60 116 29 31 19 47 46 49

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Fig. 6. The relationship between the apparent (K ) and e!ective (K ) di!usivities based upon the LORAN-C buoy results  and using the full time duration of the drifter tracking.

Fig. 7. The apparent di!usivities (K ) as a function of length scale (l ) for the ARGOS buoys (left panel) and the  LORAN-C buoys (right panel). Also plotted are Okubo's (1974) estimates for the inertial and subinertial ranges.

into account the uncertainties in the regression coe$cients, there is no signi"cant di!erence between them. They are both statistically signi"cantly higher than the l  suggested by turbulence theory (Eq. (9)) using the standard f-test. While the end length scale (l ) is used in the analysis  of K and an average length scale (l ) for K , the di!erences between the two length scales in our   study were small. On average l 'l , but only by 10%. For those clusters where convergence   occurred, the average length scale exceeded the end length scale. 4.3. Contribution of the mean velocity shears We also estimated a di!usion rate following the method purposed by Okubo and Ebbesmeyer (1976) that removes the dispersive e!ect due to the linear velocity gradients in the mean #ow. Assuming the horizontal velocity of the ith drifter at time t can be expanded in a Taylor series

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about the centroid, then *u *u u (t)"u # x # y #u , G G G *x *y G

(7)

*v *v v (t)"v # x # y #v , G G *x G *y G u and v are the velocity components relative to the centroid in the x (positive eastward) and y G G (positive northward) directions, respectively; u and v indicate the velocity residuals, and the G G overbar indicates the velocity of the centroid. If the velocity residuals are further assumed to represent turbulence, an estimate of the time-dependent anisotropic eddy di!usivity may be obtained from K (t)"cp  p V S W

K (t)"cp  p , W T V

(8)

where






L 1 L (u ), (v ) (p  , p  )" G G S T n!1  



(9)

and






1 L L (p , p )" x, y V W G G n!1  



(10)

are the turbulence intensity and mixing length components, respectively. Okubo and Ebbesmeyer (1976) argued that the constant c lay between 0.1 and 1.0. We estimated di!usivities from Eq. (8) using the least-squares "t to the drifter data to determine the mean currents, their spatial gradients and the residual currents. A c of 0.1 was chosen following Smith (1989), who found it produced results consistent with other measures of di!usivity from his studies on Browns Bank. The results show a slight tendency for K 'K but the relatively large uncertainties in the W V estimates mean the result is not statistically signi"cant (see Tables 1 and 2). An average of K and V K (K "[K #K ]/2) was compared with the bulk di!usivities estimated above (Richards and W VW V W O'Farrell, 1987). K is generally smaller than K since the latter includes the dispersive e!ect of the VW C mean horizontal velocity shears (Tables 1 and 2), but the two are highly correlated (r"0.8). The ratio K /K is 3}5 for K '100 m s\, which suggests the mean horizontal velocity shear  VW  accounts for a large percentage of the overall e!ective di!usivity. K '100 m s\ corresponds to  length scales of approximately 25 km and greater (Fig. 5). The tendency towards higher dispersion at length scales longer than 20 km on the northeastern peak of the Bank is thus believed to be due in large part to the increased contributions of velocity shears in the mean and low-frequency #ows, principally from the strong horizontal shear of the residual jet in the study area with possible contributions also from the spreading of the jet (Figs. 2 and 3). These results, especially the magnitude of the ratio, must be tempered by the uncertainty in the constant c used in calculating K and K . EG&G (1979) used a c of 1 (for the northern #ank of the V W

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bank, K was reported as 400 m s\ along 1523 T and K as 79 m s\ along 623 T). A c of 1 in our V W study would produce K and K values well in excess of K and would not be realistic. On the basis V W  of this we believe the EG&G values of K and K are over-estimates. A c value higher than the 0.1 V W we used cannot be ruled out, however. Convergence associated with the tidal front is considered to be the main contributor to the small and below-normal di!usivities at the shorter length scales. This conclusion is supported in the following section in which we examine drifter trajectories and oceanographic conditions during times when convergence was observed. The analysis also reveals other convergent processes.

