Convergence and Downwelling at a River Plume Front

JULY 1998 O'DONNELL ET AL. 1481

JAMES O'DONNELL University of Connecticut, Groton, Connecticut

GEORGE O. MARMORINO AND CLIFFORD L. TRUMP Naval Research Laboratory, Washington, D.C. (Manuscript received 14 July 1997, in ®nal form 23 September 1997)

ABSTRACT The small-scale structure of the circulation and hydrography at the frontal boundary of the Connecticut River plume in Long Island Sound has been resolved using a novel combination of instruments: a towed acoustic Doppler current pro®ler (ADCP) and a rigid array of current meters and conductivity±temperature sensors. Observations were made during the latter half of the eastward ebb tide, when the river plume was well established and the front was moving to the west at approximately 0.3 m sϪ1. Two across-front transects revealed a horizontal convergence rate in the across-front velocity components at 0.6 m of 0.05±0.1 sϪ1. This was associated with a salt-induced horizontal density gradient of 10Ϫ2 kg/m4. Observations obtained during a period in which the towed ADCP was caught in the zone of maximum surface convergence showed signi®cant downwelling with a near-surface maximum of 0.2 m sϪ1. Vertical velocities of this magnitude are consistent with observed magnitudes of the convergence rate at 0.6 m assuming volume ¯ux continuity and weak alongfront variations. Quantitative comparison of the velocity observations to the model of Garvine show reasonable agreement, though the vertical distribution of vertical shear and strati®cation could be improved. Within 20 m of the front, observations reveal regions of strong subsurface horizontal gradients in density and velocity that are not well described by the model. This limitation is a consequence of the assumption of similarity in the vertical structure of the ®elds. Both the magnitude and the across-front variation of the vertical velocity component observed agree with the theoretical predictions. The authors conclude, however, that the fundamental dynamics in the model are adequate to describe the general structure of the plume layer thickness.

1. Introduction Imberger 1987) suggested that the horizontal scale of It is well established that freshwater runoff transports variations in the density and current structure was less particulates and dissolved material from land to estuaries than 100 m and comparable to the resolution of the mea- and the coastal ocean and that a quantitative understand- surements. Qualitative estimates of the width of the lines ing of the mechanisms of mixing and dispersion of this of foam and detritus that are often associated with frontal ef¯uent is essential to improving our prediction capability convergences are much smaller, of order 1 m. This small- for estuary and ocean circulation. Though the ¯ow mag- er scale is also consistent with the results of laboratory nitude and the geometry of every river estuary is unique, experiments on gravity currents, for example, Simpson during periods of high discharge, many have been ob- and Britter (1979), which indicate that the horizontal served to form a large plume of brackish water at their scale of the front should be a few times the thickness of mouths (Garvine 1974b; Stronach 1977; Ingram 1981; the buoyant layer. Freeman 1982; Lewis 1984; Luketina and Imberger Recent development of models of the dynamics of the 1987). Undoubtedly, many more smaller, and seldom sur- interior of river plumes (Garvine 1984, 1987; O'Donnell veyed, rivers exhibit this behavior intermittently. 1988, 1990) have suggested that the ¯ow at the frontal Convergent surface fronts are a common feature in boundary in¯uences the dynamics in the interior of the reports of observations of river plumes. Systematic ob- plume. This suggests that advancement in the understand- servations of the morphology of fronts have been few. ing of plumes requires a more detailed appreciation of Early work (e.g., Garvine and Monk 1974; Luketina and the properties of the front. The wide variety of, and the uncertainty in, the spatial scales of variability in river plumes, from 1 to 103 m, together with their transient nature has made detailed observations of their properties Corresponding author address: Dr. James O'Donnell, Department of Marine Sciences, University of Connecticut, 1084 Shennecossett dif®cult. However, technological advances in navigation Road, Groton, CT 06340-6097. and current measurement have provided new tools with E-mail: [email protected] which to observe the nature of river plume fronts. In this

