Seasonal variation of the threedimensional ... - Wiley Online Library

2 downloads 0 Views 2MB Size Report
framework for the observed seasonal circulation: (1) tidal rectification, present ..... tions is presented by LN93, for the case where F(Ri) - 1 and without wind or ...
JOURNAL

Seasonal

OF GEOPHYSICAL

variation

RESEARCH,

VOL. 99, NO. C8, PAGES 15,967-15,989, AUGUST

of the three-dimensional

15, 1994

residual

circulation on Georges Bank Christopher E. Naimie Dartmouth College, Hanover, New Hampshire

John W. Loder Department of Fisheries and Oceans, Bedford Institute of Oceanography,Dartmouth, Nova Scotia, Canada

Daniel R. Lynch Dartmouth College, Hanover, New Hampshire

Abstract. The seasonalvariation of the low-frequency circulation in the Georges Bank region is studiednumericallyby computingsix bimonthly circulation fields subjectto forcingfrom the barotropicM2 tide, mean baroclinicpressuregradients,and mean wind stresses.The model is three dimensional,diagnostic,and nonlinear, with quadraticvertical eddy viscosity that is stratification-dependent.Tidal forcing is imposedat the boundary of the domain, and an extensive set of density and wind data is used to determineclimatologicalmean forcings.The magnitudeof the M2 tidally rectified around-bankvelocities and transportsis sensitiveto stratificationinfluenceson the eddy viscosity, with up to a 50% intensificationrelative to computationswhich assumeno influences.The dependenceoccurs throughboth the local advective tidal stressterms and the large-scalebarotropic pressurefield. The six bimonthly solutions (January-February, March-April, May-June, July-August, September-October, November-December) indicate important contributionsfrom tidal rectification, baroclinicpressuregradients,and mean wind stressto the seasonalintensificationof the GeorgesBank gyre. Tidal rectification and baroclinicity are the dominant forcings, while wind stressgeneratesopposingaround-bankflow and cross-banksurface drift in winter. Overall, the solutionsare in approximateagreementwith observedEulerian around-bankcurrents and transports,althoughthere are both local and bank-wide discrepancies.The seasonalintensificationof recirculation around Georges Bank is well producedby the model, with estimatesof the recirculatingtransportincreasingfrom under 0.02 Sv (January-February)to over 0.13 Sv (September-October). 1.

Introduction

Circulation in the vicinity of submarine banks is a key feature of the coastal ocean. It can play an essentialrole in the dispersal or retention processesfor heat, nutrients, phytoplankton, zooplankton, and larval fish. The combination of abrupt, shallow topographywith seasonallyvarying atmospheric inputs of heat and momentum creates the potentialfor distinctive seasonalchangesin circulationpatterns which can be critical to bank ecology. We focus here on the seasonalmean circulation, in a shelf region where it is believed to be a major contributor to the subtidalcirculation. Under these conditionsone may conceptualizethe subtidal circulationvariability as the overlay of stochasticprocesses and events at all time scales,upon a deterministic seasonal mean which is cyclic. GeorgesBank boundsthe tidally energeticGulf of Maine at the shelf break (see Figure 1). Its horizontal extent is of the order of 300 (150) km in the along-shelf (cross-shelf) direction(see Figure 2), while the depth variesfrom lessthan Copyright 1994 by the American Geophysical Union. Paper number 94JC01202. 0148-0227/94/94JC-01202505.00

30 m on top of the bank to over 300 m on the gulf side. It has been studiedextensively [Backusand Bourne, 1987]. Observations indicate a partly closed, clockwise, low-frequency

circulation aroundthebankof theorderof 5-50 cms-•, with distinctive

seasonal variation

and several

well-established

features [e.g., Butman et al., 1987]. The large-amplitude semidiurnaltide resultingfrom the shallow topographyand the near-resonancein the adjacent Gulf of Maine/Bay of Fundy dominates the current record on the bank, with significantrectification on the bank sides. Associated with the seasonal cycle in temperature and salinity, the tide producesa mixing front encirclingthe bank at roughly the 60-m isobath, with a characteristic baroclinic structure of seasonallyvarying intensity. Mean winds also vary season-

ally, both in magnitudeand direction. Finally, the shelf/slope front lies along the southern flank at roughly the 100-m isobath, with shoalward migration from winter to fall. In a previouspaper [Lynch and Nairnie, 1993]we considered the three-dimensionalmodeling of tidal rectification on GeorgesBank for a barotropic fluid, conceptuallythe seasonallyinvariant part of the circulation. Herein we extend the modeling approach of Lynch and Nairnie [1993] to include seasonallyvarying stratification, baroclinicity, and wind stress.Our goal here is to provide a first estimate for

15,967

15,968

NAIMIE ET AL.' SEASONAL CIRCULATION 70ø

68ø

ON GEORGES BANK

66ø

64ø

62ø

45 ø

45 ø

44 ø

44 ø

GULF OF MAINE

43 ø

SHELF

43ø

OOOrr WILKINSON 42 ø

42 ø

GEORGES NANTI

41 ø

41 ø

SHOALS

NEW ENGLAND

SHELF

40 ø

40 ø I

i

70 ø

i

68 ø

i

66ø

t

64 ø

62ø

Figure 1. Gulf of Maine/GeorgesBank locator map.

the three-dimensional, bank-wide circulation cycle and to

evaluateits strengthsand weaknessesin the light of available observations. Our investigation is part of the developmentof realistic

three-dimensional

circulation

models

for

the

Georges Bank region, for use in particle-tracking applications such as the tracking of fish eggsand larvae [Werner et al., 1993; Tremblay et al., 1994; Lough et al., 1994; Ridderinkhof and Loder, 1994]. The calculationsare diagnostic,that is, densityis obtained from data. Both density and wind stressare estimatedfrom the most comprehensivesourcesavailable, in an attempt to obtain the climatological mean seasonalforcing. The diagnostic approach conceptualizes the seasonal cycle as a progressionthrough quasi-staticcirculationfields. The processesgoverningthe transition amongthese statesdemand greater sophisticationin the modelingapproachand are left for future study. We begin, in section 2, with a brief review of processes believed to make important contributions to the seasonal circulation on Georges Bank followed, in section 3, by a descriptionof the observationaldata used in model forcing and evaluation.

In section 4 the finite element model and our

applicationstrategyare described,followed in section5 by some model results which illuminate the significance of stratification-dependentinternal friction to tidal rectification.

Our primary resultsare presentedin section6 where, for six bimonthly periods grouped by the degree of stratification, the model flow fields are described, interpreted, and compared to observations.We concludewith a discussionand summary in section 7.

2.

Background

Butman et al. [1987] summarized the observed seasonal circulation on Georges Bank and reviewed the role of various processes believed to drive the circulation. They describeda generalincreasein along-bankspeedfrom winter (January-February) through late summer (September), with late summer current speedstypically twice those in winter. The seasonal variation

of northward

recirculation

in Great

SouthChannelindicateda partly closedresidualgyre around Georges Bank with maximum recirculation in late summer and minimum

recirculation

in winter.

Examination

of the

various forcing mechanismsled to the following conceptual framework for the observed seasonal circulation: (1) tidal rectification, present year-round, creates a basic clockwise recirculationtendency, (2) seasonallyintensifying stratification, and the associatedtide-induced frontal structure encircling the bank, reinforce the tidally rectified circulation, (3) winter wind stress contributes to off-bank near-surface

flow

NAIMIE ET AL.: SEASONAL CIRCULATION ON GEORGES BANK

15,969

toward the south and diminishes the tidally rectified northward recirculation in Great South Channel; wind is less of a

factor in other seasons,(4) the seasonallyvarying shelf/slope front dominates the circulation

seaward of the 100-m isobath

along the southern flank, and (5) an additional forcing, possibly an along-shelfpressuregradient, contributes to an along-shelfflow inside of the 100-m isobath on the southern flank, but its nature is unclear. An additional element of this conceptual framework was contributed by Loder and Wright [1985]: the impact of stratification-dependent friction on the tidal residual. The depth-dependent tidal rectification model of Wright and Loder [1985] was applied to cross-bank transects representative of the northern and southern flanks of Georges Bank, with vertically uniform eddy viscosity which varied with the bulk Richardson number. An idealized density field representative of the observed

summer frontal structure was used

and the response compared with the constant-densitycase (winter). The reduction in friction in summer increased the tidally rectified along-bank flow by 50% (northern flank) to 100% (southern flank). Adding the baroclinic pressure gradient, as given by Garrett and Loder [1981], contributed additional along-bank flow and significant structure. Favorable comparison with observations led to the conclusion that, shoalward of the 100-m isobath on the southern flank,

stratification-dependent tidal rectification plus baroclinic frontal

circulation

accounts

sonal intensification

for much of the observed

of the around-bank

circulation.

sea-

It is

therefore important to recognize two dynamical effects of seasonal baroclinicity: the stratification effect on vertical friction and the baroclinic pressure gradient. Numerical model studies on realistic full-bank geometry [e.g., Greenberg, 1983; Isaji and $paulding, 1984; Lynch and Nairnie, 1993] have demonstrated, with increasing detail, the significantcontribution of topographic tidal rectification around the entire bank and have also confirmed

'" •-' 20Ore--

'

.

