A numerical study of the continental shelf circulation of the U.S. South Atlantic Bight during the autumn of 1987

Continental Shelf Research, Vol. 13, No. 8/9, pp. 971-997, 1993. 027~4343/93 $6.00 + 0.00 Printed in Great Britain. © 1993 Pergamon Press Ltd

A numerical study of the continental shelf circulation of the U.S. South Atlantic Bight during the autumn of 1987

FRANCISCO E . WERNER,* JACKSON O. BLANTON,* DANIEL R . LYNCHt

a n d DANA K. SAVIDGE*~

(Received 29 May 1991; in revised form 9 April 1992; accepted 6 May 1992)

Abstract--The autumn circulation on the inner- and mid-shelf of the U.S. South Atlantic Bight (SAB) is examined numerically. Using data collected in 1987 during the Fall Experiment (FLEX) the alongshore structure of the currents and the coastal sea level fluctuations were found to be correlated to local winds which were strong and persistently northeasterly. The observed inshore distribution of freshwater during FLEX, characterized by the presence of a coastal front confined to the coast inside the 25 m isobath, reflects the local autumn discharge subjected to strong and persistent downwelling winds. The freshwater signal found outside the 25 m isobath is suggested to be the previous summer's discharge advected northward by the summer winds subsequently returning south forced by the autumn winds.

1. I N T R O D U C T I O N

DURING the fall of 1987, the Fall Experiment (FLEX) was conducted on the inner- to mid-continental shelf of the U.S. South Atlantic Bight--the SAB (Fig. 1). One of the goals of FLEX was to determine the fate of the fresh, low density water arising from local river discharge during autumn in the SAB. Climatological studies of the SAB winds (WEBER and BLANTON, 1980) and the hydrography of its shelf waters (ATKINSON et al., 1983) suggest a transition of summer to fall regimes much like the 1987 observations indicated. As such, 1987's summer and autumn may be considered typical.

Summer winds are southwesterly, and generally upwelling favorable (Fig. 2; also WEBER and BLANTON, 1980). Previous studies (BLANTON and ATKINSON, 1983; BLANTON et al., 1989) have found that these winds spread the freshwater seaward, while at the same time the water column becomes vertically stratified with relatively weak horizontal gradients. October's winds and hydrography are completely different. The winds are downwelling favorable with strong, persistent winds from the northeast (Figs 2 and 3). Climatological hydrographic data, as well as data collected during FLEX, reveal a salinity structure wherein the October freshwater discharge is advected southward hugging the coast, forming a vertically well mixed coastal front with weaker horizontal salinity gradients in the mid- and outer-shelf regions (Fig. 4). Lastly, since tritiated waters are indicative of

*Skidaway Institute of Oceanography, P.O. Box 13687, Savannah, GA 31416, U.S.A. tThayer School of Engineering, Dartmouth College, Hanover, NH 03755, U.S.A. ~Now at: Marine Science Program, University of North Carolina, Chapel Hill, NC 27514, U.S.A.

971

972 F . E . WEg~ER et al.

3 4 O N .

3 2 ° .

3 0 ° .

2 8 ° .

83 ° 81 ° 7 9 ° 770 7 5 ° W

Fig. 1. U.S. South Atlantic Bight continental shelf. Wind station is located at the Savannah Light Tower (SVL), current meter locations are indicated as Stas 2 and J. Depth in meters.

having originated from the Savannah River (BUSH, 1988), the FLEX measurements shown in Fig. 4c suggest that some fraction of freshwater found 60-70 km offshore was discharged by the Savannah River.

In this paper we numerically examine selected mechanisms that affect the distribution of freshwater on the SAB shelf under typical summer and fall conditions. We focus on the flow field induced by winds, tides and externally imposed mean sea level pressure gradients. Our results may be summarized as follows. Freshwater discharged during summer months onto the SAB shelf is generally transported northward by the winds. Offshore transport due to winds and small-scale processes such as wind and tidal shear dispersion acting throughout the summer months contribute to the spreading of the freshwater over the shelf out to the shelf edge where some of the freshwater is entrained in the Gulf Stream and lost to the deep ocean. The remaining portion of the shelfwaters (that portion not lost to the deep ocean) may be considered as "tagged" by freshwater. In October, the winds become strongly northeasterly forcing newly discharged water to move southward and hug the coast forming the coastal front with its characteristic pronounced horizontal salinity gradients (Fig. 3; also AT~INSON et al., 1983). Shelf waters north of the new discharge, with a broader (more diffuse) cross-shelf freshwater distribution are similarly advected southward and flank the inner-shelf front. Thus, the freshwater found

Autumn circulation of South Atlantic Bight 973

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I ' I ' / ' I ' I

(~.uJo seu~p) sse~lspu!M "IAS

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974 F.E. WERNER et al.

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. . . .~/ v ~ i r ~ - I " ~ ' - ' ~ , "/~°'' "~* ' ~ ~ " ~ /

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. . . . .,oort / : ,~-I ,.., I "~-~' ',7 \ ,..~..--~ "% ,,'/

== °-I,'~ ,','~ ~ - v ~ , . ~ ~,~

a--3o I , i , 1 , 1 ~ 1 , i , i , i , i , i , i , i , i , i , i , 1 , 1 , 1 r F r 1 5 9 13 17 21 25 29 2 6

October November 1987

Fig. 3. Time series of measured windstress (dynes cm -2) at the Savannah Light Tower (SVL); currents at Stas J (JTOP) and 2 (C201 and C202) in cm s -1, demeaned coastal sea level at Charleston, Ft. Pulaski (Savannah) and Mayport (Jacksonville) and demeaned subsurface press-

ure at Sta. J (JBOT).

seaward of the October coastal front, could be considered as "relict", i.e. discharged as early as the previous summer when it was advected northward and subsequently caught in a southward transit caused by the strong autumn northeasterly wind regime.