᭧ 1998 American Meteorological Society

Unauthenticated | Downloaded 09/28/21 03:08 AM UTC 1482 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 paper we report some results of an expedition to resolve the structure of the plume of the Connecticut River in Long Island Sound with a rigid array of current and conductivity±temperature sensors and a towed acoustic Doppler current pro®ler (ADCP). We then evaluate the consistency of the different types of observations and compare them to the predictions of the model of Garvine (1974a). In the next section we describe the main features of the Connecticut River plume and review prior observations of the frontal structure. Observations of dynamically related features are also summarized. Based on these observations and the theoretical work of Garvine, we estimate the scale of the horizontal convergence and consequent downwelling velocity with emphasis on its dependence on the horizontal scale of variation. In section 3 we describe the methods and equipment that we employed and then present the results in section 4. The observations and the model of Garvine are compared in section 5. The techniques and analyses are discussed and the paper summarized in section 6.

2. Review a. Observations During the spring freshet, the Connecticut River can deliver 2000 m3 sϪ1 of freshwater to Long Island Sound (LIS). The fate of this water was the subject of a series of reports by Garvine (1974b, 1975, 1977) and Garvine and Monk (1974). This work established that a large area FIG. 1. (a) Garvine and Monk's (1974) observations of the density (␴t) structure of the plume front. Dots show sample locations. (b) of eastern Long Island Sound was covered by a thin (2 Garvine and Monk's (1974) observations of the across-front velocity m) surface layer of brackish water that was separated component (cm sϪ1) measured in the front relative frame. Dots show from the Sound water by a line of foam and detritus, sample locations. referred to as a front. This river plume was observed to be strongly in¯uenced by the tidal ¯ow in the sound and was located to the east of the river mouth on the ebb and sor. The velocity ®eld was obtained (in a frame of ref- to the west on the ¯ood. The motion ®eld in the plume erence moving with the front) using a mechanical current during its formation was observed by Garvine (1977) meter lowered from a vessel that maintained a ®xed dis- using drifters and drogues that were tracked visually by tance from the front. Though these techniques yielded aerial photography. These measurements revealed that the ®rst detailed picture of the frontal structure, dynamic there was little spatial structure in the velocity ®eld in interpretation was limited by the relatively large uncer- the buoyant layer, that there was strong circulation normal tainties resulting from platform positioning, motion and to the tidal ¯ow in the denser water, and that the buoyant rotation, and nonsynoptic sampling. An example of their layer had negligible in¯uence on the deeper motion. Most observations is presented in Fig. 1. In a qualitative sum- importantly, the observations con®rmed the existence of mary of their observations, Garvine and Monk suggested strong horizontal shear and convergence in the surface that the characteristic horizontal scale of variation of the motion at the front. temperature, salinity, and density was between 20 and Garvine and Monk (1974) reported observations of the 50 m; however they noted that qualitative observations density and motion ®eld in the vicinity of the front with of water color showed signi®cant changes over scales of a resolution of approximately 20 m. They circumvented order 0.5 m. Other exploratory measurements of the ver- navigation problems by making observations in a ref- tical component of velocity in the front with dye tracked erence frame that moved with the front and measured by divers suggested a downwelling of several centimeters distance from the front by stretching line between a small per second. boat in the frontal convergence and the instrument plat- Observations of a similar, but much less buoyant plume form. Their hydrographic observations were obtained us- front in Koombana Bay, Australia, were reported by Lu- ing a pump to sample water at a variety of depths and ketina and Imberger (1987, 1989). Measurements of the pass it through an on-deck conductivity±temperature sen- hydrography and current velocity were obtained using a

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vertically pro®ling CTD and current meter mounted on Here ␳ϱ is the density of the denser ambient water, ␥ is a submerged tower and supplemented by a ship-towed one-half the density anomaly of the surface water at the

CTD package. Though the quality of the velocity ob- plume-front boundary xb, and r(x) describes the across- servations was superior to those of Garvine and Monk front variation of the surface buoyancy. Note that both (1974), the spatial resolution in the vertical pro®les in ␥ and r(x) must be speci®ed and that the depth of the the vicinity of the front was approximately 50 m and pycnocline, D(x), is the only characteristic of the density insuf®cient to properly resolve the scales ϳO(10 m) re- ®eld that is predicted; D(x) must satisfy D(0) ϭ 0 and vealed by the hydrographic observations. D(xb) ϭ Db. Thus, the model describes rapid horizontal