-50

-100

-150 -200

-250

-300 1 O0

150

] 200

250

distance

300

350

400

450

(kin)

Figure 2. Mercator projection of the model bathymetry (60-, 100-, and 200-m isobaths) in the vicinity of Georges Bank. The solid lines labeled NF, SF, GSC, and NEP indicate the location of vertical sections used for Figures 4, 7, and 10 as well as Tables 2, 3, and 5. The northern flank section (NF) extends from 41.82øN, 67.67øW, to 42.20øN, 67.95øW, the southern flank section (SF) extends from 40.60øN, 67.19øW, to 41.39øN, 67.86øW, the Great South Channel section (GSC) extends from 41.01øN, 68.37øW, to 40.90øN, 69.03øW, and the Northeast Peak section (NEP) extends from 41.89øN, 66.80øW, to 42.41øN, 66.80øW. The (x, y) "viewport" shown is identical to that used in Figures 3, 5, 8, 9, 11, 12, and 13.

that

tidal rectification alone cannot account for the gyre intensity Beardsley, 1987]. For comparisonwith the model flow fields, (particularly in summer). Lynch et al. [1992] demonstrated bimonthly mean currents have been computed for each baroclinic enhancement of the bank-wide circulation using a vertical level by averagingover all months and years in each three-dimensional density field representative of summer. bimonthly period. The major features of the seasonally averaged residual Generally, it appears that three-dimensionalmodels should be capable of capturing the primary features of the seasonal circulation on Georges Bank are apparent in the bimonthly mean circulation on realistic topography, given correct sea- mean current distributions (Figure 3) for the near-surface, near-bottom, and intermediate-depth regions. The currents sonE forcing and proper resolution. are generally directed clockwise around the bank throughout the year but demonstrate strong seasonal, horizontal, and 3. Observational Data vertical variations in magnitude. The currents are generally 3.1. Currents strongestin summer and fall, in the near-surfaceregion, and Our primary source of quantitative information on ob- along the bank edge particularly on the northern side. Peak served residual currents is a database of monthly mean near-surfacespeedson the northern (southern) flank are 0.4 currents assembled from historical

moored measurements

at

28 different horizontal positionson GeorgesBank. Observations by various United States agencies during 1975-1980 [Butman et al., 1982, 1987] are supplemented by measurements taken by the National Marine Fisheries Service in 1985-1986 (J. Manning, personal communication, 1993) and the Department of Fisheries and Oceans in 1978 [Loder and Horne, 1991] and 1988-1989 [Loder and Pettipas, 1991]. Monthly means for a particular instrument/depth are included

for

each

month

with

at least

360 hours

of data.

Typically, each site has data from two or three depths and 1 or 2 years, although station A on the southernflank has data from 2-4 years dependingon the depth level [Butman and

(0.25) m s-• in summerand 0.2 (0.15) m s-• in winter. Recirculation of the gyre (northward flow) in Great South Channel is greatestin early fall. The primary deviationsfrom gyrelike circulation are flow from the outer southern flank toward the Mid-Atlantic Bight and an off-bank near-bottom (Eulerian) current on the northern flank; note, however, that tidal rectification models [e.g., Loder and Wright, 1985] predict a significant and partially offsetting cross-bank Stokes velocity in that area. For additional observational information on Georges Bank residual currents we draw on literature values of transports at key sectionsand recirculation times from drifters. Based on various observations in 1975-1980 and historical data,

15,970

NAIMIE

,

a),J

ET AL.: SEASONAL CIRCULATION

....

ON GEORGES BANK

f •

intermediate :c

I

near-bøtt?m_: ø ,

t

,b) Mgrch-•pril,

,

,d) J•ly-A,•½ust,

,

I I

,, e) ,Sept•mber70cto•er Figure 3. Bimonthlymeancurrentsfromavailablemooredmeasurements for near-surface (within15m), near-bottom (4-15 m abovebottom),andintermediate-depth regions,computed by verticalaveraging.The 60- and 100-m isobathsare displayedfor reference.

NAIMIE ET AL.: SEASONAL CIRCULATION

Flagg et al. [1982] estimated clockwise around-bank transports for winter (summer) of 0.34 (0.77), 0.43 (0.65), and 0.04 (0.38) Sv for the northern flank, southern flank, and Great South Channel, respectively. Other available estimates are 0.91 Sv for the northern edge of the Northeast Peak in early summer 1988 [Loder et al., 1992] and 0.10 Sv for the eastern side of Great South Channel in September-October 19851986 (J. Manning, personal communication, 1993). Information on Lagrangian recirculation rates is limited. Flagg et al. [1982] proposed stratified and unstratified regimes on the basis of 19 drifters drogued at 10 m in 1978-1979. Between November 1 and July 9 no drifters completed circuits of Georges Bank, whereas between July 10 and October 31 all five drifters moving along the southern flank made complete circuits, suggestinga summer-fall recirculation time of about 50 days. For tidal elevations

and currents

we use the same obser-

vational data sets as Lynch and Naimie [1993]. 3.2.

Density Fields

Climatological mean density fields for each of the six bimonthly periods (January-February, March-April, MayJune, July-August, September-October, NovemberDecember) were obtained from a historical temperature/ salinity database assembled from national archives and recent cruises. The temporal range of the data was 19121991, with highest data density from 1964 on in general. For each period all bottle (with reversing thermometer) and conductivity-temperature-depth(CTD) data from a 4-month interval centered on the period midtime, and which passed standardquality control, were used as input. The number of input stations/profiles over the greater Gulf of MaineScotJanShelf region ranged from about 11,000 for JanuaryFebruary to about 21,000 for September-October. A three-dimensionaldensity field centered on the midtime of each period was estimatedusingfour-dimensionaloptimal linear interpolation [Bretherton et al., 1976]. Density (as well as temperature and salinity) values were estimated for each horizontal node on the model grid and for specified vertical levels: at 10-m intervals from 0-60 m, 25-m intervals for 75-250 m, 50-m intervals for 300-500 m, and 100-m intervals

for 600-1200 m (the CTD profiles were decimated to these levels prior to input). Estimates of the data's spatial and temporal correlation scales were specified as input to the optimal interpolation procedure, which assumed that the data covariance C depended on the pseudodistancer (in x, y, z, t space) between data points according to

C(r) = e -r(1 d-r + r2/3).

(1)

ON GEORGES BANK

15,971

sections across the northern and southern flanks (Figure 4) and the areal distributions

of the surface-to-bottom

differ-

ence (Figure 5). In January-February and March-April (henceforth referred to as the "weak stratification" periods) there is little density structure over the bank plateau, with stratificationlimited to the shelf/slopefront at the shelf break and the deeper waters north and east of the bank. By May-June (henceforth the spring "transition" period), significant stratification has developed in the upper layers surroundingand over the outer flanks of the bank, resulting in a weak tidal front circumscribing the bank's central vertically mixed area. The ambient stratification and crossbank density gradients are generally strongest in JulyAugust and September-October (henceforth the "strong stratification" periods), except for the upper 25 m in the latter period. Finally, in November-December (henceforth the autumn "transition" period) the stratification in the upper layers is reduced, and the subsurfacedensity structure is similar to May-June. In general, the fields show agreement with previous descriptions of the seasonalhydrography on GeorgesBank [e.g., Flagg, 1987], such as partial closure of the bank's tidal front in the Great South Channel region in late summer and early fall. 3.3.

Other Forcings

The other observational data used as model input are the

M2 tidal elevations on open boundaries and mean wind stress for the bimonthly periods. The tidal elevations (D. Greenberg, personal communication, 1991) were taken as the same for all periods and are identical to those used by Lynch and Naimie [1993]. The wind stresseswere based on the Comprehensive Ocean-Atmosphere Data Set [Woodruff et al., 1987] for the area 40ø-42øN, 66ø-70øW, centered over Georges Bank. Stresseswere computed using monthly statistics for 1946-1979, the approximation method of Wright and Thompson [1983], and the neutral-stability speeddependentdrag coefficientsof Isemer and Hasse [ 1987]. The resulting climatological means (Table 1) show a strong seasonalvariation consistent with that discussedin previous studies [e.g., Butman and Beardsley, 1987].

4.

4.1.

Circulation

Model

Governing Equations

The circulation model solves, using the harmonic finite element method, the nonlinear three-dimensional shallow water equations with conventional hydrostatic and Bouss-

For time, 45 days was used for the correlation scale in January-February and March-April and 30 days for the other periods. For the shelf in general the spatial correlation scales were taken as 30-40 km for the horizontal and 15 (30) m for the vertical above (below) 75 m. However, in view of the anisotropy imposed on the density field by the Georges Bank topography and the overall sparsity of the database,

inesqassumptionsand eddy viscosity closurein the vertical. Forcing is included from tides, surface wind stress, and the baroclinic pressure gradient computed from a prescribed density field. The model employed differs from that presented by Lynch and Naimie [1993] (hereinafter LN93) throughthe inclusionof the baroclinic pressuregradient and wind stressforcings [Lynch et al., 1992], the reduction of the scales of 20 km and 60-100 km were used for the cross- and vertical eddy viscosity based upon the gradient Richardson along-isobath directions, respectively, in selected subareas number, and the inclusion of background current contribuof Georges Bank. In addition, larger spatial scales were tions to viscosity and bottom stress. specifiedin the deep ocean, particularly for the along-shelf The equationssolved are the three-dimensionalcontinuity direction.

The spatial and temporal structure of the resulting density fields in the Georges Bank region is illustrated by vertical

equation V.v=O,

(2)

15,972

NAIMIE

,

i

ET AL.: SEASONAL

i

CIRCULATION

ON GEORGES

BANK

,

,

%,

,

,

,

,

i

i

Figure 4. Vertical sectionsfor the northern flank (NF) and the southern flank (SF) of Georges Bank showingthe density (ort units) computedfrom the historicaldatabasefor the six bimonthly periods. The contour interval is 0.5 crt. The weak local density inversionsare associatedwith inhomogeneitiesin the input data distribution but do not have a major influence on the baroclinic pressure gradients. The horizontal (vertical) length scaleis 10 km (50 m) per division. The sectionlocations are indicated in Figure 2.