The results we discuss here focus on the region of the inner- to mid-shelf, i.e. roughly from the 5 m to the 40 m isobath. We evaluate idealized scenarios wherein we assess the importance of the various forcings independently. We then describe the cases forced by observed winds over the FLEX period between early October to mid-November of 1987 and the longer period starting in July. Our approach is first to understand the flow features during autumn 1987 alone, i.e. we attempt to explain the observations collected during F L E X using only the conditions observed at that time. Second, we examine the role that the circulation during the months leading up to F L E X may have played in the observed hydrography.

A u t u m n c irculat ion o f S o u t h A t l a n t i c B ight 975

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The SAB is bounded by Cape Hatteras and Cape Canaveral at its northern and southern ends, respectively (Fig. 1). Our study focuses on the sub-region between Cape Romain and Cape Canaveral. The topography is relatively smooth, isobaths tend to be parallel to the curved coastline and, while the shelf tends to be broad between Cape Romain and St Augustine (120 km off Brunswick and Savannah), it narrows to 50 km in width off Cape Canaveral. The average depth over the shelf is 30-35 m and the shelf break is approximately 75 m deep. Previous studies of the SAB have found three regimes on its continental shelf (ATKINSON et al. , 1983): (i) the inner shelf where local winds and river runoff are the primary forcings, (ii) the mid-shelf (from the edge of the inner shelf, approximately the 20 m isobath, to the 40 m isobath) where local winds dominate the flow at sub-tidal frequencies and the stratification varies seasonally, and (iii) the outer-shelf where Gulf Stream meanders and related disturbances strongly influence the observed flows. See LEE et al. (1985) for a review and additional references.

Several modeling efforts of the SAB's circulation have appeared in the last decade. BLUMBERG and MELLOR'S (1983) three-dimensional diagnostic calculations included the baroclinic field associated with the Gulf Stream region as far offshore as the Hatteras abyssal plain (Blake Plateau). Although this study included part of the continental shelf, its main focus was on the flow affected by the presence of the Gulf Stream located seaward of the 40 m isobath. On the other hand, studies such as those of WANG et al. (1984), KOURAFALOU et al. (1984) and LORENZETTI et al. (1987) addressed the flow on the continental shelf, out to the shelf break. These studies considered the wind-, tide- and longshore pressure gradient-induced motions on the shelf with barotropic and two-layer formulations finding, in general, good agreement between the local wind-forced model responses and the observed currents. Evidence for remotely-forced subintertial coastal trapped waves has been generally difficult to find in the SAB (PIETRAFESA and JANOWITZ, 1980; SCHWING et al. , 1988; and BRINK, 1990).

2. OBSERVED CONDITIONS DURING FLEX

Current meters were deployed during the period, 17 August-14 November 1987 (see Fig. 1 for locations) and hydrographic sections were mapped between 25 October and 5 November (CHANDLER et al., 1988). Throughout these time periods wind records are available from the Savannah Light Tower (SVL) located on a platform off Savannah at the 15 m isobath and on a pier in St Augustine. A summary of the field measurements follows; a more complete description of the field data is given in BLANTON et al. (in press).

Beginning on 8 October and to the end of FLEX the wind stress was predominantly southwestward (downwelling favorable) and peaked at about 2 dynes cm -2 (1 dyne cm -2 = 0.1 Pa) off Savannah (Fig. 3). Brief relaxation events occurred on 21-22 October, 27-28 October and 5-6 November. For the time period in question, the winds were well correlated at all stations between Charleston and St Augustine, with perhaps a decrease in the magnitude of the wind stress at the southern locations.

The sea level and sub-surface pressure fluctuations as well as the measured alongshore component of currents (only Stas J and 2 are available) followed closely the fluctuations in the alongshore windstress component (Fig. 3). While peak sea level set-ups coincided with peak downwelling-favorable winds, the sea level was depressed coincident with weak


upwelling-favorable winds on 21 and 28 October and the relaxation periods of 30 October-1 November, and 5-7 November. During peak southward wind events, peak 40 h low-passed currents in J and 2 were also southward at 15-25 cm s -1, and little vertical structure was observed.

Hydrographic observations during this time-period indicated that the water column was well mixed vertically and horizontally stratified (Fig. 4). The surface salinity distribution (Fig. 4a) shows a low-salinity band of water next to the coast rising from 33 ppt off Savannah to about 35 ppt off Cape Canaveral. The freshwater signal, defined by the location of the 36 ppt isohaline (Fig. 4a), is furthest (70 km) from the coast off Brunswick. (ATKINSON et al., 1978, found the 36 ppt isohaline to be a reasonable indicator of waters containing a freshwater fraction since Gulf Stream surface waters are seldom less than this value and any subsurface water that might be advected onto the shelf is higher than 36 ppt.) The offshore extent of the freshwater signal and the vertically mixed water column (Fig. 4b) persisted throughout the 2-week hydrographic sampling period--23 October to 6 November--with only smaller quantitative perturbations (CHANDLER et al., 1988; BLAN- TON et al., in press). Figure 4c shows the surface tritium distribution measured during FLEX (taken from KIM, 1990). Note the offshore maximum during the 23-25 October measurements.

The sources of freshwater in the SAB are distributed between Cape Romain and Brunswick. North to south the largest rivers are the Pee Dee (Cape Romain), the Cooper- Santee (Charleston), the Savannah and the Altamaha (Brunswick) with smaller rivers found throughout this stretch of coast. The approximate distance between these locations is: 200 km (Pee Dee to Cooper-Santee), 100 km (Cooper-Santee to Savannah) and 100 km (Savannah to Altamaha), respectively. The magnitude of the discharge for the Cooper- Santee and the Savannah during October of 1987 was of the order of 100 m 3 s 1 and 200 m 3 s -1, respectively. The Altamaha (at Brunswick) was closer to 60 m 3 s -1 . For about one week in late September the Pee Dee peaked at 500 m 3 s -1 but returned to levels of about 100 m 3 s -1 during October.