More recently, technological developments in navi- variations in the frontal zone, 0 Ͻ x Ͻ xb, and a smooth gation, current measurement, and hydrographic pro®ling transition to the plume interior, x Ͼ xb, where horizontal have permitted surveys at much higher spatial resolution variations are relatively weak. than those mentioned above. In particular, Marmorino Garvine (1974a) then assumed that the vertical struc- and Trump (1996) used a tow-yowed CTD and a towed, ture of the across-front horizontal velocity component vertically pro®ling ADCP and CTD package called in the front-following frame of reference, u(x, z), had a TOAD (described in more detail later) to observe the quadratic vertical structure above the pycnocline and evolution of a front in the James River. The spatial res- was uniform in the ambient ¯uid; that is, olution of the near-surface density and horizontal velocity  ®elds obtained in these experiments was 5±15 m. This z 2 front had a density change of approximately 1 ␴t in 10 u ϩ [u Ϫ u (x)] ,  s ϱ s D(x) m, a much smaller density variation than that at the Con- u(x, z) ϭ  ΂΃ necticut River plume front. The across-front velocity ϪD(x) Յ z Յ 0 (2) component at 2-m depth also changed across the front  Ϫ1 by as much as 0.25 m s in 10 m, yielding a convergence uϱ, z Յ ϪD(x). rate of 0.025 sϪ1. This strong convergence was correlated with strong downwelling, measured by the ADCP to be He parameterized the magnitude and horizontal distri- Ϫ0.15 m sϪ1. bution of the mass ¯ux due to vertical entrainment as The vertical ADCP pro®les were augmented by across- a linear function of the relative ambient ¯uid velocity front horizontal pro®les obtained by turning the ADCP uϱ and a spatially variable entrainment coef®cient E(x); to orient two beams parallel to the water surface. This that is, qe ϭϪE(x)uϱ. Similarly, he parameterized the innovative application of the ADCP provided much high- turbulent interfacial stress using a quadratic dependence er resolution of the across-front velocity component and on uϱ and a second coef®cient, Cf (x), so that ␶ xz ϭ 2 yielded even larger across-front convergence rates of 0.24 ␳ϱuϱCf (x). Garvine then considered several different Ϫ1 Ϫ1 ms /6.0 m ϭ 0.04 s . values and spatial structures of E amd Cf and obtained semianalytic solutions to the momentum and continuity equations. Note that Garvine (1974a) allowed the pos- b. Theory sibility that qe Ͼ 0, but since we agree with his con- Motivated by his observations in the Connecticut River clusion that this is inconsistent with observations, we plume and a desire to identify the fundamental dynamics, do not carry this additional complexity forward in this Garvine (1974a) developed a diagnostic model of the brief summary. We also simplify his presentation by steady-state structure of a two-dimensional plume front considering only cases in which the spatial structure of overlying an in®nitely deep ambient ¯uid. Since we will mixing and friction are exponentially diminishing with show and discuss comparisons of model predictions and distance from the surface front, since he demonstrated observations, a brief summary of the model is necessary. that there is little sensitivity to the details of the distri- Garvine assumed that the baroclinic pressure gradient and bution. This form is also attractive because it permits inertia in the frontal zone are balanced by the divergence the layer depth in the frontal zone to approach a constant of turbulent stress. He de®ned the across-front coordinate value at large x thereby smoothly joining the plume. Consequently, we take E(x) aT(x) and C (x) faT(x), x to be normal to, and move with, the surface expression ϭ f ϭ where T(x) exp( x/ x ). Here a sets the magnitude of the front and to be directed toward the plume. He then ϭ Ϫ ␤ b of entrainment and f C /E is the relative magnitude speci®ed the density ®eld, ␳(x, z), as a linear function of ϭ f depth between the surface and the pycnocline, z ϭ of the friction and entrainment coef®cients, which are assumed constant. As noted above, x is the width of ϪD(x), such that b the frontal zone and ␤ dictates the decay scale for mix-  ing and friction within the frontal zone. Calculation of z the model solutions for u (x) and D(x) then requires the 1 Ϫ 2␥r(x)1ϩ , s ␳(x, z) D(x) numerical integration of two simultaneous differential ϭ  ΂΃ ␳ (1) equations. To ensure that the layer depth Db at the ϱ  ϪD(x) Յ z Յ 0 boundary of the frontal zone, xb, equals that in the 1, z Յ ϪD(x). plume, Garvine showed that the parameters must satisfy