NAIMIE ET AL.: SEASONAL CIRCULATION ON GEORGESBANK

I

'

I

I

I

I

'

ß

,

,

a) • Janu•ry-eiebrugry

,

I

Figure 5. Areal view of the bottomto surfacedensitydifference(ITt Units)computedfrom the historical databasefor the sixbimonthlyperiods.The contourintervalis 0.5 o-t . The (x, y) "viewport" is identical to that shown in Figure 2.

15,973

15,974

NAIMIE

ET AL.' SEASONAL CIRCULATION

Table 1. Bimonthly Wind Stress for Georges Bank Region From the Comprehensive Ocean-Atmosphere Data Set [Woodruff et al., 1987] Wind

and Furnes, 1980; Davies and Jones, 1992] and vertically and horizontally based on the gradient Richardson number to account for the effects of stratification:

Stress

N(x, y, z, t)= F(gi),Nolrvl 2 + 0.002.

Magnitude,

Bimonthly Period

ON GEORGES BANK

Pa

Direction*

Jan.-Feb.

0.0955

118.5

March-April May-June July-Aug. Sept.-Oct.

0.0472 0.0136 0.0138 0.0186

121.4 49.4 51.0 145.6

Nov.-Dec.

0.0730

118.7

(7)

The contribution of unmodeled currents to friction is approximated (linearly) through the last term in each of (6) and (7)

where0.00035m s-• in (6) is Ca timestheassumed average magnitude of unmodeled flowsand0.002m2 s-• in (7) is used as the background viscosity. The gradient Richardson number (Ri) is computed via the relationship Op

*Degrees clockwise from true north.

Oz

Ri = -

(8)

/9 o

its two-dimensional vertical average

•Ot + Vxy' (hV)= -Vxy' (r/V)'

,

(3)

where the horizontal velocity shear is used in the denominator. While a variety of expressionsfor F(Ri) are presented in the literature, we focus on that presented by Munk and

and the horizontal components of the three-dimensional Anderson [1948]: momentum equation

1

--+

Ot

f x v + #Vr/ -

N

F(Ri) = (1+ 10Ri)•/2.

= -v ßVv

•zz•

(9)

Like LN93, we use the value No = 0.2 s recommendedby

•1•zrt •7xy pdz,

(4)

Po

Davies and coworkers and which, along with their previ-

ously mentioned recommended value of Ca, provides a high-quality tidal solution in the present model.

with surface and bottom boundary conditions 4.3. Ov

Free surface

N -- = h• Oz

(5)

Ov

Bottom

N

Oz

Calvlv+ 0.00035v,

(6)

in which

The frequency domain expansion of the governing equations is presented by LN93, for the case where F(Ri) - 1 and without wind or baroclinic forcing. The addition of wind and baroclinic forcing at the residual frequency yields linear terms that are handled as discussedby Lynch et al. [1992]. As in thesepreviouspapers, we use the harmonicexpansion in time:

r/(x, y, v(x, y, z, V(x, y, h(x,

t) t) t) y)

h•(x, y) f -- f•

free surface elevation; velocity; vertical average of v; bathymetric depth (more precisely, the depth of a position in the bottom constant stresslayer at which boundary conditions are applied, typically about a meter above the seafloor); wind stress;

Coriolis vector, assumedconstant at 43.5øN;

N(x, y, z, t) t/ p(x, y, z)

vertical eddy viscosity; gravity;

seasonalmean density, obtainedfrom observations;

Po reference density; (x, y) horizontal coordinates; z vertical coordinate, positive upward with z = 0 at the surface;

Vxy horizontalgradient(O/Ox,O/Oy); Ca 4.2.

Harmonic Expansion

bottom drag coefficient,taken as 0.005.

Parameterization

of Friction

The vertical eddy viscosity varies horizontally and temporally based on the vertically averaged velocity [Davies

•(x,y,t)=• Z ;n(X' Y)eJø•nt (lO) (11) v(x,y,z,t)=• Z Vn(X' Y'z)eJø•nt'

in which t.o n is the radian frequency of the nth harmonic constituent, with complex amplitudes (•n, Vn), and j =

(-1) •/2. It is assumed that •o_n = -•on andthat, correspondingly, (•-n, V-n) = (Srn, ¾n)*, with the asterisk indicatingcomplex conjugation. It is also assumedthat n = 0 representsthe time-independentconstituent, with ro0 = 0

andIm(•o, V0) = 0. With this conventionthe tidal residual is one half of the zero-frequency component' 1

(•'r,Vr)-' • (•'0,V0)'

(12)

Substitutionof (10 and 11) into the governing equationsis identical to LN93 and Lynch et al. [ 1992] for all terms except for the vertical diffusion term in (4). To obtain the frequency domainrepresentationof this term we first expand (7)-(9) in

NAIMIE

ET AL.: SEASONAL

CIRCULATION

ON GEORGES

BANK

15,975

the harmonic basis. In the expansionof (8) we consider only the time-invariant part of Ov/OzßOv/Ozto maintain consistency with our use of the time-invariant Op/Oz. Following Snyder et al. [1979], the time-invariant part of Ov/OzßOv/Oz

+•- 2V-I'Vr•zz • OZ /

(herein•2) takesa formvery similarto the time-invariant partof Ivl2 (defined asA2 by LN93):

+ 2Vr'V1 •ZZ• OZ

1t• OVn OV_n, t A2 it• - = -

oz oz

(13)

V

(14)

ßV_

+ •zz [NøA2S; +0.002] Oz/

_ OVr __ (

+T 8Vr'V, OZ/ oz

Thus the time-invariant forms of (8) and (9) become Op g•

az

• =•

(15)

po•2

• =(1+ 10•)1/2' herein:

-OzN •zz= •' •

• 2• + 0.002] eitomt •zz[Not rn=-oo OZ]

+TZ k

ozl

l•-k

The resulting governing equationscan be rea•anged such that the left sides make up the conventional threedimensional shallow water equations in lineadzed form and the right sides contain the nonlineadties. We consider only the M2(n = m1) and residual frequencies, effectively discarding the nonlinear terms outside of the harmonic basis (as

givenby LN93).Underthisconstraint, •2 andA2 become

•2=• 2 oz

oz

+4•.oz

(18)

1

A2 = 4_ (2•1 ' •-1 + 4•r' •r) '

(19)

and the diffusion term takes the form

(20)

Note that this term simplifiesto the form presentedby LN93 for the case where stratification effects on the vertical eddy viscosity are ignored (• = 1) and there is no background cu•ent

(16) 4.4.

The harmonic expansion of the diffusion term is now straightforward using (13) from LN93 and (7), (11), and (16)

2

contribution.

Finite

Element

Method

Solution

The computational task is to iteratively solve the linearized three-dimensional shallow water equations subject to forcing from the nonlinear terms, using the finite spectrum of the M2 (period is 12.42 hours) and residual (infinite period) frequencies. During each iteration we follow the finite element method solution strategies presented by Lynch and Werner [1987] and Lynch et al. [1992] at each frequency, whereby the vertically averaged governing equations are solved for the free surface elevation, followed by a vertical computation for the horizontal velocities and solution of the three-dimensional continuity equation for the vertical velocities. Thus the solution strategy we employ is identical to that discussedby LN93. Forcings at the M2 frequency are via the M2 tidal amplitudes at all open boundaries and the nonlinear terms discussed by LN93 as modified herein. Forcings at the residual frequency include the bimonthly climatological wind stress, the baroclinic pressure gradient, as discussedby Lynch et al. [1992], and the nonlinear terms as above. The density gradient is computed on level z surfacesand then interpolated onto the finite element mesh in the vertical. Boundary conditions on the residual include no normal transport across the truncated Bay of Fundy boundary and geostrophic outflow across the New England Shelf. Residual elevations derived from the density field to produce zero-geostrophic bottom velocity normal to the boundary are prescribed for the balance of the open boundary, allowing cross-boundary flows with a near-bottom "level of no motion."

•Oz N

=

[NoA2S; +0.002] OV-1 Oz

4 8Vr' V-1•zz•; OZ/ eja, -it

+V-løV-1 •ZZ • OZ /

2

+{a( •zz [NøA 2•+0.002] O••r/

The model mesh (see Figure 6) and bathymetry are identical to the refined and extended mesh discussedby LN93. The mesh extends from the New England Shelf to the Laurentian Channel and from the deep ocean (false bottom at 1200 m) to the upper Bay of Fundy. There are 12,877 horizontal elements and 6756 vailably spaced nodes that provide increased resolution over Georges Bank. There are 21 nodes in the vertical, whose unequal spacing provides increased resolution (2.5 m) of the surface and bottom Ekman layers. During preliminary model runs it was found that including the baroclinic pressure gradient within the iteration resulted

15,976

NAIMIE

ET AL.: SEASONAL

Figure 6.

CIRCULATION

Horizontal mesh used in the finite element model.

in small-scalenonphysicalanomalies in the poorly resolved Scotian Shelf region which failed to converge. These local effects resulted from the Vr ' VVr portion of the advection term. Further analysis revealed that neglectingthis part of the advection eliminated the convergence problem and did not significantly affect the solution in the Georges Bank region. All solutions presented herein were computed with the contribution of Vr' VVr neglected. The solutions do, nevertheless, include advective nonlinearities involving tidal-tidal and tidal-mean current interactions, as well as continuity and various frictional nonlinearities.

5.

Variability of Tidal Rectification Due to

Stratification

Influences

current associated with rectification of the barotropic M2 tide when stratification influences on the eddy viscosity are Thus for the model runs of this section we include

forcing from the barotropic M2 tide and the stratification influences on the eddy viscosity, but we do not include forcing from the wind stressor baroclinicpressuregradients. In addition

to the extension

to strongly (July-August and September-October) stratified periods.This increaseis illustratedby comparison(Table 2) of the around-banktransportsat key sectionsduringthe different periodswith thosepredictedby the model when the influences of stratificationare ignored(i.e., F(Ri) = 1). The stratification influenceson the eddy viscosity significantlyincrease the tidally rectified currents for all periods. The largest increase occursfor the strongstratificationperiods,with approximately 50% increasein transport. Based on the systematic intensification of flow from the weakly to stronglystratifiedperiods, we focus on the periods representingthe extreme values of stratification: JanuaryFebruary and July-August. The velocity sections in Figures

on Friction

First, we consider the seasonal evolution of the residual

included.