3. MODEL FORMULATIONS

In this study we used a suite of three-dimensional hydrodynamic models. A description of the diagnostic model used is given in LYNCH et al. (1992). It is a linearized subset of the non-linear formulation of LYNCH and WERNER (1991) described next.

LYNCH and WERNER (1991) solve the three-dimensional hydrodynamic equations with the conventional Boussinesq and hydrostatic assumptions and with no horizontal shear stresses. The formulation is a nonlinear, three-dimensional time-stepping finite element formulation. A general eddy viscosity formulation is used to represent the vertical shear stress and is assumed to be time- and space-dependent with no restrictions on its functional dependence. Using conventional notation:

v(x, y, z, t) is the fluid velocity, with Cartesian components (u, v, w), (x, y, z) are the Cartesian coordinates where z is positive upward, t is time, ~(x, y, t) is the free surface elevation, h(x, y) is the bathymetric depth, H(x , y, t) is the total fluid depth, H = h + ~,

978 F.E. WEm~ER et al.

N(x, y, z, t) is the vertical eddy viscosity, g is gravity, f is the Coriolis vector, V is the gradient operator , Vxy is the horizontal gradient operator ,

we write the three-dimensional equations for continuity

V - v = 0 (1)

and horizontal momentum

O__~v + v" Vv + f × v = -gVxy ~ + R + O--(NOV]" (2) Ot Oz \ Oz]

The baroclinic term is

- g l ~ R(x, y, z, t) = P Vpdz.

Z

We rearrange the depth-averaged forms of (1) and (2) to obtain the Shallow Water Wave Equation

32H

oF OH

- - -]- T ° --cql - - V x y " [ v x y " (H¥~) + gHVxy~ +

f × H ~ - r o H ¥ - H ~ + H F - H R ] = 0 ( 3 )

where the overbar indicates a vertically averaged quantity. These equations are solved subject to conventional horizontal boundary conditions on

elevation or normal transport and to vertical boundary conditions on shear stress. At the surface, we enforce the atmospheric shear stress

N 0v = H~It (4a) Oz z=~

and at the bot tom we use a conventional slip condition relating shear to the bottom velocity

F(Vb) = KlVblVb. (4b)

Inserting (4a,b) into (3), we arrive at the final form of the Wave Equation

0 2 H OH 0 T + T ° ~ - -- Vxy" [Vxy" (HV~) + gHVxy ~ +

f x H ¥ -- roH¥ -- HaF + KIVbIV b -- MR] = 0. (5)

We solve (5) for ~; (2) for the horizontal components of v; and (1) for the vertical velocity W.

We use a semi-implicit algorithm in which the basic linear gravity wave terms are treated in a centered, implicit manner, and the depth, horizontal velocity and vertical velocity are obtained sequentially rather than simultaneously. A straightforward Galerkin discretization of the equations is used. The basis function of choice is the linear (six-node) three- dimensional element. The governing equations are transformed into terrain-following or o-coordinates. The formulation of the model equations with the arbitrary constant to,


introduced by KINNMARK (1985) and set here to 2.0 × 10 -4 s -x, increases the efficiency of the computations. The only modification to LYNCH and WERNER (1991) is the implementation of an open-boundary/outflow condition described below. We use this condition in all cases except where tidal forcing requires sea level to be specified on all open boundaries.

Based on current measurements off the Georgia coast (BLANTON et al., 1989) bot tom drag coefficients range between 2 x 10 -3 and 5 x 10 -3, the higher values associated with measurements closer to the bottom. Thus, when we compute bot tom stress from a quadratic drag law based on the velocity at the bottom, we use 5 × 10 -3 as the nondimensional drag coefficient; when we use a linear drag law (also computed with bot tom velocities) we use 2.5 x 10 -3 m s -1 as the dimensional drag coefficient.

Based on near-bot tom tidal velocities of the order 10-20 cm s -1, similar wind induced velocities, and depths between 10 and 30 m, estimates of the vertical eddy viscosity N range between 0.005 and 0.0150 m E s-1. In vertically homogeneous waters of depth smaller than the Ekman depth, CSANADY (1976) suggests the parameterization for the vertical eddy viscosity N -- u,h/20 where u , is the friction velocity--measuring either surface (wind) stress or bot tom stress--and h is the depth of the water. In the discussions that follow we will use a constant N = 0.01 m E s -1 (u , ~ 0.01 m s -1 and h ~ 20 m) unless otherwise stated. The constant N cases set N = 0.01 m E s - l ; the spatially and temporally variable N case is based on DAVIES and FURNES' (1980) formulation where N = N0lv[ 2, v is the vertically averaged velocity and No is constant at 0.2 s. A minimum N of 0.01 m 2 s -1 is kept in all cases.

The cross-shelf boundary condition

We describe next the t reatment of the open boundary whereby the expression for the normal transport at the boundary is replaced by the corresponding terms of the tangential momentum equation. See LYNCH et al. (1992) for the equivalent t reatment in the harmonic domain. Focusing on the Wave Equation (5), and expanding H and ~ in the basis Wi

H(x, y, t) = ~ H,<t)W](x, y) (6)

i

~(x, y, t) = 7 , ~i(t)Wj(x' y) (7)

i

we find its Galerkin (weak) form

dHj IW.W.~ • ] = [d2Hj (WjWi) + r + ~j(ghVWj VWi) V / , . [ dt 2 o dt " j '" 3 1

- - < [ V x y • (HV9) + g~Vxy ~ + f X H¥ - ro/-N - H * + / - /F - H R ] . VxyWi>

where the overbar indicates a vertically averaged quantity, ( ) and ~ represent integration over the (x, y) plane and its boundary, respectively, and fi is a unit normal vector pointing


outward at the boundary. The natural boundary condition of (8) is the normal transport /-/~. ft. When known, the transport enters the boundary integral in (8). In cases where the time-history of the sea surface is known, equation (8) is discarded and the elevation is prescribed directly; thus knowledge of the transport is not necessary. These two cases are the classical Dirichlet (elevation known) and Neumann (transport known) boundary conditions. A radiation boundary condition is intermediate--neither elevation nor transport is known apriori, but a relation among them is enforced in the boundary integral. One such implementation is described next. [Work is ongoing to relax the offshore boundary condition to a radiation-like condition. Preliminary studies are given in JOHNSEN et al. (1991)].