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␥gD Ri ϭ 3␤ f Ϫ 3.6␤2 Ϫ 4.2␤ Ϫ 0.6 ϭ b , (3) b 2 uϱ where g represents the acceleration of gravity. He also showed that the magnitude of the entrainment coef®- cient determined the frontal scale ratio so that a ϭ Db/ xb. Examples of the model predictions will be discussed later. The behavior at the front, however, can be written explicitly and the results are used here to estimate the order of magnitude of the surface convergence and downwelling and to assess the sensitivity of the estimates to the resolution of the observations. Garvine used these limits to constrain and help select appropriate parameter values and also to initiate the numerical integration of the model momentum and continuity equations. The surface velocity at the front can be shown to be FIG. 2. (a) Garvine's (1974a) model depiction of the density ®eld u (0) 1 s ϭ q ϭ [3 Ϫ 5 f ϩ 5( f 21/2Ϫ 2.8 f ϩ 1) ], (4) in the front of a river plume with parameter values chosen to simulate u 0 8 the data of Garvine and Monk (1974). The thick line shows the ϱ predicted level of the base of the pycnocline. (b) The across-front which requires f Ն 2.38 for q 0 to be real. In the limit velocity component is consistent with the density ®eld shown above. → → The velocity of the ambient ¯ow, below the pycnocline, is uniformly f ϱ, no entrainment takes place and q 0 Ϫ0.5. Reducing f increases the magnitude of downward en- 50 cm sϪ1. trainment (i.e., reduces q 0) and increases the rate of surface convergence at the front. constraint that the ambient ¯uid must decend under the Using q 0, the slope of the pycnocline at the surface front. The second term is the additional velocity due to outcrop can then be found from the downward entrainment out of the plume. 1 dD Ϫ3 The magnitude of the vertical velocity at the front (0) ϭ . (5) obtained using the parameter values above and Eq. (6) adx 2q0 ϩ 1 Ϫ1 is large, w0 ϭϪ0.18 m s . This impressive down- Note that for dD/dx to remain ®nite some entrainment welling is the result of the exponential-like growth of must take place and q 0 ϽϪ0.5. the model pycnocline depth near the front (see, e.g., To evaluate model predictions Garvine (1974a) chose Fig. 2a); w diminishes rapidly with x as the layer depth parameter values that described a density ®eld similar tends to the plume value at xb. The maximum magnitude to the observations of Garvine and Monk (1974) shown of w is quite uncertain, however, because the estimate in Fig. 1a. The surface buoyancy was speci®ed using ␥ of dD/dx(0) is sensitive to the spatial resolution of the Ϫ3 ϭ 7.5 ϫ 10 and r(x) ϭ 1 Ϫ exp(Ϫx/bxb) with xb ϭ hydrographic surveys. Garvine (1974a) chose the upper 118 m and b ϭ 0.055. Using (4) and (5) f ϭ 5.52 was limit of the range of reasonable values consistent with selected so that dD/dx(0) matched the slope of the ␴T the data of Garvine and Monk (1974). ϭ 18 isopycnal at the front. The observations of the An estimate for the scale of the vertical velocity in current shown in Fig. 1b were used to estimate uϱ ϭ the frontal zone as a whole can be obtained by assuming Ϫ1 → 0.5ms , and the condition D(x xb) ϭ Db ϭ 2m that all the ambient ¯ow is diverted under the plume then required ␤ ϭ 0.1 and a ϭ 0.017. The model density and that the entrainment effect is relatively small. The and velocity ®elds computed by numerical integration kinematic condition at the front then yields O(w) ϭ W are shown in Fig. 2. These are qualitatively consistent ϭ uϱDb/xb. Taking the scale of the frontal pycnocline with the data (Fig. 1) and exhibit similar values [us(0) slope as Db/xb, parameters estimated using the observed Ϫ1 ϭϪ0.29 m s ] for the surface velocity in the plume. hydrography (Fig. 1a), then W ϭ uϱDb/xb ϭ 0.01 m The jump of Ϫ0.79 m sϪ1 predicted in the surface sϪ1. Though this value is an order of magnitude less velocity at the front is accompanied by downwelling. than that computed using the model, they are not in- With the surface velocity at the front, (4), and the slope consistent since Eq. (6) predicts the maximum value of the front, (5), the vertical velocity at the front (the and the scale estimate applies over the whole frontal maximum in the domain) can be obtained from conti- zone. Since both estimates are sensitive to the spatial nuity and written as resolution of the hydrographic ®elds, considerable un- 2 dD certainty in the scale of the frontal zone and the vertical w(0, z Ͻ 0) ϭϪ uϱ(1 Ϫ q0) (0). (6) velocity remains. 3 dx An alternative, independent, order of magnitude es- The ®rst term on the right arises from the kinematic timate of the vertical velocity can be obtained from the