ON GEORGES BANK

to three dimensions

Table 2. Around-Bank (Clockwise) Eulerian Transport Across the Vertical Sections Shown in Figure 2 for

BarotropicM2 Tidal Forcing With Stratification-Dependent Eddy Viscosity Transport, Sv Bimonthly Period

NF

SF

GSC

NEP

Jan.-Feb.

0.19

0.22

0.09

0.35

March-April May-June July-Aug. Sept.-Oct.

0.19 0.20 0.21 0.22

0.21 0.23 0.25 0.25

0.09 0.10 0.12 0.12

0.35 0.35 0.34 0.33

Nov.-Dec.

0.20

0.24

0.10

0.34

No stratification

0.13

0.17

0.07

0.24

the model

includes an improved representationof frictional nonlinearities compared to most previous studies [e.g., Loder and Wright, 1985; Tee, 1985]. For all friction parameterizations consideredthe model solutions show a clockwise gyre over Georges Bank and a counterclockwisegyre over GeorgesBasin, qualitativelysimilar to those describedby LN93. However, with the stratification-dependentverticaleddy viscositywe find an enhancement in the around-bankcurrent on GeorgesBank as stratification evolvesfrom the weakly (January-Februaryand March-April)

The transport is computedusing the componentof the Eulerian velocity normal to the respective sections. For comparison,transports are also included for tidal forcing with no stratification influences.

NAIMIE ET AL.: SEASONAL CIRCULATION ON GEORGES BANK

15,977

G$C

GSC

Figure 7. Vertical sectionsfor the northern flank (NF), southernflank (SF), and Great South Channel (GSC) showingisotachs(in centimetersper second)of the around-bankvelocity (positiveinto the page)

andvectorsof the cross-bank velocityfor solutionscomputedusingforcingby the barotropicM2 tide with stratification-dependent eddy viscosity.Vectors are plottedat theft point of origin (indicatedby dots), and the vector scalesare shownin Figure7a. The horizontal(vertical)lengthscaleis 10 km (50 m) per division. 7 and 8 and the transport streamlinesin Figure 9 detail the changesin velocity as stratificationintensifies. The northern flank jet strengthens with stratification, with maximum

very similar for all stratification cases, with a general increase in current speed (and vertical velocity) for the strong stratification periods. The transport stream function proaround-bank velocities risingfrom18to 24 cm s-•. On the vides a useful quantitative measure of the recirculating southern flank section the shelf break jet (centered above a componentof Eulerian transport around GeorgesBank, with depth of about 100 m) is very similarfor these two periods, recirculation values of 0.13 Sv for January-February and while the maximum velocity of the broaderjet in shallower 0.16 Sv for July-August associated with barotropic tidal water increases from 5.8 to 7.9 cm s-•. The increased rectificationfor stratification-dependentfriction. These comstratification has the largest relative impact on the Great pare to the value 0.11 Sv found by LN93 for the case of no South Channel section, where the maximum around-bank

stratification

influences.

velocityrisesfrom4.6to 6.6cms-• andtransport increases On the Northeast Peak section (not shown in Figure 7) by 33%. Since stratification changes on this section are generally smaller than on the other sections, the greater (relative) seasonal change appears related to the overall three-dimensionalresponse of the gyre (rather than local friction changes).The cross-bankvelocities (Figure 7) are

there is a slight increase in the maximum around-bank velocity but a slight reduction in the net transport between January-February and July-August. The transportreduction occursbecausethe increased strengthof the Georges Bank gyre here is offset by decreased transport in the Georges

Figure 8. Horizontal sectionsof the residualcirculationfor solutionscomputedusing forcing by the barotropicM2 tide with stratification-dependent eddy viscosity.Depth is 30 m below the surface.Vectors are plotted at their point of origin (indicated by dots).

15,978

NAIMIE

recirc:

,

ET AL.: SEASONAL

.13

CIRCULATION

Sv

a) , Janu•ry-F•ebru•ry



,

ON GEORGES

BANK

recirc:

.16

Sv

,b) J•ly-A•gust,



Figure 9. Stream function plots of the Eulerian residualtransportvelocity for solutionscomputedusing forcing by the barotropic M2 tide with stratification-dependenteddy viscosity (see LN93 for the computational procedure for the streamfunction). The total recirculation around Georges Bank (indicated in individual panels) is estimatedby the differencebetween the value of the streamfunction for the largest streamline encircling the bank and the minimum value of the stream function on the bank. The contour interval

is 0.05 Sv.

Basin gyre. This is illustrated by the stream function estimates of 0.21 Sv and 0.19 Sv for the recirculatingtransport in the latter gyre in January-February and July-August, compared to 0.15 Sv for the case of no stratification influences. It is unclear why the Georges Basin gyre is less intense during strong stratification, but it appearsrelated to a more complex sensitivity of this gyre to friction. To explore the sensitivity of these results to the form of the gradient Richardson number used in the vertical eddy viscosity, we have obtained model solutionsfor tidal rectification in July-August with two alternative specificationsof F(Ri): those of Bowden and Hamilton [1975],

overall deviations for various elevation and current parameters that are very close to those found by LN93, where the influences of stratification

were not considered.

At local sites

with strong seasonalchangesin stratification there are small changesin the vertical structure of the tidal currents consistent with expectations,but the overall structure of the M2 solution

is not sensitive

to stratification

influences

on the

eddy viscosity. It is important to note that while the present model results support the conceptual point of a significant influence of stratificationon tidal rectification through friction, they also confirm inadequaciesin the detailed representation of frictional and advective nonlinearities given by Loder and 1 Wright [1985]. Additional model solutions indicate that Loder and Wright's approximations of "weak nonlinearity" (i.e., no influences of the residual solution on the tides) and and Kent and Pritchard [1959], linearized friction (without representation of time1 dependenceinfluences)result in a general overestimation of the residual current strength, consistent with previous findings [Loder, 1980; Tang and Tee, 1987; Wright and Loder, For a given stratification both of these parameterizations 1988]. Furthermore, model solutions with a vertically unipredict larger values of F(Ri) than the Munk and Anderson form viscosity dependent on a bulk Richardson number, as [1948] parameterization, which has the effect of increasing given by Loder and Wright [1985], give July-August transthe viscosity. The resulting residual flow fields have essen- ports that are 44% larger than that in Table 2 for the tially identical features to the July-August panels in Figures Northeast Peak section and 9% larger for the other sections. 7-9, with the around-bank transports at all sectionsin Table These differences appear related to the bulk parameteriza2 reduced on average by 17% (13%) for the parameteriza- tion underestimatingthe viscosity in the near-bottomregion, tions of Bowden and Hamilton (Kent and Pritchard). The togetherwith the general frictional sensitivity of the Georges lower transport and velocity results throughout the domain Basin gyre. Collectively, the present and past studiespoint (including the Georges Basin gyre) for the larger viscosity to a significantfrictional sensitivity of tidal rectification on casesindicate that the strength, but not the general pattern, Georges Bank and the need for careful representation of of the circulation depends upon which formulation of F(Ri) temporal and spatial variability influencesin the parameter-

F(Ri) (1+7Ri) 1/4,

(21)

F(Ri) - (1+2.43Ri) 1/2.

(22)

is used. In the above

ization solutions

with

different

stratification

influ-

enceson the eddy viscositythere is little variation in the M: elevations and currents. Quantitative comparisonswith observational data (not broken down by season)yield average

of friction.

To understandfurther the nature of the friction sensitivity of tidal rectification on Georges Bank, we have examined the vertically averaged tidal and residual momentum balances on the

cross-bank

sections

in selected

model

solutions.

NAIMIE

ET AL.: SEASONAL

CIRCULATION

ON GEORGES BANK

15,979

tional data set used by LN93 the average deviations of elevation amplitude and phase are 2.4-3.3 cm and 3ø, respectively, for the six bimonthly periods. The average deviations of the major (minor) axis and phase (orientation) of the current ellipses are within the ranges 6.2-6.9 (4.7-5.4) cm