On the cross-shelf boundary we assume negligible acceleration of the vertically averaged cross-shelf flow Fs, i.e. DFs/DT = 0, reducing the cross-shelf (or tangential) momentum balance to

0¢ f i n = --g~ss + ~s - Fs (9)

where (n, s) is a right-handed orthogonal coordinate system with n pointing outwards and s tangentially. We relate the normal transport required by the line integral in (8) to the tangential forces via (9)

In the notation of LYNCH and WERNER (1991), the Galerkin form (8) is summarized as

= r w i (11) J

with the unknown A~/=-- ~,+1 _ ~f-1. Implementation of the boundary condition (9) requires adjustments to both Agj and rwi, as follows. The first, geostrophic, term is evaluated implicitly using the time-centered approximations

(~t + r°) ~ = 2AtA~+ ro [2A~ + ~ k _fl(~k ~k--1)] (12)

where 0 -</~ -< 1 is a weighting factor. Expanding the elevation in the basis Wj, and moving the unknown A~ to the left-side, results in the additional contributions A~ to Aq [equation (27b) in LYNCH and WERNER, 1991; row i, column j]

where Bq= } g-g-n °wj

as W~ ds

(13)

(14)


• N 5~

Depth (m) . I ~

' , l / i j

Fig. 5. Model domain mesh (a) and model bathymetry (b) in meters.

while the right-hand side rwi [equation (27c) in LYNCH and WERNER, 1991; row i] will contain an additional term r*wi involving ~k and ~k-1

r*wi = [ ( 1 - + ( 1 5 )

J

The remaining wind and bottom stress terms in (10) contribute the adjustment r**to rwi:

r,w,= _At2 ~ f [(1~s - Fs) ' - ( ' s - Fs) ' - 1 ] 2IT + ro(~s - rs) k Wi ds (16)

where a first order backward difference is used to approximate the time derivative.

Model domain

The model domain extends from Cape Canaveral at the southern end to Cape Hatteras at the northern end (Fig. 5a and b). The inshore extent is the 3 m isobath where we place a vertical coastal wall; the offshore extent is the 70 m isobath corresponding approximately to the location of the shelf break. The horizontal discretization is a mesh of 972 nodes and 1728 linear triangular elements (Fig. 5a); the model bathymetry is shown in Fig. 5b. Under each horizontal node we use 11 equally spaced nodes in the vertical.

4. RESULTS

We examine diagnostically the effect of idealized winds, longshore pressure gradients, tides and stratification on the circulation on the shelf in Section 4.1. The response to observed winds and the ME tidal component is presented in Section 4.2.


Steady Winds . /f"

2_ ,( h / / --.Zv ; / /

( . , - / /

"X ?,

N 6a

20 cm s "1

L 6b

Fig. 6. Model response to steady wind forcing: (a) sea surface elevation in cm; (b) surface velocity (cm s-l). The southward wind component is 0.7 dynes cm -2 and the westward component

0.4 dynes cm -2.

4.1. Diagnostic results

In this section we present the linear response to individual forcings and refer to these as diagnostic results. The individual forcings are combined (within the limits of linear superposition) to approximate conditions observed during FLEX. In all the diagnostic computations the vertical eddy viscosity is constant, N = 0.01 m 2 s -1 and the bottom drag law is linear, directly proportional to bot tom velocity, with the drag coefficient set to 0.0025 m s - t . The solid wall boundary conditions are free-slip and the sea surface is specified at the seaward and northern boundaries. The southern cross-shelf boundary condition is analogous to (9).

Winds. Based on the correlation between winds, sea level and currents displayed in Fig. 3, we begin by discussing the wind-forced response. The observed winds are persistently southwestward with fluctuations in the latter half of the record of about 7 days. Between 17 October and 6 November the southward winds relax on 21 October, 28 October and 6 November- - roughly at 1-week intervals. The prescribed winds are of the form

Tpe r = T s -4- T f COS (cot)

where zf = ( -0 .80 , -0 .45) dynes cm -2 is the amplitude of the fluctuating component , rs is the steady component of magnitude 0.8 dynes cm -2 (0.7 dynes cm -2 southward and 0.4 dynes cm -2 westward), and ~o corresponds to a 7-day period. This value Ofrs is the average windstress magnitude and direction measured at the SVL from 8 October to 8 November. With the particular choice of rf, the magnitude rper will peak at about - 1.7 dynes cm-2 and

A u t u m n circulation of South Atlantic Bight 983

I~odl¢ Winds

/

/

A :'/-?/'/° ....... / / o.,,

i \

7a 7b

~/ } .f-J" , / 2 ~ / / / /

/, /;,//"

I'/ 42,0.

3 1

/ f/f//j/ i.

7c

Fig. 7. Model sea surface response (cm) to 7-day period wind forcing [rper = ra cos (tot)] at (a) t = 0 h; (b) t = 42h ; and (c) t = 48h .

will reverse weekly to +0.1 dynes cm -2 approximating the observed fluctuations of the winds after 17 October shown in Fig. 3.