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FIG. 3. Schematic of (a) the SCUD array, (b) TOAD, and (c) the relative positions of SCUD and TOAD during an observation transect. velocity ®eld directly. Using the notation de®ned above magnitude smaller than the maximum downwelling ve- and the data shown in Fig. 1b, the surface convergence locity at the front. in the top meter of the water column can be approxi- Since the velocity data leave the question of the hor- x ഠ 0.8 m sϪ1/40 m ϭ 0.02 sϪ1. Assuming izontal scale of the plume front and the magnitude ofץ/uץ mated by that the alongfront variations in the alongfront velocity the vertical velocity unresolved, it is appropriate to con- are small, which is consistent with the observations that sider the laboratory analogs studied by Britter and Simp- the front is locally straight, then we must conclude that son (1978), Simpson and Britter (1979), and Simpson -w and Linden (1989). These authors studied the propaץ uץ ϭϪ , (7) gation of gravity-driven fronts in long, shallow tanks z and developed empirical relationships between theץ xץ z ഠ buoyancy of the layer and the propagation speed of theץ/wץ since water is almost incompressible. Then Ϫ0.02 sϪ1. Assuming that the vertical velocity at the gravity current head. Though they have not addressed free surface is zero, integration of Eq. (7) from the level the horizontal scale of the frontal regions explicitly, their of the pycnocline (z ϭϪ1 m) to the surface yields the shadowgraphs of the ¯ow structure (see Figs. 1, 3, and estimate W ϭ 0.02 m sϪ1, essentially the same as that 4 of Simpson and Britter 1979) suggest that the scale based on the kinematic approximation and the observed of variations at the boundary is of the same order as pycnocline slope. Note that this estimate is the order of the depth of the plume layer. magnitude of the 40-m scale average, which if gradients On the basis of these laboratory experiments and the at smaller scales are signi®cant, could be an order of qualitative observations of the width of the foam line

Unauthenticated | Downloaded 09/28/21 03:08 AM UTC 1486 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 at the front of the plume of the Connecticut River, and the observations of the front in the James River (Mar- morino and Trump 1996), we hypothesize that previous observations have not resolved the dominant scale of variations in the current and density ®eld and that the convergence results in downwelling of ambient water with an order of magnitude W ϭ 0.1 m sϪ1. Since this is certainly above the detection threshold of an acoustic Doppler current pro®ler, we designed and executed an observation program to test the hypothesis.