These balances support the conclusions of past process studies [e.g., Loder, 1980; Huthnance, 1981] that the sensitivity of tidal rectification to friction occurs in spite of the bottom stress being a relatively small term in the tidal equation, that the advective tidal stressterm is an important along-isobath forcing in the residual equation, and that along-isobath bottom stress generally limits the residual current. However, the present results indicate that the residual momentum balances over the realistic Georges Bank topography are more complicated than in idealized models which assume uniformity along isobaths. In particular, there are significant (and sometimes dominant) contributions from the large-scale pressure field and, in many cases, it is through this large-scale response that the sensitivity to friction occurs. This illustrates the importance of the use of realistic geometry and inclusion of the overall tidal system in three-dimensional circulation models. Summarizing, we find the following: 1. The model M 2 elevations and currents on Georges Bank are not strongly influenced by stratification-dependent reductions in viscosity. This is consistent with the general successto date in modeling the barotropic tide in both two and three dimensions [Greenberg, 1979; LN93]. 2. The tidal residual is sensitive (up to 50% increase) to stratification influences on the eddy viscosity, in general agreement with the findings of Loder and Wright [ 1985]. The increased sensitivity of the residual circulation compared to the tidal currents is consistent with the tidal stress forcing terms involving nonlinear products of the tidal velocity and velocity gradient that are nearly in quadrature. 3. Even in winter, when the baroclinic structure is weakest on Georges Bank, there is a substantial increase in the tidal residual via stratification-dependent viscosity. 4. The residual current generated by tidal rectification on Georges Bank, and its sensitivity to friction, have important

sion to the residual currents, although there are local changesin tidal current structure associatedwith baroclinicity and wind. Vertical and horizontal sections of the bimonthly Eulerian residual circulation are presented in Figures 10 and 11. For all periods the dominant circulation is clockwise around Georges Bank with maximum velocities above regions of maximum bathymetric gradient on the northern and southern flanks. The seasonal evolution of the density field (see Figures 4 and 5) intensifies the around-bank circulation through increases in the cross-bank baroclinic (and associated barotropic) pressure gradient, as well as through reductions in the vertical eddy viscosity (section 5). Southward surface velocities during the weak stratification periods affirm the importance of the wind forcing during these periods. Smaller-scale eddylike structures are apparent in shelf regions away from the bank, particularly in areas with strong topographic variability, but the focus here is on Georges Bank. The retentive nature of Georges Bank and its strong seasonal variation are illustrated by the residual transport stream functions for the bimonthly solutions (Figure 12). The amount of recirculation is critically dependent on the flow in Great South Channel in general and the wind stress magnitude for the near-surface region, with the seasonal variation ranging from less than 0.02 Sv in January-February to a maximum exceeding 0.13 Sv in September-October. For all periods there is a general tendency for the (vertically averaged) southwestwardflow seaward of about the 70 m isobath

contributions

on the southern

from both the local advective

tidal stress terms

and the bank-scale barotropic pressure field. This indicates the importance of including the Gulf of Maine in Georges Bank modeling efforts. 5. Variations in the detailed form of the eddy viscosity dependence on the gradient Richardson number do not alter the basic circulation pattern associated with tidal rectification, though they do have an impact (of the order of 15%) on the residual current strength. Generally, closures that diminish the near-bottom viscosity increase the residual circulation.

6. Bimonthly Flow Fields With Tidal, Density, and Wind Forcing 6.1.

Overview

In this section we present model results for the bimonthly residual circulation associatedwith combined forcing by the M 2 tide, mean density fields (and associated boundary conditions), and mean wind stresses (Table 1). The density field now contributes through both stratification influences on the vertical eddy viscosity and baroclinic (and associated barotropic) pressure gradients, as well as through smaller effects on the contributions of the other forcings via nonlinear interactions.

The overall structure of the M 2 solutionsfor the different bimonthly periods shows only a weak dependence on the addition of baroclinic and wind forcing. For the observa-

s-• and9ø-11 ø(80-9ø),respectively. We limitfurtherdiscus-

flank to continue

toward

the Mid-Atlantic

Bight. Comparison of Eulerian transports at the selected sections (Table 3) and Eulerian velocities at the mooring sites (Figures 13 and 14, Table 4) with the observational data presented in section 3 indicates both qualitative and overall quantitative agreement, although there are local discrepancies.

In the following three subsections we expound on the description of the bimonthly circulation fields and their comparison with observations, grouped by the influence of stratification. In the comparison with observations we give primary emphasis to the dominant around-bank flow component and the transports as integrated measures of this flow, in view of the problematic nature of the weaker cross-bank flow [e.g., Butman et al., 1987] and the expectation for local current discrepanciesassociatedwith smoothing of the density fields and interannual variability (e.g., spatial shifts) in current and frontal structures. We also present (Table 5) an approximate partitioning of the transport contributions of the three primary forcings: tidal rectification (including stratification influences on friction), baroclinic pressure gradients and associated barotropic flow (through the upstream boundary conditions), and wind stress. For tidal rectification the transports are taken from Table 2, while the estimates for baroclinic and wind forcing represent the additional transports upon inclusion of these respective forcings in nonlinear model runs (e.g., baroclinic contributions are taken as transports with full

15,980

NAIMIE

ET AL.: SEASONAL

CIRCULATION

ON GEORGES BANK

-4

/"'•k•,•, -

' ' •••::



,

, NFI V

:• •:-

/- '

'•

,

2o

•'

2cm

, aI Jan, uary,-Feb,ruar2• , , , SF '

. . _ : ........... -••'•

• •



• • :

• ......

•: •



; •:•

--•

= : :• '

-•

Figure 10.

Vertical sectionsfor the northern flank (NF), southern flank (SF), and Great South Channel

(GSC) showingisotachs(in centimetersper second)of the around-bankvelocity(positiVeinto the page) and vectors of the cross-bankvelocity for bimonthly solutionscomputedusingforcing by the barotropic M 2 tide, baroclinic (and associatedbarotropic) pressure•adients, and wind stress,with stratificationdependent eddy viscosity. Conventions and scfles are the same as in Figure 7.

NAIMIE

ET AL ß SEASONAL

I

CIRCULATION

ON GEORGES

BANK

I

/

ß•

/

20

s-•

/

e) ,Sept•mber70cto•er

,

Figure11. Horizontalsections of theresidualcirculation for bimonthlysolutions computed usingforcing by thebarotropic M 2 tide,baroclinic (andassociated barotropic) pressure gradients, andwindstress,with stratification-dependent eddyviscosity.Depthis 30 m belowthe surface.Vectorsareplottedat theirpoint of origin (indicated by dots).

15,981

15,982

NAIMIE

ET AL.' SEASONAL

CIRCULATION

ON GEORGES

b)

I

reclrc:

,

.06-.07

• c) •ay-J•une

recirc-

.13-.14

Sv



Sv

, e) ,Sept•mberrOcto•er



reclrc:

,

,

BANK

M rch-

ril

I

I

.12-.13

.01-.02



Sv

,d) J•ly-Apgust,

recirc:

I

,

Sv

f) ,Nover•ber-pecem•er

Figure 12. Residual stream function plots for bimonthly solutions computed using forcing by the barotropic M2 tide, baroclinic (and associatedbarotropic) pressure gradients, and wind stress, with stratification-dependent eddy viscosity. The stream function and recirculatingtransport (indicated in individual panels) are computedin the sameway as for Figure 9. The contour interval is 0.1 Sv.

NAIMIE

ET AL.'

SEASONAL

CIRCULATION

forcing except wind, minus the transports in Table 2). This does not represent an exact partitioning by forcing since this is not possible in a nonlinear system.

Eulerian

circulation

for the weak

stratificationperiods. The flow on the northern flank section is dominated by a narrow (10 km) northeastwardjet near the

bankedgewitha maximum velocityof 19cm s-1 . Off-bank of this jet, there is a southwestward flow (reversal) of the

orderof 3 cm s- 1at depth,supplied by thenorthernlimbof the (counterclockwise) Georges Basin gyre and smaller local eddies. Near the surface of the northern flank transect, the relatively high southeastward wind stress for these periods results in cross-bank velocities with large on-bank components and reduction of the along-bank velocity magnitudes (see Figure 10). The effects of the wind are particularly prominent on top of the bank in January-February, where the effects of tidal rectification and the baroclinic pressure gradient are small. At depth on the northern flank transect the cross-bank

velocities

are off-bank

near the bottom

and

generally on-bank in the middle of the water column. Proceeding around-bank on the Northeast Peak, the jet largely follows the bank edge, although there is a weak vertically averaged southward flow across the Northeast Peak in January-February (Figure 12) associated with the crossbank Ekman transport. Flow on the southern flank in these periods is dominated by southwestward flow in both the shelf break jet, with a

maximumspeedof 20-25 cm s-1 and a broaderflow shoalward of the 80-m isobath, with a maximum speed of 7

cms-1. Thereare,however,localdisruptions of thesouthwestward

flow seaward of the 200-m isobath associated

15,983

Table 3. Net Around-Bank Eulerian Transport at Vertical Sections Shown in Figure 2 for Bimonthly Flow Fields With Tidal, Density, and Wind Forcing

Bimonthly Period

The January-February and March-April panels of Figures similar

BANK

Transport, Sv

6.2. Weak Stratification Periods: January-February and March-April 10 and 11 detail

ON GEORGES

Jan.-Feb. March-April May-June July-Aug. Sept.-Oct. Nov.-Dec.

NF 0.33 0.25 0.21 0.03 0.49 0.40

(0.36) (0.27) (0.27) (0.24) (0.54) (0.42)

SF

GSC

NEP

0.51 0.42 0.53 0.56 0.73 0.65

-0.00 0.01 -0.01 0.08 0.11 -0.02

0.62 0.58 0.77 0.53 0.91 0.90

The transport is computed using the component of the Eulerian velocity normal to the respective sections, with positive values indicating clockwise transport. For the NF section the transport of the clockwise-directed portion is shown in parentheses.

the average magnitude of currents in the model being only about 70% of that observed, average magnitude deviations between

model and observations

near 50% of the observed

average magnitude, and average angular deviations of 38ø-50ø. Detailed comparison of the observed (Figure 3) and model (Figure 13) currents indicates (at least) two contributing factors to these differences: stronger near-surface cross-bank flows in the model suggestinga possible overestimation of wind influences and weaker along-bank model flows at the edgesof Georges Bank edges suggestingspatial smoothingof the current jets. For station A with the largest observational data set (Figure 14) the comparison shows approximate agreementfor the vertical shear, but the alongbank currents in the model are low by a few centimeters per second.