The steady-state sea surface elevation and the surface flow response to a wind stress field rs is shown in Fig. 6a and b. The highest sea level occurs south of Savannah where the coastline curvature is such that the winds change from almost alongshore (north of Savannah) to almost onshore (south of Savannah). Such distribution of sea level-- the mound south of Savannah--arises from the geometric effect of curved coastline (see ASKaR] et al., 1989) which is equivalent to the response obtained by imposing a windstress of non-zero curl on a straight coastline (CsAr~ADV, 1980). The bottom currents are weaker - -bu t still southward, or parallel to the coast at all depths. While veering with depth is observed on the mid- to outer-shelf, on the inner shelf where the Ekman depth is large compared to the water column depth the currents are close to unidirectional in the vertical.

Keeping the windstress magnitude equal to that used for the results of Fig. 6, we examined the effect of imposing spatial structure to the steady winds. In one case we imposed nearly shore-parallel winds throughout the domain. In the other, we imposed winds that were northerly off Cape Hatteras, veering anticyclonically as a function of latitude to becoming almost easterly off Cape Canaveral. Neither case alters the above results significantly and thus we will focus on the spatially constant wind-forced case for the remainder of this discussion.

The motion due to the fluctuating component alone, i.e. with rs = 0, is shown in Figs 7 and 8. When the wind is maximum to the southwest (t = 0 h) the flow is very close to the steady wind solution (compare Figs 7a and 8a to Fig. 6). As the winds relax to zero (at t = 42 h) and shift direction to become northeastward, a horizontal shear develops wherein the currents on the inner shelf reverse before the mid-to-outer shelf currents (Figs 7b and 8b for t = 42 h and Figs 7c and 8c for t = 48 h). The quick response of the shallow inner shelf to wind reversals is explained by the depth-integrated longshore balance which requires the wind stress and the bot tom stress to balance in shallow water. In shallow water, where

984 F.E. WERr~ER et al.

Fig. 8. Model surface current response (in cm) to 7-day period wind forcing [rpcr = ra cos (oJt)] at (a) t = 0h; (b) t = 42 h; and (c) t = 48 h.

the depth H of the water column is less than the Ekman depth, the wind impulse appears as longshore momentum and the spin-up time

H Ts - 2u ,V '~d

is about 3 h in 10 m of water (CSANADY, 1982, p. 175ff). We have assumed u, = 0.01 m s -1 (which is the friction velocity computed for a windstress of 1 dynes cm -2) and Cd = 0.0025. In deeper water the spin-up time of the currents in deeper water is longer and thus it takes longer for the flow to reverse.

During the "collapse" of the coastal sea level maximum (Fig. 8b) the currents north of the sea level maximum reverse earlier than the currents south of the maximum. In the initial phases of the wind's reversal, south of the coastal sea level maximum the southward coastal pressure gradient causes the currents to continue to flow southward (despite a northward wind component) . North of the coastal sea level maximum however, the currents' reversal is aided by the direction of the coastal pressure gradient force: the alongshore pressure gradient force and the winds add, causing the currents' quicker reversal. Thus the flow bifurcates on the inner-shelf with currents north of the sea level maximum flowing northward and, south of the sea level maximum, southward (Fig. 8b; also see SEND, 1989). During times of wind relaxation, the surface flow field has an offshore component (Fig. 8c). However , because of the short duration of these reversals (Fig. 3) the net episodic offshore transport of material/freshwater induced by the reversals appears to be small. A quantitative study of the offshore freshwater flux during these reversals is given in BLANTON et al. (in press). Finally, at t = 56 h, the currents are mainly northward over the entire shelf (not shown).

Tides: the M2 component . From its 40-50 cm value at the shelf break, the M2 tidal elevation amplifies at the coast, peaking at about 1 m near Savannah, and dropping off to about 40 cm at Cape Canaveral and Cape Hatteras. The arrival of the tide to the edge of the shelf is approximately simultaneous with a phase difference of about 10 ° between Cape


M2 Surface Maximum Speed (cm s'l).._~

ji': /,,,'

',:; , 9a

", ~ " + J 25 cm s"

\ . . . . ; '~ 9b

Fig. 9. Model M 2 tide: (a) maximum surface speed (cm s 1); and (b) tidal ellipses of the depth averaged flow (the tidal ellipses have been subsampled for clarity).

Hatteras and Cape Canaveral. At the widest section of the shelf the M 2 tide reaches the coast about 30 min to 1 h after reaching the shelf edge (REBFmLD, 1958; SCHWIDERSKI, 1979). Other characteristics of the M2 tide can be found in PIETRAFESA et al. (1985) and WANG et al. (1984). The N2 and the $2 have similar spatial characteristics as the M 2 but reach peak amplitudes of only 20 cm. The main diurnal tides are the O1 and the K1; their amplitude is relatively constant over the shelf at about 10 cm.

A satisfactory quantitative simulation of the SAB's M2 tide has not been possible due to uncertainties in some of the offshore and the calibration stations. Forcing by offshore boundary conditions from SCHWIDERSra (1979) however provides qualitative agreement with existing data. Figure 9a shows the distribution of the maximum surface currents with a broad area of maximum speeds greater than 30 cm s-1 on the mid-shelf between Savannah and Brunswick. A subsample of the model-computed tidal ellipses of the depth averaged flow is shown in Fig. 9b. Particle excursion during the ebb (or flood) portion of a tidal cycle is of the order of 5 km and in the Savannah-Brunswick region the ellipses are mainly on-offshore.

Overtides, compound tides and tidal residuals are not strong in this region. Eulerian residuals computed with the non-linear formulation are less than 1 cm s -1. Lagrangian drifts/velocities were also small, reaching peak values of 0.5 cm s-1.