5. Examples of convergence 5.1. 2}5 July 1988 : light winds in early summer On 2 July 1988 when there was a classical tidal-mixing front within 20 km of the Bank edge (Fig. 2), two undrogued ARGOS buoys were released along 673W approximately 4 km apart. Their subsequent movements over a 3-day period with wind speeds around 5 m s\ were described by Loder et al. (1992a, 1993). Hydrographic data collected with the BATFISH shortly after deployment indicate that the buoys were placed in weakly strati"ed waters. They drifted eastward with a mean speed of 0.2 m s\ while displaying the typical large rotary motion due to the tides (Fig. 8). Within 20 h the buoys were separated by less than 1 km, a distance they maintained for the next half-day (Fig. 8). They then moved 2}3 km apart and remained so for approximately a day before converging again. A CTD section along the main mooring line taken 26}31 h after deployment, and computationally adjusted for tidal advection to the time when the buoys crossed the line (Fig. 1 in Loder et al., 1993), indicates that the buoys were in a zone of high surface-temperature gradient about 10 km north of the mixed-water boundary. Approximately 70 h after they were deployed, the buoys were recovered(1 km apart, in a visible surface convergence line that contained large quantities of foam, seaweed and jetsam. Seabirds congregated along this line, which stretched roughly east}west. Current meter data 7 km WSW of the recovery site and a satellite infrared image taken 8 h after recovery suggest the buoys were recovered in weakly strati"ed water, still about 10 km north of the mixed-water boundary (Fig. 9). During the "rst 16 h of tracking, repeated temperature sections near the cluster were obtained from BATFISH tows (Loder et al., 1992a). Approximately 7 h after deployment, at the time of maximum o!}bank position of the buoys, the northernmost buoy was located near the hydraulic jump at the northern edge of the Bank (Fig. 10). As the internal soliton propagated onto the Bank, the separation distance between the buoys decreased from 4.5 km to(1 km within 9 h, indicating an average speed of convergence of 0.11 m s\. Thus the soliton appears to have contributed to the convergence, although the convergence continued as the currents switched to o!-bank #ow. This example suggests that an additional contributor (besides the ageostrophic frontal circulation) to surface convergence in the vicinity of the tidal-mixing front on northeastern Georges Bank may be the on-bank propagating internal waves generated at the Bank edge. This could occur through transient surface convergences and/or enhanced transport of surface material towards the front as suggested by Shanks (1983) and Lamb (1997).

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Fig. 8. The drift tracks of the two buoys deployed on 2 July 1988 (top panel) and the time series of the separation distance between the buoys (bottom panel). The solid line in the top panel is the track of buoy 2750 and the dashed line buoy 2757. The x- and y-distances in the bottom panel are the absolute values of the separation in the east}west and north}south directions, respectively.

5.2. 27}28 August 1988 : light winds in late summer On 27 August 1988, when the frontal-zone strati"cation was near its seasonal maximum (Fig. 2), four undrogued ARGOS drifters were released over a distance of 15 km near 673W. Two buoys (2757 and 4447) were placed in the mixed water, and two (4440 and 2754) in weakly strati"ed water (Fig. 11). They drifted for almost 30 h under predominantly calm wind conditions and were recovered with separation distances of about 6 km for the northernmost pair and 3 km for the southernmost pair. The mean currents were southeastward with the magnitude in the strati"ed water (0.12}0.13 m s\) approximately four times that in the mixed water (Drinkwater et al., 1992). This current shear resulted in the orientation of the cluster rotating clockwise from one that was primarily cross-frontal to one that was more along-frontal, although the end position of the centroid was near its initial position (Fig. 12). Note that although the buoys were all deployed near

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Fig. 9. Sea-surface temperature on Georges Bank 8 h after the buoys were recovered as derived from a NOAA-9 satellite image. The locations of the buoys at release (#) and recovery (solid triangle), adjusted to the stage of the tide when the image was taken, are shown together with the current meter sites (circles).