The processpartitioning of the transports (Table 5) indicates that tidal rectification

and baroclinic

circulation

make

with

comparablecontributionsto clockwise around-bank flow in meanders of the generally northeastward flow in the deeper the weak stratification periods, except on the Great South water offshore, but the spatial and temporal realism of these Channel section where tidal rectification is the primary features is unclear. The primary features of the cross-bank contributor to recirculation. It should be emphasized, howcurrents are offshore flow in the surface Ekman layer and ever, that the baroclinic circulation includes contributions upwelling with on-bank flow at the shelf break. The latter from both the local baroclinic pressure gradient and the generally dominatesthe downwellingfound by Werner et al. larger-scale barotropic pressure field which is influenced by [1993] in the absence of baroclinic forcing, but the cross- the upstreamdensity field and boundary conditions. Indeed, bank flows, in general, are sensitiveto the choice of coordi- much of the southward "baroclinic" transport on the Great nate system, interannual wind stressvariations [e.g., Lough South Channel section is associated with the barotropic et al., 1994], and the limited density data set. pressurefield, so that it has increased sensitivity to approxIn the Great South Channel, baroclinic and wind forcing imations upstream. Except on the southern flank, wind partially override the persistenttidal contribution of a flow stress is also a significant contributor to transport in the field saddlepoint with northwardflow on the easternside of around-bank direction during these periods but in the oppothe selected section but southward flow on the westward site senseto the clockwise tidally driven flow. The primary side [e.g., Ridderinkhof and Loder, 1994]. Tidal rectification influence of wind stress in these periods is offshore flow in prevails atdepthwithnorthward flowupto2.6cms- 1onthe the surfaceEkman layer, yielding the conceptualmodel of a eastern side, but wind-driven southward flow prevails at the two-layer system with cross-bank near-surface drift overlysurface in January-February. As a result of the limited ing a clockwise gyre with limited recirculation. northward flow on the channel's eastern side, the stream function estimates for (Eulerian) recirculating transport on Georges Bank are only 0.02 and 0.05 Sv in JanuaryFebruary and March-April, respectively. Consideringuncertaintiesin the meanscomputed from the observational current and density (and hence model solutions) data, the around-banktransports(Table 3) in JanuaryFebruary and March-April are in good agreement with the observational estimates (section 3.1). The comparison of local currents (Table 4) shows greater discrepancies, with

6.3. Strong Stratification Periods: July-August and September-October

Figures 10-12 show intensified recirculating flow for the two strong stratification periods. The northern flank jet is intensified, and significantly broadened in September-

October,witha maximum velocityof 27 cms-1. The deep off-bank current reversal is strengthenedwith peak veloci-

ties of 9-13 cm s-1 and peaktransportof (-)0.21 Sv in July-August (compared to 0.24 Sv in the bank edge jet).

15,984

NAIMIE

I

I

I

ET AL.' SEASONAL

I

CIRCULATION

ON GEORGES BANK

I

1

10cms

10 cm s-1



intermediate :c near-bottom:

, I

I

I

o

,b) Mqrch-,April,

,

I

I I I I I•

,

, c) •ay-J•une ,

J , ,d) J•ly-A•gust, ,

I I I I I•

I I I I I I•

, e) ,Sept•mbervOctoper

I , f),Nover•ber-pecem ,

ß

Figure 13. Bimonthlymean currentsfrom model solutionsunder full forcing,for observationaldepths and sitesin Figure 3. The 60- and 100-misobathsare displayedfor reference.

NAIMIE

ET AL.: SEASONAL

CIRCULATION

ON GEORGES BANK

15,985

o

-2O

-2o

-4O

-40

-6O

-60

-85

-85 -10

-5

10 -5

0

5

10

-lO

-5

5

0

lO -5

o

U (cms-1)

V (cms-•)

U (½ms-•) a)

0

15

b)

January-February

10

15

March-April

o

,

5

V (cms-•)

,

,

,

5

10

15

10

15

+

-2o

-2o

-4o

-40

-6o

-60

-85

-85

:

-10

-5

0

5

10 -5

0

5

10

-lO

15

-5

o

10 -5

U (cms-1)

V (cms-!)

U (cms-1)

0

V (cms-!) July-August

c ) May-June o

,





i

-2O

-2o

-4O

-40

t

•0

-85

-10

-5

0

U(cms-')

5

10 -5

0

5

10

V (cms-')

e) September-October

15

-85

:

-10

-5

0

5

10 -5

0

5

U (cms-1) V (cms-') f) November-December

Figure 14. Bimonthlymeancurrentsat stationA (totaldepthis 85 m) from the modelsolutionsunderfull forcing(the solidcurvesthat extendover the verticalextentof eachplot) and observationalstudies(means indicatedby the plus signs,with horizontallines extendingover 1 standarddeviationin each direction).

15,986

NAIMIE

ET AL.' SEASONAL

CIRCULATION

Table 4. Statistics of the Comparison Between Observed and Modeled Residual Currents at Mooring Sites

Speed,cms- 1 BimonthlyPeriod Jan.-Feb.

March-April May-June July-Aug. Sept.-Oct. Nov.-Dec.

IObsl

IModl

IDevl

7.2

4.9

3.4

6.2 7.7 13.2 11.7

4.6 6.9 8.5 9.0

2.9 3.1 6.0 5.1

8.2

7.0

3.1

ON GEORGES BANK

speedof 12-13 cm s-•. The cross-bank currentson the

southern flank section have significant differences during these periods, but this appears related to (weak) meandering Angle, of the dominant along-bank flow and associated sensitivity to degrees IDevl the coordinate system. On the eastern Great South Channel section there is substantial strengtheningand broadening of 38 the northward flow in the strong stratification periods, with 50 29 29 33 51

IObslindicatesthe averageof the observational data, IModl

maximum speeds of 6.8 cms-1 in July-August and11.5cm s-1 in September-October. As a result,the recirculating transport on Georges Bank increases to 0.12-0.14 Sv, and the key saddle point in the flow field is present over the entire water

column.

indicates the average of the model results at the observational sites,

Overall, the transports (Table 3) and local current comandIDevlindicatestheaveragemagnitude of thedifference between parisons (Table 4) indicate that the model flow fields for the observed and computed quantities at the observational sites, shown for both the vector velocity difference and the angular difference strongstratificationperiods show good qualitative and rough between the observed and modeled velocities. quantitative agreement with observations, but there are some notable discrepancies. In transport the primary discrepancy is the extent of the northern flank flow reversal in However, detailed examination of the model solution indi- July-August. While observations indicate a seasonallyvarycates that the expanded and intensified reversal is associated ing flow reversal at depth associatedwith Slope Water inflow with a complex three-dimensionalflow field just north of the to the Gulf of Maine [e.g., Brooks, 1990] and eddy structures north of the bank, observational support for a persistent flow bank whose observational realism is unclear (see below). The primary differences in the cross-bank flows from those reversal of the extent in the July-August solution has not in the weak stratification periods are reduced near-surface been reported. The other notable transport discrepancy is currents and the presence of relatively strong on-bank cur- with the large [Flagg et al., 1982] estimate (0.38 Sv) for Great South Channel, but subsequentmoored measurements rents in the near-bottom region. Continuing around the bank, the bank edgejet partially spreadsacrossthe Northeast Peak (J. Manning, personal communication, 1993) raise questions during the strong stratification periods, consistent with to- about the estimate's reliability. The model and observed pographic influences on the seasonal advance of the tidal currents have relative overall differences that are similar to those in the weak stratification season,raising the possibility front [e.g., Loder et al., 1993]. On the southernflank the shelf break jet is similar to that of common contributing factors. One difference (compare in the weakly stratified periods with maximum speeds of Figures 3 and 13) is that the observed currents near the bank 20-25 cm s-1 while the broad southwestwardflow shoal- edge now have larger cross-bank components; this is most ward of the 80-m isobath is intensified, with a maximum apparent on the northern side of Georges Bank where

Table 5.

Approximate ProcessPartitioningof Bimonthly Transportsat Vertical SectionsShown in Figure 2 Transport at Key Sections, Sv

Bimonthly Period

Jan.-Feb.

Process(es)

NF

SF

M2 tide

0.19

0.22

imposed pressuregradients

0.33

0.29

-0.06

0.00

-0.03

0.21 0.19

0.09 -0.07

0.01

-0.01

wind

March-April

M2 tide imposedpressuregradients wind

May-June

July-Aug.

Sept.-Oct.

0.19 0.15 -0.09

M2 tide

0.20

0.23

imposedpressuregradients

0.05

0.34

wind

-0.04

M 2 tide imposed pressuregradients

0.21 -0.14

wind

-0.04

M 2 tide imposedpressuregradients wind

Nov.-Dec.

-0.19

M 2 tide imposedpressuregradients wind

0.22 0.28 -0.01

0.20 0.34 -0.14

-0.04

0.25 0.35 -0.04

GSC

0.09

0.10 -0.11 0.00

0.12 -0.04 0.00

0.25 0.46

0.12 -0.01

0.02

-0.01

0.24 0.42

0.10 -0.10

-0.01

-0.02

NEP

0.35 0.41 -0.14

0.35 0.30 -0.07

0.35 0.45 -0.02

0.34 0.22 -0.03

0.33 0.59 -0.01

0.34 0.68 -0.12

Processesare partitionedinto three categories:(1) barotropicM2 tide with stratification-dependent eddy viscosity("M2 tide," takenfrom Table 2), (2) baroclinic (and associatedbarotropic) pressuregradients("imposed pressuregradients"), and (3) "wind." The transport is computed using the component of the Eulerian velocity normal to the respective sections, with positive values indicating clockwise transport.