A steady density field. The surface and bottom velocity solutions arising from imposing a density field confined to within 40 km from the coast is shown in Fig. 10. The density variation from the (fresh) nearshore zone to the (salty) offshore boundary is 1 at unit. There is no imposed alongshore density variation and the water column is vertically mixed. The surface velocity is weak and mainly across-shore or across-front, with a return flow found at the bottom. In GARRETr and LODER'S (1981) discussion on the sensitivity of these solutions to the vertical Ekman number Ev [Ev = N/(fH2)] this on-offshore circulation

986 F.E . WEaNEg et al.

) f . - ?,. f / T " - f ' . ~ , f

/ , . : : ~,~3"t "..'. : / ~.'~1":- " ' ; / < ' - . "

" " - \ i /

: ; % y . . . / . • ~.',x • / - ~

I ~ .~ ~"., ' / I cm s'1

\ : , & . . i \ :.-::.%,, . I

\ C ~ ' ~ . ' ~ l O a

. / , :~\- , ~ , - - " 1 M- .~'x2~" ,," F - i

' " b , ' : , t / ' i t - . . . . . . . ,'

/

/ - , //

i' i / / c>

t / 1 cm s "1

I I

1 \ ~ : " 1

\ : : -% ~. • l O b

Fig. 10. Model currents (cm s- i ) induced by steady baroclinic forcing: (a) surface and (b) bottom.

occurs in cases where Ev - 0.1. In the inner-to-mid shelf region of the SAB, it is not unreasonable to expect the strong FLEX winds coupled with tidal currents to generate values of Ev of this order.

A shelf-edge longshore pressure gradient. The result of imposing a steady pressure gradient along the shelf edge associated with the Gulf Stream is shown in Fig. 11. The

-11

/ / / ! , / / ,

11 I 11

Fig. 11. Model response to steady barotropic longshore pressure gradient imposed at the shelf break: (a) sea surface elevation (cm); and (b) surface currents.


magnitude of the slope along the shelf edge is 10 -7 (STURGES, 1974). A 2 cm setdown towards the coast along the northern boundary is also imposed. The surface velocity field reveals that the effect of the pressure gradient--in the region off Savannah and Brunswick--is confined to the region seaward of the 30 m isobath. For regions shallower than the 30 m, the velocities are less than 1 cm s-1.

The upstream boundary condition. All cases considered here have clamped (specified) the northern boundary condition on sea surface. Experiments addressing the flow sensitivity of the northern boundary condition alone revealed that its effect does not extend significantly below Cape Fear, i.e. 200 km southwest of Cape Hatteras (Fig. 12a and b). This is a consequence of the shallow and frictional nature of this shelf. An experiment with the same mesh but with a fiat 70 m deep bottom revealed that the effect of imposing a 2 cm cross-shelf tilt only on the northern boundary extended noticeably throughout the model domain (Fig. 12c and d). We conclude that the solutions south of Cape Romain do not "feel" the clamping of the northern boundary at Cape Hatteras. The sensitivity of continental shelf flows to the upstream boundary (upstream relative to the direction of propagation of sub-inertial coastal trapped waves) has been documented in deeper basins or shelves by WRIGHT et al. (1986), HUKUDA et al. (1989) and LYNCH et al. (1992) and others.

The combined (diagnostic) response. The combined effect of the five forcing mechanisms--steady and fluctuating winds, tides, steady baroclinic field, and shelf edge longshore pressure gradient--is shown in Fig. 13. The trajectories of a set of drogues released in the surface layer off Cape Romain (Fig. 13a) and Savannah (Fig. 13b) are shown for a 40 day period. The mean displacement in all cases is southward along the coast. The bottom drogue trajectories (not shown) indicate a weaker flow with the drogues still confined within the 25-30 m isobath. The drogue distribution for a Cape Romain release with only the steady plus fluctuating winds is shown in Fig. 14. Comparisons to the results of Fig. (13b) show that a large portion of the trajectory can be explained invoking wind effects alone.

Summary. The conditions generated by these idealized FLEX forcings indicate persistent southward advection along the coast, with little on-offshore advection except during brief, episodic, events of wind-relaxation or reversal. The offshore trajectory during the relaxations or reversals was generally less than 5 km. Most of the alongshore advection appears to be wind-induced. Based on these results and examining Fig. 3, it appears that processes during FLEX can lead to the formation and maintenance of the coastal front inside the 20-25 m isobath. At the same time, a mechanism to export the freshwater signal 70 km offshore during FLEX is not readily apparent.

4.2. Forcing with observed winds

We describe next the response of the flow to the M 2 tide and the measured winds (Fig. 2). Experiments which included the external longshore pressure gradient and the steady baroclinic components did not differ significantly and thus are not discussed. The model domain is the same used in the diagnostic calculations and the model formulation is that described in Section 3. The bottom drag law is quadratic, with a constant bottom drag

988 F . E . WERr~ER et al.

.1.5"2~ Elevation (cm) .~ -1v, g:- ~

/ - - ~

/ j / ? .... / J

/ / ( / ( / 'k /

i, (

\.......3 12a

Surface Currents ~ . ~

/ i l l / f / 5 cm s"

! /

Elevation ( c m ) / / ~ -,,s~ //'~//

/ i t / - / ~ / 'i[ .0.s /

\t' ,2cl

Surface Currents

J,,,, ;;.;.;.,.,,,,

i~7"" sc.s-,

""~ 5cms'l 12d

Fig. 12. Model response to upstream boundary forcing with realistic topography: (a) sea surface elevation in centimeters and (b) surface currents; and with flat 70 m bottom (c) sea surface

elevation in centimeters and (d) surface currents.

coefficient (0.005), the boundary condition at the coast is of free-slip and the model time-step was 0.10 h.

The F L E X period. First we consider only the results between October and early November. A comparison between the observed alongshore velocity and model results at Savannah is shown in Fig. 15. The agreement between the observed and computed low- passed currents from 26 September, i.e. Julian Day 269 (JD 269), and 6 November (JD 310) is very good (Fig. 15a). The model underpredicts the observations on JD 280 and 286

I!

Fig. 14.

t=O

3a 131o

Fig. 13. Surface drogue trajectories during a 40-day period with combined forcing by steady winds, periodic winds, tides, steady density field and shelf-edge longshore pressure gradient.