Fig. 10. The temperature distributions from two BATFISH sections along 66347W on 2 July. Times (UTC) and the near-bottom (57 m) cross-bank vector at site 2 are shown beneath each section. The current meter sites are denoted along the distance axis by circles. ARGOS buoys 2750 and 2757 are denoted by the letters X and Y, respectively. Letters A and B denote internal wave features. See Loder et al. (1992a) for more detailed discussion.

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Fig. 11. The temperature and p sections along 673W on 27 August 1988 at the time of deployment of the ARGOS buoys. F

Fig. 12. (A) Trajectory of the centroid for the cluster of undrogued ARGOS buoys deployed on 27 August and (B) the position of the buoys relative to the centroid as a function of time. The numbers adjacent to the positions of the centroid in (A) indicate the time in hours.

673W, by the time the full suite of drifters were released and the "rst common "x obtained, the cluster centroid had been advected almost to 66.93W. The minimum cluster size occurred approximately 10 h after release (Figs. 12B and 13) when the cluster centroid was at its northernmost location (Fig. 12A). Thereafter, the cluster size increased due to horizontal current shear, speci"cally due to the continual separation in the east}west direction of the buoys in the mixed and strati"ed waters. On the other hand, in the north}south (y) direction, which was approximately perpendicular to the orientation of the front, there was an overall convergence of the four buoys. Further evidence of cross-frontal motion is suggested from the surface-to-bottom density di!erences (*p ) at the release and recovery sites. They indicate movement towards the strati"ed R side for the 2 buoys deployed in mixed water (*p "0 on deployment to 0.1 on recovery for buoys R 2757 and 4447) and towards the mixed side for the northernmost buoy (*p "0.8 to 0.2 for 2754); R i.e. convergence in the frontal zone. On the other hand, the *p for buoy 4440 changed from 0.1 to R 0.6 indicating movement to more strati"ed waters.

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Fig. 13. The length scale of the cluster of undrogued ARGOS buoys deployed on 27 August as a function of time from release.

This example provides evidence for signi"cant cross-frontal surface convergence, even in the presence of considerable shearing by the seasonal along-frontal #ow. 5.3. 7}10 October 1988 : strong winds in autumn Seven LORAN-C buoys, drogued at 10 m, were deployed on 7 October 1988 during light winds following a 24-h period (4}5 October) with southwestward winds of 20 m s\ that pushed strati"ed water onto the Bank (Fig. 2). Two of the buoys failed immediately, two others worked for slightly less than 2 days (Drinkwater et al., 1992). The remaining three buoys were tracked over 3.5 d while a second intense storm passed over the Bank. They were released in the vicinity of the tidal-mixing front near 673W (Fig. 14), two in weakly strati"ed water (buoys 22 and 25; *p "0.2) and the other R (26) in more strongly strati"ed water (*p "0.9). Shortly after their release, the wind turned R southwestward again and increased speed, reaching a maximum around 30 m s\ near the end of 8 October (Fig. 15). The wind speed then declined and the direction gradually shifted eastward and eventually northward. In response to the storm, the buoys moved southwestward for the "rst 2.5 d, then eastward for the remaining day (Figs. 14 and 15). This current pattern was consistent with the near-surface (11 m) current-meter data from mooring site 4 (Loder and Pettipas, 1991), and involved a broad reversal of the along-bank #ow in the frontal zone (Figs. 2 and 15). The current meter indicated a slightly greater #ow than the buoys during the southwestward winds, consistent with it being in more highly strati"ed water and hence a shallower Ekman layer. Following the peak wind stress, the current meter indicated a stronger and more southeastward #ow than the drifters, consistent with the spatial pattern in the mean circulation over the Bank. All three buoys were recovered on the central Bank in relatively mixed waters (*p (0.04). R Somewhat surprisingly, the size of the cluster decreased rapidly during the "rst 10 h after deployment and continued to decrease to a minimum approximately 36 h after deployment (Fig. 16), which coincided with the peak in the wind speed (Fig. 15). The separation distance