NAIMIE ET AL.' SEASONAL CIRCULATION ON GEORGES BANK

15,987

significant baroclinic tidal current interactions are known to surface velocities by the high wind stress. The off-bank shift occur [e.g., Loder et al., 1992]. At stationA (Figure 14) the of the northern flank jet, as comparedto the strong stratifiJuly-Augustsolutionis in closeagreementwith the observed cationperiods,is consistentwith reducedfrontal structureat bimonthlymeancurrentswhile the along-bankflow in Sep- the bank edge during November-December (see Figure 4). tember-October is 20-30% weaker than observed, associ- On the southernflank the southwestwardflow has a peak ated with lower vertical

shear.

velocityof over20 cm s-• at the shelfbreakand 15cm s-•

The processpartitioningof the transports(Table 5) indi-

within the broad flow shoalward of the shelf break. While

cates that tidal rectification and baroclinic circulation domthis feature doesresult in the secondlargest southernflank inate the circulationduringthe strongstratificationperiods. transport for the bimonthly periods (see Tables 2 and 5), the Tidal rectificationis a major factor all aroundthe bank and, southernflank model currentsat site A (Figure 14) are very in the present solutions, the sole contributor to the recircu- similarto the observedvalues. As in the January-February lation in Great South Channel (the baroclinic circulation period, the high wind stressresultsin a significantreduction contributes to the seasonal increase in recirculation in the in the around-bankvelocities except on the southernflank channelthrough reduced opposingflow). Elsewhere on the (Table 5) and limits the recirculatingtransportto 0.01-0.02 bank, the barocliniccirculationis the primary contributorto Sv (Figure 12). The comparison of model and observed the seasonalintensificationof the gyre, although,becauseof currents (Table 4) demonstrates an underestimation of vethe current reversal, it does not make a net contribution to locitiesby the model similarto the other bimonthlyperiods, clockwise transport on the selectednorthern flank sectionin thoughthe angulardeviation is at the high end of the range. July-August. Comparisonof the observed(Figure 3) and modeled(Figure

6.4.

13) currents at observational sites indicates that, like the

Transition Periods:May-June and

weak stratificationperiods, the primary disagreementis in the Great South Channel, where the currents are relatively

November-December

The various velocity distributions (Figures 10-12) and quantitativesummaries(Tables 3-5) indicatethat the spring (May-June) and autumn (November-December) transition periodsare intermediatestepsin the seasonalprogressionof Georges Bank circulation but with significantdifferences between the periods. These differences result from the contrastsin the near-surfacebaroclinic pressuregradients (Figure 4) and wind stress(Table 1). During the springtransitionperiod the impact of interme-

small in magnitude.

7.

Discussionand Summary The bimonthlyflow fieldspresentedin section6 provide a

detailed three-dimensional

idealization of the seasonal mcan

circulation in the vicinity of Georges Bank on realistic topography. Dynamically, the results arc generally consistent with and reinforce prevailing theories regarding the diate near-surface stratification and low wind stress are persistenceof tidal rectificationthroughoutthe year and the apparentin the results. The northernflank jet is of interme- roles that seasonalvariations in wind stressand the density diate strengthwith a maximumaround-bankvelocity of 21 field have on the circulation in the region. Although the cms-i, although thenettransport ontheselected section is seasonallyaveragedforcing used in the model may rarely (if lower thanin winter becauseof a flow reversalat depth.This ever) exist, favorable overall agreement with observational reversal is more limited in vertical extent than that in data supportsthe conceptualizationof an evolving, deterJuly-August, more closely resemblingthe seasonalSlope ministic seasonalcirculationaround GeorgesBank that can Water inflow. Flow on the southernflank is againcharacter- largely be explained by the set of processes considered

ized by broad southwestwardflow with a shelf breakjet, althoughthejet is weaker here than in the other periodsand displacedonto the shelf. The cause and reliability of this shift are unclear, since the frontal structure on the southern

herein.

The modeled circulation demonstratesthe importance of three-dimensional spatial structure to realistic flow fields for applicationssuch as Lagrangian drift in the Georges Bank region. While two-dimensional(x, z) models have been used

flank shows a gradual on-bank progressionbetween the weak and strongstratificationperiods(Figure 4). The cross- to identify important dynamicalrelationshipson the bank's bank currentson the southernflank are remarkablysimilar sides,they are unable to capture the circulation at the bank to those in July-August. The tidally driven northward flow ends or the interaction between Georges Bank and the on the eastern side of the Great South Channel is also larger-scalecirculationin the Gulf of Maine. An important intermediatebetweenthat in the weak and strongstratifica- example of this is Great South Channel, which is the key tion seasons,resultingin a recirculatingtransportof 0.06- branch point in the bank-wide recirculation. Additionally, 0.07 Sv. The comparisonof model and observed currents three-dimensional geometric closure around the entire bank (Table 4) is comparableto (but slightlybetter than) those in is more likely to capture the delicate cross-bankflows which the other periods. At station A (Figure 14) the May-June arc both hard to measureand sensitiveto modelingassumpsolution is in close agreementwith the observed currents at tions. The sensitivityof model results to the temporal and depth, though the model around-bankcurrentsare larger spatial parameterizationof friction emphasizesthe limitathan observed within 20 m of the surface. tions of models, in general, and two-dimensional(both x, z During the autumntransitionperiod the high wind stress and x, y) models in particular. (similar in magnitudeand directionto January-February) Observationsof the seasonalmcancirculationarc sparse, and the absence of near-surface

stratification

result in a

typically, estimatesof the seasonalmean current are at a few

circulationthat is substantiallydifferent than the spring depths at 10-20 different (horizontal) locations in the comtransitionperiod. The northernflankjet has an intermediate plex field, basedon mooredmeasurementsfrom 1 or 2 years

peakaround-bank velocityof 23 cm s-1, but thispeakis which often differ for each location. On the whole, the subsurface due to the reduction of the around-bank near-

current measurementsand transport estimatesarc compati-

15,988

NAIMIE

ET AL.' SEASONAL CIRCULATION

ON GEORGES BANK

ble with model results, indicatingthat the primary seasonal for flowswith strongspatialand temporalvariabilitybecause processesare representedin the model. In general, it is not of inherentnonlinearitiesin the Euler-Lagrangetransformaclear whether the detailed differences between the model tion. For somequestions,detailedanalysisof specificevents andobservational resultsare dueto modeling assumptionsin specificyears is necessary,even in the Eulerian context. or limitations in the observational data (either for the cur- In many casesthe seasonalmean circulation may only be a rents or for the wind and density forcingsin the model). The point of departure,as a base state of the circulatory system consistentdiscrepancywhereby around-bankflows in the subject to disturbances.However, for Georges Bank the modelare a few centimetersper secondlesson averagethan strength and persistenceof the tidal and low-frequency those observedmay indicate that an unmodeledprocessis residual currents (particularly in the seasonswith strong making a significant contribution to the circulation. On the stratificationand weak winds), as evidenced in both moored other hand, the mismatchbetweenaveragingperiodsfor the measurements[e.g., Loder et al., 1993] and drifter trajectoinput data and current observationsor the spatialaveraging ries [e.g., Flagg et al., 1982;Beardsleyet al., 1991],suggests in the density field estimatesmay be major factors in the that focus on the seasonal mean is a reasonable initial discrepancy. approach, as a background for examination and inclusion of In addition to discrepancieswith observationssomecom- current variations at other time scales. puted features of the model solutions deserve further atten-

tion. The well-documentedshelf break jet on the southern Acknowledgments. We thank our numerouscolleagueswho have flank is, in part, of nonlocaldynamicalorigin, relatedto the contributedto this paper by providing observationaldata or assist-

large-scale shelfwater/slope waterfront.Its strength in the

ing with the model developmentand application.In particular,we

present model solutionsis dependenton the upstreamdensityfieldandboundaryconditionswhichwere obtainedin an

are grateful to Mary Jo Gra•a for invaluable assistance with the

observationair'databases anddensity fieldestimation' andwethank

andJimManning objectivebut coarsemanner.On the northernsideof the BradButman,WendellBrown,DickLimeburner,

bank the GeorgesBaSingyre providesa potentiallyimportant transport pathway onto the bank, and the deep flow reversalshowssomeresemblanceto the known SlopeWater inflow. However, the extent of the flow reversal in July-

for providingrecentdata;Ken Drinkwater,RogerPettipa s, Peter Smith,and JosephUmoh for contributionsin makinghistoricaldata available' Dave Greenberg, Charles Hannah, and Francisco Werner for assistancewith the model application;and CharlesHannah, Dan Wright, and two anonymousreviewers for comments on the manu-

script. This is contribution13 of the U.S. GLOBEC program, Augustis suspiciouk andmayreflectartificialflowfeatures funded jointly by NOAA and NSF. This work is alsofundedby the

associatedwith the sparse density data set and the joint effect of baroclinicity and relief [e.g., Huthnance, 1984]. This is an examplewhere a detailedanalysisof the reliability of the estimated baroclinic pressuregradientsin relation to topographic gradients might be instructive. Cross-bank

(Canadian)Panelon Energy, Researchand Development. References

Backus,R. H., and D. W. Bourne(Eds.), GeorgesBank, 593 pp.,

MIT Press, Cambridge, Mass., 1987. flows, in general,are both observationallyand theoretically Beardsley, R. C., R. Limebruner, and C. Chen, Summertime problematic, with an additional difficulty being their sensiLagrangiancirculationin the Great South Channel/GeorgesBank tivity to the definition of the local coordinatesystem. Firegion (abstract),Eos Trans. AGU, 72(44), Fall Meeting suppl., 260, 1991. nally, the critical role of friction in the seasonalcycle

suggests the need for more advanced turbulence closure schemes.

Bowden, K. F., and P. Hamilton, Some experimentswith a numerical model of circulationand mixing in a tidal estuary, Estuarine

CoastalMar. $ci., 3, 281-301, 1975.