Drogues were released simultaneously (a) north of Cape Romain and (b) off Savannah.

II


Surface drogue trajectories during a 40-day period (as in Fig. 13a) but forced only by steady and periodic winds.

990 F.E. WE~:r,rE~ et al.

Alongshore velocity lit Savannah

-1(

-1~

-2.' 265

: : W

;/'!

151 270 27s ~ ~ ~o ~ ~o ~ 3~o 315

0

-10

-1~

.2C

-25

Modeled Alongshore velocity at Savannah

i ,"

! :' no lk~t

~ t~el

~,,,

Julian Days 1987

Fig. 15. Model and observed currents off Savannah (Sta. J): (a) observed currents (dashed line) and 40-h low-passed model results (solid line) forced by winds and tides; (b) model results forced only by winds (dashed line) and 40-h low-passed model results forced by winds and tides (solid

line). Julian Day 270 corresponds to 27 September.

by about 5 cm s - 1 and misses a reversal in the current around JD 307. Off Brunswick the fluctuations of the current were properly captured, but their magnitude in particular between JD 283 and JD 293, was underestimated by as much as 15 cm s - 1 (not shown).

The effects of the tides, through their contribution to N and bot tom friction, is apparent in Fig. 15b. Al though during weaker wind periods and during times of reversals the model results with and without tides are in reasonable agreement, during peak winds from JD 283 to JD 300 the wind-only results are consistently larger than the wind-and-tide solution.

Observed and model coastal sea levels at Charleston and Savannah (with means removed) are shown in Fig. 16a and b. The agreement in the phasing of the fluctuations is in all cases apparent; however , the magnitude of fluctuations is not as good. From JD 283 to JD 293 the magnitude of the fluctuations is underpredicted by 10-20 cm. On the other hand, a comparison of the alongshore gradients---Charleston minus Savannah-- i s more satisfactory (Fig. 16c).

Autumn circulation of South Atlantic Bight 9 9 1

E

50

4 0 -

3 0 -

2 0 -

10 -

0

-10 -

- 2 0 -

-30 -

-40 265

5O

'° t 3O

20

10

0

40

-20

-30

-40 265

0

-2

-4

-6

- 8

-10

Savannah Coastal Sea Level - demeaned

observed

, ~ , ~ J

k; i'Ji I I V 16a

~o d~ 40 ds ;o d,s do d5 71o 315 Charleston Coastal Sea Level - demeaned

.~ observed

/ ~ !,

4"iV\ lk I,,? ~"l'l ~ ~ i "~i I I I | l i f

\ j v "d 16b I I I I I I I I I I

270 275 280 285 290 295 300 305 310 315

Charleston minus Savannah Sea Level

I I i V ,

observed

I I mode ,j

16c 5 2 0 2 5 280 2 5 290 5 300 3 5 310 3

Julian Days 1987

Fig. 16. Demeaned, 40-h low-passed model (solid lines) and observed coastal sea surface elevations (dashed lines) at: (a) Savannah; (b) Charleston; and (c) Charleston sea level minus Savannah sea level, model (solid line) and observed (dashed line). Julian Day 270 corresponds to

27 September.

In Fig. 17 we display the wind- and t idal ly-forced surface trajectories of three drogues located initially off Cape R o m a i n and released on 26 September . There is a mean sou thward displacement o f about 400 km in 40 days, or roughly 10 cm s -1. All drogues remain inside the 20 m isobath. These results are consistent with the idealized case discussed in Section 4.1 (Fig. 13).

Fig. 17.

18a

Surface drogue trajectories from 26 September to 6 November forced by observed winds at SVL and the M2 tide. Drogues were released off Savannah.

~start (1 July)

(8 Nov) ifinish (8 N o v , _j ) 18b


Fig. 18. Surface drogue trajectories during a 130-day period (1 July-8 November 1987) forced only by observed SVL winds and the M 2 tide: (a) released off Savannah; and (b) released off

Charleston.

The 1 July-8 November period. W e cons ide r the resul ts o b t a i n e d by inc luding the wind forc ing of the s u m m e r m o n t h s p r e c e d i n g F L E X . T h e d i s t r ibu t ion of sur face d rogue s r e l e a s e d on 1 Ju ly off S a v a n n a h and C h a r l e s t o n , and end ing on 8 N o v e m b e r is shown in Fig. 18. T h e mos t s ignif icant a spec t of the d r o g u e s ' t r a j ec to r i e s is tha t desp i t e the s u m m e r


upwelling favorable winds, many of the drogues remained on the shelf. Their northward trajectories ended (roughly on 20 September) between Cape Romain and Cape Fear at which time the winds began shifting. The northward excursion of the Savannah-released drogues was Cape Romain (Fig. 18a); that of the Charleston-released drogues was Cape Fear (Fig. 18b). On about 7 October the winds became strongly northeasterly and the drogues essentially retraced the results of Fig. 17.

5. DISCUSSION

The results presented above indicate that during autumn conditions in the SAB's inner- and mid-shelf the alongshore currents and the sea level fluctuations are adequately explained by local winds with the tides playing an important part in the momentum balance. With respect to the hydrography of the autumn season, the results suggest that the freshwater measured off Savannah and Brunswick during FLEX is likely to be a combination of water discharged up to 4 months earlier, during summer, as well as freshwater discharged more recently. The "relict" discharge may be found as far offshore as 70 km and the more recent discharge confined inshore within the coastal front.

On longer time-scales of 2-4 months associated with the suggested freshwater's residence time, various smaller scale processes will contribute the horizontal spread of the freshwater in addition to the advective component of flow discussed thus far. One mechanism in the SAB may be tidal shear dispersion. Episodic southward wind events acting on the "pool" of summer freshwater can mix the water column vertically (see BLANTON et al., 1989, for a related spring-time study). Coupled to the action of the tides, these vertical mixing events can be an effective cross-shelf dispersion mechanism. (TAYLOR, 1954 details the mechanism by which vigorous vertical mixing in vertically sheared flows enhances longitudinal dispersion). Other mechanisms such as frontal instabilities are certain to also play a role in the spread of the freshwater. CSANADV (1973) and FISCHER et al. (1979) provide comprehensive discussions of the "diffusive" nature of geophysical flows.