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Fig. 14. (A) The cross-bank temperature and p sections on 7 October 1988 at the time of deployment, and (B) the drift F tracks of drogued LORAN-C buoys 22, 25 and 26 with circles indicating mooring sites.

between buoys 22 and 25 gradually decreased over the "rst day and a half from 12 to 1 km. For the remainder of the time they generally stayed within 1}2 km of one another. Buoy 26 approached within 4}5 km of the other buoys but began to diverge after approximately 36 h. Four undrogued ARGOS buoys released at the same time in the same area displayed a similar response to that of the LORAN-C buoys, including southwestern movement and convergence during the build-up of the storm, and eastward #ow and dispersion after the storm peaked. The currents derived from the ARGOS buoys were generally higher and more southward than those from the LORAN-C buoys were. The former is consistent with expected higher velocities at the surface compared to 10 m. A similar pattern of drift onto the central Bank and associated convergence also was observed for clusters of LORAN-C and ARGOS buoys during the earlier southwestward windstorm on 3}6 October (Tables 1 and 2). The leading candidate for the cause of the initial rapid convergence in these experiments is spatial variability in the depth of the Ekman layer, with the buoys in the shallower Ekman layer in

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Fig. 15. The wind rate (bottom left panel) and direction (top left panel) during the tracking of the buoy cluster released on 7 October (vertical arrows on the time line denote the deployment and recovery times of the cluster). The drift track of the centroid of the LORAN-C drifters (solid line) and that based on the velocities at 11 m for current meter site 4, relative to the position at the time of deployment (0, 0) (right panel).

Fig. 16. (A) The length scale of the cluster of LORAN-C buoys 22, 25 and 26 tracked from 7 to 10 October and (B) the position of the buoys every 12 h during the tracking. The origin (0, 0) of the latter plot corresponds to 423N, 673W and the numbers by the triangles formed by the buoy positions denote the time-since release.

strati"ed waters moving faster than those in the deeper layer in the well}mixed region. This mechanism has been shown to occur in numerical model simulations of the wind-driven circulation over the Bank (Hannah et al., 1998b). However, another convergence process also must have been operative since the buoys continued to converge within the mixed region during the period of strong winds. A possibility for this is surface convergences associated with the complex 3-d residual circulation expected from tidal recti"cation over the pronounced sand ridges on central Georges Bank (e.g. Tee, 1987; Gross and Werner, 1994). This suggests that, although such tide}topography interactions are expected to lead to chaotic stirring and enhanced horizontal dispersion for the

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Fig. 17. (A) The temperature and p sections along 66352W on 14 October at the time of deployment and (B) the drift F tracks of the LORAN-C buoys. The current meter sites are denoted by circles.

water column as a whole (e.g. Ridderinkhof and Loder, 1994), there may be convergences and reduced dispersion for buoyant material (or drifters) in the near-surface region. This example points to additional convergence mechanisms on Georges Bank, involving wind forcing and interactions with complex topography. 5.4. 14}16 October 1988 : light to moderate winds in autumn On 14 October 1988, with the tidal-mixing front persisting but with reduced temperature and density gradients (Fig. 2), three undrogued LORAN-C buoys were deployed along 66352W. Two were placed in mixed water (buoy 26, *p "0; buoy 25, *p "0.06) and the third in weakly R R strati"ed water (22, *p "0.4; Fig. 17A). The buoys drifted for 36 h. Winds were moderate R (6}10 m s\) eastward over the "rst 24 h, then decreased to light ((6 m s\) as they shifted to near westward. All of the buoys moved approximately east}southeast at a mean rate of 0.13 ms\

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Fig. 18. The length scale of the cluster of 3 LORAN-C buoys deployed on 14 October (left panel) and the time series of the separation distance between the buoy pairs (right panel).