3. The observation program The near-surface current and hydrographic structure in the vicinity of the plume front were measured using two instrument systems deployed from the R.V. Libinia, a 10-m workboat equipped with a differential GPS (global positioning system) navigation system. The Sur- face Current and Density Array (SCUD), described in detail by O'Donnell (1997, hereafter OD97), is a rigid array of three Marsh McBirney electromagnetic current meters and ®ve conductivity±temperature sensors, mounted on the bow of the Libinia to estimate the current velocity at depths 0.7, 1.3 and 2.8 m and the density at 0.15, 0.76, 1.42, 2.21, and 2.82 m. A schematic of SCUD is shown in Fig. 3a. All of these parameters together with the ship heading, pitch and roll were sam- pled at 1.5 Hz and averaged at 2-s intervals after a position was acquired from the differential GPS navigation system. The ship velocity was averaged in time to reduce noise and the product of the ship velocity and averaging time set the limit on the horizontal resolution of the water velocity observations. The details of the data processing and some preliminary observations obtained by the SCUD array may be found in OD97. The second instrument package, TOAD, consisted of FIG. 4. (a) A map of the mouth of the Connecticut River showing an R.D. Instruments 600-kHz broadband acoustic Dopp- the coastline; isobaths at 10-m intervals and the location of the observations. (b) The curves show the ship tracks for sections 14±16 ler current pro®ler (ADCP) suspended below a surface and the asterisks symbols show the position of the surface foam line ¯oat and towed from a cleat on the starboard beam of when the ship crossed it on sections 14 and 15. The times of front the Libinia. A Sea-Bird Instruments STD19 conductiv- crossings are also shown. The plus signs show where the ship crossed ity, temperature, and pressure package was also mounted the front on section 16. The thick curve shows the part of section 16 on TOAD at 0.75 m below the surface. TOAD is illus- in which TOAD was caught in the frontal convergence. The arrows show the across- xЈ and along- yЈ front coordinate directions and the trated schematically in Fig. 3b and the relative positions direction of the front propagation. of the SCUD and TOAD when deployed are sketched in Fig. 3c. The ADCP measured the current and acoustic backscatter from 1.3 below the surface to within 1.5 m to the river mouth and bathymetry is shown in Fig. 4a. of the bottom (in 10 m of water), in 0.25-m bins at 1- During the interval of the observations discussed in this Hz sample rate. Further details of the design and per- report, 1255 to 1325 EDT, the front was oriented in an formance of TOAD are reported in Trump et al. (1995). approximately northwest to southeast direction and was In the next section we present and interpret concurrent translating to the southwest. The Libinia's track on three observations of the small-scale structure of the motion observational transects across the front are shown in and hydrographic ®elds at the Connecticut River plume Fig. 4b. Transects 14 and 15 were each approximately front with both systems. We emphasize the vertical mo- 250 m in length and were almost normal to the front. tion that has never before been measured directly. The crossings of the foam on transect 14 (1256:29 EDT) On the afternoon of 5 April 1994, we observed the and 15 (1300:46 EDT) are shown by the asterisks in front of the Connecticut River plume during the late Fig. 4b. In contrast, transect 16 approached the front at eastward ¯owing ebb in Long Island Sound to be to the an oblique angle. When the Libinia crossed the front at southwest of the river. The location of the front relative 1315:40 EDT, at the position shown by the plus signs,

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FIG. 5. Across-front transects of the salinity ®eld obtained by SCUD on transects (a) 14, (b) 15, and (c) 16. In each of these ®gures xЈϭ 0 is the location of the salinity jump and the surface front. the course was altered to parallel the front with the by dividing the distance along the normal by the time consequence that TOAD was trapped by the conver- separation between the observations. To account for the gence and moved along the foam line until 1318:46 fact that x14 and x15 were not simultaneous, the locations EDT. This segment of transect 16 is shown by the thick at the middle of the time interval, 1259:06, were com- solid line in Fig. 4b. puted. Denoting these locations as xm14 and xm15 then assuming the front moved at constant velocity, xm14 ϭ x ϩ⌬uЈ t/2 and x ϭ x Ϫ⌬uЈ t/2. The line through 4. Results 14 ffm15 15 xm14 and xm15 was subsequently used to de®ne the along- To present the hydrographic and circulation data and and across-front coordinates (xЈ, yЈ) shown in Fig. 4b to estimate the frontal propagation velocity, we de®ne and the front velocity estimated as 0.28 m sϪ1 in the the frontal coordinate system (xЈ, yЈ) in the directions direction 220Њ as shown by the vector in Fig. 4b. shown in Fig. 4b where xЈ lies 50Њ east of true north. Vertical cross sections of the salinity ®eld in the xЈ Note that though this system is oriented along and across direction obtained from the SCUD array on transects the front, it is ®xed relative to the earth. The frontal 14±16 are shown in Fig. 5. In each of these ®gures, xЈ orientation used to de®ne the coordinate system was ϭ 0 is the position of the salinity jump, which is within obtained by a predictor±corrector procedure that as- a few meters of the foam line. The presence of the sumed that the front was locally straight and moved in horizontally uniform low salinity plume on the right of the locally normal direction at constant velocity between these ®gures and the comparatively weak vertical struc- 1256:29 and 1315:40. The preliminary estimate for the ture on the left is clearly evident and consistent with orientation and front velocity was obtained by drawing the Garvine and Monk (1974) observations (Fig. 1). The a line through the two front locations on transects 14 across-front scale of salinity variations, of the order of and 15, x14 and x15, that are shown by the ``*'' in Fig. a few meters in all transects, is much smaller than that 4b. The normal to this line passing through the front resolved by Garvine and Monk (1974). crossing on transect 16, x16, was then found and the Note that both sets of observation were obtained un- preliminary estimate of the front velocity,uЈf , obtained der similar river discharge and tidal conditions. The