Estimates of the value of horizontal eddy diffusion coefficients K h in the coastal oceans will vary depending on the nature of the shelf, the season, etc. For coastal regions, an order of magnitude for g h is 100 m 2 s -1 (e.g. STOMMEL and LEETMAA, 1972; JAMES, 1978). With this value of Kh, homogeneous diffusive spreading over 3 months would result in a patch of approximately 60 km in radius (R - 2~/Kht ) . A value of 50 m 2 s- 1 yields a patch of 40 km in radius. A 40-60 km spread over the months preceding FLEX is consistent with the SAB pre-autumn scenarios found in the climatological studies of WEBER and BLANTON (1980) and ATKINSON et al. (1983). The climatological data show a rather homogeneous distribution of freshwater on the shelf for the months of July-September. (Note that these are also months of weak discharge and hence any gradients near or offshore will also be weaker.) On the other hand, the months of October and November show sharper salinity gradients confined close to the inner shelf, again consistent with the strong northeasterly (downwelling favorable) climatological winds.

Lastly, heterogeneities observed in chemical tracers, e.g. the offshore maximum in the tritium distribution (Fig. 4c), may also be evidence of the contribution of different temporal "end members" measured during FLEX. If the Savannah River is the main tritium source (BUSH, 1988), and the above summer to autumn transition scenario is correct, then the measured distribution of the tracer during FLEX contains the discharge

994 F . E . WERNER et al.

during the sampling period as well as that of the previous summer. Since the levels of tritium discharged by the Savannah River are not constant over time, the offshore maximum (Fig. 4c) may be an earlier (pre-October) release which was advected northward [mixed and diluted with waters discharged north of Savannah (e.g. the Cooper-Santee and the Pee-Dee, and possibly even some waters originating north of Cape Hatteras, STEFA, NSSON et al . , 1971)] and is now on a southward transit forced by the autumn northeasterlies. If so, the FLEX measurements may be showing the simultaneous occurrence of waters off Savannah and Brunswick that were "tritium-tagged" 3-4 months apart.

6. C O N C L U D I N G R E M A R K S

The details of the on-offshore exchange of freshwater and other dissolved and suspended substances in the SAB remain far from understood, e.g. seasonal cycles and preferred paths of offshore transport. We focused on the 1987 summer to autumn transition and our findings suggest that summer conditions in the SAB are such that freshwater is advected northward by wind forcing with transport in the surface layers with an offshore component in an Ekman upwelling sense. Variability in the summer winds and other dispersive mechanisms contribute to spread the freshwater over the shelf. After the summer season, when the fall wind regime sets in, the shelf waters are advected southward with the older offshore waters flanking new discharges that are confined within the inner- shelf coastal front (Fig. 19). Freshwater sources north of the SAB are probable contribu-

Fig. 19. Schematic suggesting the fate of summer and fall freshwater in the South Atlantic Bight. Dur ing sum mer the freshwater moves northward and offshore due to the winds, which are generally weak and to the north and northeast , and other dispersive mechanisms. Dur ing the fall, the winds are strong and to the southwest advecting the shelf waters to the south. The recently discharged freshwater hugs the coast (the darker stippled region) with the previous summer ' s

discharge flanking it. At the shelf break freshwater may be lost to the Gulf Stream.


tors to the signal measu red dur ing F L E X , however the t r i t ium found in the f reshwater

indicates that at least some fract ion or ig ina ted f rom Savannah River discharge.

We briefly discussed processes that might con t r ibu te to the s u m m e r offshore spread of the freshwater . Tidal and wind dispers ion are likely and processes such as f rontal instabil i t ies should no t be excluded. In some cases the la t ter might also explain the occurrence of pockets of offshore t racer ( t r i t ium) maxima. Add i t i ona l studies with o ther tracers (e.g. WINDOM and GROSS, 1989) and biological proper t ies (e.g. PAFFENHOFER and LEE, 1987) should provide fur ther clues. I na smuch as cross-shelf exchange, the dynamics of the inner - and mid-shelf of the SAB appear to be different in s u m m e r and a u t u m n - s u m m e r be ing more of a "sluggish" season relat ive to a u t umn . The lat ter is character ized by s t rong winds which con t r ibu ted to its quicker flushing. S u m m e r on the o ther hand is a more ben ign season when the c i rculat ion is no t subjected to pers is tent wind forcing. Thus ,

relat ive to a u t u m n when shelf waters are flushed out to the south, cross-shelf t ranspor t dur ing s u m m e r might be larger.

A closing r emark on mode l ing aspects is that the capabil i ty of descr ibing t idal- t ime

f ronta l evo lu t ion is needed to min imize rel iance on bulk paramet r iza t ions . A l though efforts are unde rway (e.g. JAMES, 1988) this is a topic deserving con t inued a t ten t ion .

Acknowledgements--We would like to thank Mike Foreman and Roy Waiters for many helpful discussions. Antonio Baptista kindly provided the code for computing drogue trajectories. We also thank Julie Amft for helping us with the data analysis, Brian Blanton for helping out on the computations and Anna Boyette and Suzanne Mclntosh for their assistance in drafting the figures. The insightful comments provided by the anonymous reviewers are greatly appreciated. This study was supported by the Department of Energy contracts DE-FG09-85ER60351 and DE-FG09-86ER60450. An early version of these results was presented at the 1990 JONSMOD at the Proudman Oceanographic Laboratory in Bidston, U.K.

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Documents

A numerical study of the continental shelf circulation of the U.S. South Atlantic Bight during the autumn of 1987