(Fig. 17B). The residual currents were highly time-dependent, however, with 98% of the net eastward displacement occurring during the "rst M tidal period.  The size of the cluster decreased slightly during the "rst day, with the minimum occurring at 15 h after deployment (Fig. 18). This was due to the movement of buoys 25 and 26 from an initial separation distance of 2 km to less than 1 km (Fig. 18). The northernmost buoy (22) was deployed approximately 4}5 km to the north of the other buoys and remained at that distance until a few hours prior to recovery when it began to separate. The buoys deployed in the mixed water were recovered in slightly-strati"ed water (*p "0.1) whereas buoy 22 moved towards weaker strati"caR tion (*p "0.2), indicating that the convergence was located in weakly strati"ed water near the R mixed-water boundary. This example indicates that there is surface convergence in the tidal-mixing front in the absence of strong cross-frontal gradients in near-surface hydrographic properties, apparently due to the pressure "eld associated with subsurface hydrographic gradients. 5.5. 27}29 July 1989 : moderate winds in mid summer On 27 July 1989, four drogued LORAN-C buoys were deployed across the tidal-mixing front near 67316W and two others approximately 30 km to the north just o! the bank in waters exceeding 200 m depth (Fig. 19A). The buoys drifted for upwards of 50 h under moderate (4}10 m s\) northeastward winds. Three were released near the mixed-water boundary: buoy 26 on the well-mixed side, 39 in weakly strati"ed water and 28 in more strongly strati"ed water (Fig. 19A). Buoys 26 and 39 were released approximately 5 km apart and remained at that separation distance for about 15 h (Figs. 19B and 20). The buoys then converged over the next 5 h and remained within a couple of hundred metres of each other until their recovery (Fig. 20). The relative velocity between the 2 buoys at the time of the rapid convergence reached upwards of 0.4 m s\ and averaged slightly over 0.2 m s\ during the 5 h period. Whereas the vertical strati"cation at release and recovery for buoy 39 was the same (*p "0.2), buoy 26 moved from mixed (*p "0.01) towards weakly R R strati"ed water (*p "0.2). Buoy 28 converged towards buoy 39 soon after deployment, then R

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Fig. 19. (A) The temperature and p sections along 67.273W on 27 July 1989 at the time of deployment of the buoys and F (B) the drift tracks of three of the LORAN-C buoys.

spread apart, reaching a maximum separation distance of over 7 km (Fig. 20). A day and a half after their deployment, the buoys again converged and remained within approximately 2 km of each other for the remainder of the time they were tracked. Density measurements at the time of recovery of buoy 28 indicate that it moved towards the mixed water. The presence, at least occasionally, of small-scale ((2 km) eddies at the front was evident as buoy 28 encircled buoy 39. A fourth buoy deployed in the mixed water approximately 7 km south of the front, remained in the mixed water throughout the tracking and gradually separated from the other three buoys due to its weaker residual current. A strong periodic convergence and divergence at the tidal frequency also was observed between drifters located on and o! the Bank (Fig. 20). This periodicity is due to the larger cross-bank tidal excursions over the Bank plateau than in deeper water around the Bank (Fig. 19). During o! (on)-bank #ow the buoys on the Bank move more rapidly to the north (south) than those in deeper waters along the northern edge, leading to oscillations in the separation distance between the buoys on and o! the Bank (Fig. 20). This e!ect is expected for barotropic tidal currents, with the associated transient convergences and divergences occurring throughout the water column. In addition to the strong tidal oscillations in the length scale of the overall cluster, there was also

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Fig. 20. The separation distances of buoys 26 and 28 from 39 (left panel), and 24 from 39 (right panel) as a function of time from the release of the cluster. Also shown in the right panel are the v-velocities (positive northward or o!-Bank) derived from buoy 39.

a gradual increase with time associated with the stronger eastward residual currents over the Bank's side (0.26}0.32 m s\) than on its plateau (0.09}0.17 m s\). This example illustrates the occurrence of persistent convergence at the tidal-mixing front and oscillatory convergence/divergence at the bank edge.