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FIG. 6. The structure of the salinity ®eld in the neighborhood of the front on transects (a) 14, (b) 15, and (c) 16. The plus signs show the locations of samples. average discharge at the lowest stream¯ow gauge (Ϫ5 Ͻ xЈϽ0 m), which is consistent with the down- (Thompsonville, Connecticut) for the week prior ob- welling that we expect. servations resulting in Fig. 1 was 1364 m3 sϪ1 and was Figure 7 shows an example of the structure of the 1501 m3 sϪ1 on the day of the survey. For comparison, near-surface circulation in the neighborhood of the front the average discharge was 1085 m3 sϪ1 during the week observed on transect 15 with the electromagnetic current preceding our surveys and was 1495 m3 sϪ1 on the day meters on the SCUD array at 2-s intervals and the the data were acquired. TOAD velocity estimates averaged over 5-s intervals. Figure 6 shows the salinity cross sections in the vi- Figure 7a shows the across-front structure of the across- cinity of the front at higher resolution with the locations front velocity component, and Fig. 7b shows the dis- of samples shown by the ``ϩ'' symbols. In transects 14 tribution of the corresponding alongfront component. and 15, the average spacing of samples in the across- Note that the SCUD current meters were at 0.6, 1.3, and front direction was approximately 3 m. Because the ship 2.8 m and that the TOAD data from bins at 1.35±1.6 approached the front at a much smaller angle in transect m and 2.6±2.85 m are shown for comparison. Though 16, the across-front spacing of observations was much the signature of the near-surface convergence is evident smaller, with an average of 0.5 m in the vicinity of the in the rapid decrease in the 0.6-m across-front velocity front. The presence of the high wavenumber structure component in the interval 0 Ͻ xЈϽ20 m, the magnitude in the higher-resolution section may re¯ect along-front of the variability and the nonuniform spacing of the variations but might also indicate that the front normal observations confounds the recognition of other coher- sections are undersampled. However, in all three sec- ent patterns. Intercomparison of the two observation tions the isohalines plunge deeper at the front (0 Ͻ xЈ systems is also dif®cult in this presentation of the data. Ͻ 10 m) than in the plume region (xЈϾ10 m), sug- To spatially smooth the velocity data we averaged the gesting that this feature is real and may be a manifes- estimates of the velocity components in 10-m bins in tation of the gravity current ``head'' structure described the across-front direction. The average number of ob- by Simpson and Britter (1979). Sections 14 and 16 also servations in the bins were 3.7 and 3.9 for transects 14 show that the 25 and 26 isohalines in the near-surface and 15. The data were slightly denser on transect 16, sound water dip downward on the left side of the front which intersected the front at an acute angle and yielded

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FIG. 7. The across-front dependence of (a) the across-front, and (b) the alongfront velocity components on transect 15 at 0.6 m, 1.3 m, and 2.8 m observed by SCUD and the data from the TOAD bins at 1.35± 1.6 m and 2.6±2.85 m averaged in 5-s intervals. Note that these velocities are relative to an earth-®xed coordinate system.