The diagnosticapproachusedherein bypassesthe need to Bretherton, F. P., R. E. Davis, and C. B. Fandry, A techniquefor establishthe long-term, large-scaleheat and salt budgets objectiveanalysisand designof oceanographicexperimentsapwhichcontrolthemassfieldanditsinterseasonal evolution, p!iedto MODE-73,DeepSeaRes.,23,559-582,1976. vastly simplifying the calculations. In addition to limitations Brooks, D. A., Currents at Lindenkohl Sill in the southern Gulf of Maine, J. Geophys. Res., 95(C12), 22,173-22,192, 1990. d•pendingon the statisticaladequacyof the densitydata set, Butman, B., and R. C. Beardsley, Long-term observations on the another consequenceis the dynamical neglectof the internal southernflank of GeorgesBank, I, A descriptionof the seasonal CYcleof currents,temperature, stratification, andwindstress,J. tide and its interactionwith steeptopography.Loder et al.

[1992]identifiedseveralfeaturesof the baroclinictidetopography interaction on the Northeast Peak in summer,

includ!ng an internalhydraulicjump duringoff-banktidal flow, internalwaves,andsurfaceconvergence. Chen[1992] found, using a model with advanced turbulence closure

[Mellor and Yamada, 1982] and prognostic temperature

simulatio n, thattherectification oftheinternal tidesmakes a significantcontribution to the around-bank circulation. Fu-

turemodeling effortsshouldaddress issuesraisedby these recent

sti•dies.

Finally, we return to the conceptualdivisionof the circulation into seasonal(bimonthly) means and variationsabout the means. The relevance of the seasonalmeanspresented here dependson three aspects' their fidelity to those which "occur" in nature, the relative strengthof the variationsat both interannual and intraseasonal time scales, and the nature of the questionbeing addressed.In general,questions of Lagrangiandrift place severedemandson model solutions

Phys. Oceanogr., 17, 367-383, 1987. Butman, B., R. C. Beardsley, B. Magnell, D. Frye, J. A. Vermersch, R. Schlitz, R. Limeburner, W. R. Wright, and M. A. Noble, Recent observationsof the mean circulation on GeorgesBank, J. Phys. Oceanogr., 12, 569-591, 1982. Butman, B., J. W. Loder, and R. C. Beardsley, The seasonalmean

circulation: Observation andtheory,in Georges Bank,editedby R. H. Backus and D. W. Bourne, chap. 11, pp. 125-138, MIT Press, Cambridge, Mass., 1987. • Chen, C., Variability of currents in Great South Channel and over GeorgesBank: Observationandmodeling,Ph.D. dissertation,283 pp., Woods Hole OceanOgraphicInstitution, Woods Hole, Mass., June 1992.

Davies,A.M., andG. K. Fumes, ObservedandcomputedM:• tidal currents in the North Sea, J. Phys. Oceanogr., 10, 237-257, 1980. Davies, A.M., and J. E. Jones, A three dimensional wind driven

circulationmodel of the Celtic and Irish seas, Continenial Shelf Res., 12(1), 159-188, 1992.

Flagg, C. N., Hydrographic structure and variability, in Georges Bank, edited by R. H. Backus and D. W. Bourne, chap. 10, pp. 108-124, MIT Press, Cambridge, Mass., 1987. Flagg, C. N., B. A. Magnell, D. Frye, J. J. Cura, S. E. McDowell,

NAIMIE

ET AL.' SEASONAL CIRCULATION

and R. I. Scarlett, Interpretation of the physical oceanographyof GeorgesBank, final report to New York Outer Continental Shelf otfice, Bureau of Land Management, 901 pp., EG&G Environmental Consultants, Waltham, Mass., 1982. Garrett, C. J. R., and J. W. Loder, Dynamical aspectsof shallow sea fronts, Philos. Trans. R. Soc. London, A, 302,563-581, 1981.

Greenberg, D. A., A numericalmodel investigationtidal phenomena in the Bay of Fundy and Gulf of Maine, Mar. Geod., 2, 161-187, 1979.

Greenberg, D. A., Modeling the mean barotropic circulation in the Bay of Fundy and the Gulf of Maine, J. Phys. Oceanogr., 13, 886-904, 1983.

Huthnance, J. M., On mass transports generated by tides and long waves, J. Fluid Mech., 102, 367-387, 1981.

Huthnance, J. M., Slope currents and "JEBAR", J. Phys. Oceanogr., 14, 795-810, 1984. Isaji, T., and M. L. Spaulding, A model of the tidally induced residual circulation in the Gulf of Maine and Georges Bank, J. Phys. Oceanogr., 14, 1119-1126, 1984.

ON GEORGES BANK

15,989

on finite elements, I, Linearized harmonic model, Int. J. Numer. Methods Fluids, 7, 871-909, 1987.

Lynch, D. R., F. E. Werner, D. A. Greenberg, and J. W. Loder, Diagnosticmodel for baroclinic, wind-driven and tidal circulation in shallow seas, Continental Shelf Res., 12(1), 37-64, 1992. Mellor, G. L., and T. Yamada, Development of a turbulence closure model for geophysical fluid problems, Rev. Geophys., 20, 851.

875, 1982.

Munk, W. H., and E. R. Anderson, Notes on a theory of the thermocline, J. Mar. Res., 7, 276-295, 1948.

Ridderinkhof, H., and J. W. Loder, Lagrangiancharacterizationof circulation over submarine banks with application to the outer Gulf of Maine, J. Phys. Oceanogr., 24, 1184-1200, 1994.

Snyder, R. L., M. Sidjabat, and J. H. Filloux, A study of tides, setup and bottom friction in a shallow semi-enclosedbasin, II, Tidal model and comparison with data, J. Phys. Oceanogr., 9, 170-188, 1979.

Tang, Y., and K.-T. Tee, Effects of mean and tidal current interaction on the tidally induced residual current, J. Phys. Oceanogr.,

17, 215-230, 1987. Isemer,H. J., andL. Hasse,TheBunkerClimateAtlas of theNorth AtlanticOcean,vol. 2, Air-SeaInteractions,252 pp., Springer2 Tee, K.-T., Depth-dependent studies of tidally induced residual

Verlag, New York, 1987. Kent, R. E., and D. W. Pritchard, A test of mixing length theories in a coastal plain-estuary, J. Mar. Res., 18, 62-72, 1959.

currents on the sides of Georges Bank, J. Phys. Oceanogr., 15, 1818-1846, 1985.

Tremblay, J. M., J. W. Loder, F. E. Werner, C. E. Naimie, F. H. Page, and M. M. Sinclair, Drift of sea scallop larvae Placopecten Loder,J. W., TOpographic rectification of tidalcurrentsonthesides magellanicuson Georges Bank: A model study of the roles of of Georges Bank, J. Phys. Oceanogr., 10, 1399-1416, 1980. mean advection, larval behavior and larval origin, Deep Sea Res., Loder, J. W., and E. P. W. Horne, Skew eddy fluxes as signatures Part H, 41, 7-49, 1994. of nonlineartidal currentinteractions,with applicationto Georges Werner, •F. E., F. H. Page, D. R. Lynch, J. W. Loder, R. G. Lough, Bank, Atmos. Ocean, 2.9, 517-546, 1991. R. I. Perry, D. A. Greenberg, and M. M. Sinclair, Influencesof Loder, J. W., andR. G. Pettipas,Mooredcurrentandhydrographic mean advection and simple behavior on the distribution of cod measurements fromthe GeorgesBankfrontalstudy,1988-89,in and haddock early life stageson Georges Bank, Fish. Oceanogr., CanadianData Report of Hydrography and Ocean Sciences,Rep.

94, 139pp., Dep. of F•sh.andOceans,Dartmouth,Nova Scotia,

2(2), 43-64, 1993.

Woodruff, S. D., R. J. Slutz, R. L. Jenne, and P.M. Steurer, A Loder,J. W., andD. G.•Wright, Tidalrectification andfrontal comprehensiveocean-atmospheredata set, Bull. Am. Meteorol. Soc., 68, 1239-1250, 1987. circulation on the sides of Georges Bank, J. Mar. Res., 43, 581-604, 1985. Wright, D. G., and J. W. Loder, A depth-dependentstudy of the Loder, J. W., D. Brickman, and E. P. W. Horne, Detailed structure topographicrectification of tidal currents, Geophys. Astrophys. Fluid Dyn., 31, 169-220, 1985. of currents and hydrography on the northern side of Georges Wright, D. G., and J. W. Loder, On the influences on nonlinear Bank, J. Geophys. RES., 97(C9), 14,331-14,351, 1992. bottom friction on the topographic rectification of tidal currents, Loder, J. W., K. F. Drinkwater, N. S. Oakey, and E. P. W. Horne, Geophys. Astrophys. Fluid Dyn., 42, 227-245, 1988. Circulation, hydrographicstructureand mixing at tidal fronts: The Wright, D. G., and K. R. Thompson,Time-averagedforms of the view from Georges Bank, Philos. Trans. R. Soc. London A, 343, nonlinear stress law, J. Phys. Oceanogr., 13, 341-345, 1983. 447-460, 1993. Lough, R. G., W. G. Smith, F. E. Werner, J. W. Loder, F. H. Page, C. G. Hannah, C. E. Naimie, R. I. Perry, M. M. Sinclair, and J. W. Loder, Department of Fisheries and Oceans, Bedford D. R..Lynch, The influence of wind-driven advection on the Institute of Oceanography, P.O. Box 1006, Dartmouth, Nova interannual variability in cod egg and larval distributions on Scotia, Canada B2Y 4A2. D. R. Lynch and C. E. Naimie, Dartmouth College, 8000 Hinman, Georges Bank: 1982 vs 1985, Int. Counc. Explor. Sea Mar. Sci. Hanover, NH 03755. Syrup., in press, 1994. 1991.

Lynch, D. R., and C. E. Naimie, The M2 tide and its residualon the outer banks of the Gulf of Maine, J. Phys. Oceanogr., 23, 2222-2253, 1993. Lynch, D. R., and F. E. Werner, Three-dimensionalhydrodynamics

(Received October 22, 1993' revised February 16, 1994; acceptedApril 8, 1994.)