6. Discussion and summary Detailed Lagrangian current observations obtained on the Northeast Peak of Georges Bank in the vicinity of the tidal-mixing front during July, August and October 1988, and July 1989 provide the "rst direct measurements of near-surface convergence in the Georges Bank frontal zone. Estimates of the e!ective horizontal di!usivity (K ) on Georges Bank determined from the time  rate of spread of the cluster during tracking ranged from !100 to 450 m s\ for length scales of 5}60 km. Di!usivity generally increased with the length scale of the buoy cluster. For l(10 km, K was typically near zero and many of clusters converged, resulting in negative values. Between  length scales of 10}20 km, K rose slightly but remained low with several clusters still exhibiting  convergence. Above length scales of 20 km, K rose rapidly with most estimates between 200 and  400 m s\ but with large variability. Estimates of the apparent horizontal di!usivity (K ) from the Georges Bank drifter data were compared to those derived principally from dye studies (Okubo, 1974) after accounting for the "nite size of the drifter cluster at release. The Georges Bank apparent di!usivities were lower than Okubo's for length scales (20 km and generally higher above 20 km, resulting in a rate of increase in the di!usivity as a function of length scale that was higher (l ) than the l  measured by Okubo (1974) and predicted by the similarity theory of turbulence. The higher apparent di!usivities at longer length scales on Georges Bank are in large part due to the horizontal shears in the mean #ow, especially in the case of clusters that straddled the Bank edge with drifters both on and o! the Bank. Other processes, perhaps associated with the strong tidal currents also may contribute to the higher di!usivities.

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The e!ective horizontal di!usivities are smaller by approximately a factor of 2 compared to those reported for the northern #ank of Georges Bank by EG&G (1979). Di!erences may be partially accounted for by the high spatial variability in the dispersion characteristics around the Bank (EG&G, 1979). They did not report convergence on the northern #ank; however, their deployments were generally to the west of ours and may not have been in close proximity to the tidal-mixing front. The low di!usivities at scales of (15}20 km are related to the presence of near-surface convergence zones on the northern #ank of Georges Bank, primarily associated with the tidalmixing front. First, in the absence of strong winds, buoys deployed near the front often drifted towards one another and were recovered closer together than when they were initially placed in the water. Second, the buoys were usually recovered in visible convergence lines where foam and other debris were observed. Third, hydrographic data collected at the buoy release and recovery sites indicated that for those clusters that converged, buoys released on the strati"ed side of the front tended to move into less-strati"ed waters whereas those deployed on the mixed side were recovered in slightly strati"ed waters. Thus there was near-surface movement towards the mixed-water boundary from both the strati"ed and mixed regions. Convergence at the tidal front was observed in all months (June, July and October) in both years (1988 and 1989) and by both the undrogued ARGOS buoys and the drogued (10 m) LORAN-C buoys. It appears to occur over a length scale of approximately 5}10 km on each side of the mixed-water boundary. Buoys placed beyond this distance from the boundary tended to diverge over time relative to those near the boundary due to the large horizontal current shear in the mean #ow. It should be noted, however, that not all buoy clusters deployed in the immediate vicinity of the tidal front converged. While idealized models suggest steady convergence in the vicinity of a front, our observations indicate a highly time-dependent process. Rapid convergence with velocities of 0.2}0.4 m s\ was observed over relatively short periods (hours) with little suggestion that it was related to a particular stage of the tide. Once convergence occurred, the buoys often remained together for upwards of several days although, on occasion, a buoy did diverge from the rest of the cluster. The cause of this rapid convergence and later divergence is unclear but may be related to baroclinic frontal dynamics, impinging internal waves and/or the presence of small-scale eddies at the front. Such eddies were suggested by the relative rotary motion of the buoys and are sometimes evident on satellite thermal imagery. One-third of the clusters with initial length scales of (20 km exhibited overall convergence (negative K ) measured over the full duration of the tracking and for one-half  of the clusters K (20 m s\, indicative of low dispersion. On the other hand, of those clusters  released with initial length scales exceeding 20 km, none converged over the full duration of the tracking and 80% had an associated K in excess of 100 m s\.  Other near-surface convergent processes are also operative on the Bank. Perhaps the most surprising of these occurred during two intense windstorms, both in October 1988. Strong southwestward winds pushed the buoy clusters into the mixed central part of the Bank. Convergence was most rapid as the winds increased and is believed to be due to spatial variability in the depth of the Ekman layer, with the buoys deployed in the shallower upper layer in strati"ed waters being accelerated faster than those released in the mixed region. A similar mechanism has been shown to occur in models of the wind-driven circulation over the Bank (Hannah et al., 1998b). Convergence continued to occur through to the height of the storm at which time the buoys were all believed to be within the mixed region of the Bank. The cause of this continued convergence is

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uncertain, but it seems likely that it was related to the complex 3-d circulation cells expected to arise from nonlinear tidal current interactions over the pronounced topographic features on the central Bank. We also documented an oscillatory convergence and divergence over the tidal cycle between water on and o! the Bank. This is caused by di!erences in the strength of the cross-bank tidal currents over the deep and shallow portions of the Bank, resulting in a transient convergence/divergence zone throughout the water column over the Bank's sides. Finally, on at least one occasion the buoys appeared to be in#uenced by the on-bank propagating solitons that evolved from the internal hydraulic jump at the edge of the Bank. This resulted in rapid but intermittent convergence and divergence. These results indicate that, at least in its near-surface waters, the combination of strong tides, topography and frontal structures on Georges Bank in summer and fall result in horizontal convergence mechanisms that can often o!set the tendencies for rapid dispersion by strong tidal, residual, wind-driven and other currents.

Acknowledgements We are grateful to our many colleagues who helped with the data collection and analyses from the Georges Bank Frontal Study. Particular thanks go to Gareth Harding, Ed Horne and Neil Oakey for leadership in the "eld program; Mary Jo Grac7 a, Liam Petrie and Roger Pettipas for assistance with data analyses; Peter Smith for providing programs for the di!usivity calculations; and Peter Smith, Charles Hannah, David Mountain and two anonymous reviewers for providing helpful comments on an earlier draft of the paper. We also acknowledge the funding support of the (Canadian) Federal Panel for Energy, Research and Development (PERD). US GLOBEC contribution 136.

References Bigelow, H.B., 1927. Physical oceanography of the Gulf of Maine. Bulletin U.S. Bureau Fisheries 40, 511}1027. Brickman, D., Loder, J.W., 1993. The energetics of the internal tide on northern Georges Bank. Journal of Physical Oceanography 23, 409}424. Butman, B., Beardsley, R.C., Magnell, B., Frye, D., Vermersch, J.A., Schilitz, R., Limeburner, R., Wright, W.R., Noble, M.A., 1982. Recent observations of the mean circulation on Georges Bank. Journal of Physical Oceanography 12, 569}591. Canadian Coast Guard, 1988. Radio aids to navigation. Supply & Services Canada catalogue CT51}5/1988E, Ottawa, Ont., 93 pp. Chen, C., Beardsley, R.C., 1998. Tidal mixing and cross-frontal particle exchange over a "nite amplitude asymmetric bank: A model study with application to Georges Bank. Journal of Marine Research 56, 1163}1201. Chen, C., Beardsley, R.C., Limeburner, R., 1995. A numerical study of strati"ed tidal recti"cation over "nite-amplitude banks. Part II: Georges Bank. Journal of Physical Oceanography 25, 2111}2128. Crawford, W.R., 1988. The use of Loran-C drifters to locate eddies on the continental shelf. Journal of Atmospheric and Oceanic Technology 5, 671}676. Dempsey, R.I., 1988. Low cost oil tracking drifter. ARGOS Newsletter 33, 14}15.

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