an average of 8.3 estimates in the 10-m bins. The TOAD data were also bin averaged where more than one estimate occured in a 10-m interval. Figure 8 shows the distribution of the averaged across-front component from transects 14 (a), 15 (b), and 16 (c). The alongfront velocity components are not presented because no signi®cant across-front variation can be detected. At each level, the SCUD data are displayed as a shaded band that is two standard deviations wide and centered at the mean value. The binned TOAD data at the 1.3-m level are shown by the solid black line and at the 2.7-m level by the dashed black line. Clearly, the two instrument systems yield consistent observations. The data in Fig. 8 reveal that the across-front component of velocity at the 2.8-m level does not change signi®cantly on crossing the front and is approximately 0.2msϪ1. At the 1.3-m level, both the SCUD and TOAD measurements show that the across-front component decreases from approximately 0.2 m sϪ1 to Ϫ0.1 m sϪ1 and passes through a minimum in the vicinity of the surface front. The most dramatic characteristic of the

FIG. 8. The across-front dependence of the across-front velocity circulation pattern, however, is the strong convergence components averaged in 10-m bins on transects 14 (a), 15 (b), and in the across-front velocity components observed at the 16 (c). SCUD observations at 0.6, 1.3, and 2.8 m are shown by the 0.6-m level in all three sections. gray shaded bands centered at the mean value and two standard de- Quantitative estimates of the magnitude of the across- viations wide. The data from TOAD are displayed by the solid black line (1.5 m) and the dashed line (2.7 m). Note that these velocities front divergence rate, duЈ/dxЈ, are obtained by comput- are relative to an earth-®xed coordinate system. ing the ®rst-order ®nite difference approximation to the

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symbols in Fig. 4b, TOAD was trapped in the foam line associated with the frontal convergence. The salinity at 0.6 m observed by the TOAD's CTD and the vertical structure of the acoustic backscatter recorded by the ADCP are shown as functions of time in Figs. 10a and 10b. The intervals when TOAD crossed into and out of the frontal convergence zone are marked emphatically by the abrupt transitions in salinity and the reduction in the intensity of the backscatter. These periods are also shaded gray and labeled F1 and F2 in Fig. 10a. Between these strips, TOAD was trapped in the foam line. The vertical structure of w during this segment of transect 16 is shown in Fig. 10c. Though there is large variability in both time and depth, there is strong bias toward negative values during the interval between F1 and F2 when TOAD is in the front. The vertical pro®le of the temporal mean in the plume (data averaged to the left of F1 and to the right of F2) is displayed in Fig.

FIG. 9. The across-front dependence of the across-front divergence, 11a. The shaded stripe is two standard deviations wide. duЈ/dxЈ, estimated using velocity components averaged in 10-m bins Clearly, there is no signi®cant vertical velocity. on transects 14 (a), 15 (b), and 16 (c). Estimates using 5-m bins are To contrast the observations in the front, the average shown in (d) for transect 16. The gray shaded bands show the de- is computed within and between the intervals labeled tection threshold. F1 and F2 and shown as a function of depth in Fig. 10b together with two standard deviations of w in the frontal derivative using the bin-averaged data obtained by the region. The vertical velocity is strongly negative in each SCUD array (see Fig. 8). Since differencing the series of these curves obtained in the vicinity of the front with will amplify the variability, it is important to estimate a magnitude between Ϫ0.15 and Ϫ0.20 m sϪ1 at 4 m, the uncertainty of the estimate of duЈ/dxЈ. Taking the diminishing to Ϫ0.05 m sϪ1 at 9 m. There is no sig- average of the standard deviations of all the bins, ␴uЈ ni®cant difference between the pro®les obtained while ϭ 0.05 m sϪ1 as the uncertainty in the velocity estimates, crossing the front (F1 and F2) and the frontal zone av- then the uncertainty in duЈ/dxЈ can be estimated as erage. There is a suggestion of slightly larger magni- Ϫ1 1.4␴uЈ /10 ഠ 0.007 s . tudes since the F1 and F2 means tend to be greater, but The across-front distributions of duЈ/dxЈ for all three the limited number of observations makes that inter- transects are displayed in Figs. 9a±c together with a pretation uncertain. shaded band enclosing plus and minus twice the uncertainty estimate. Values lying outside of the shaded 5. Discussion area are signi®cantly different from zero. The maximum magnitudes appear within 20 m of the front in all three The consistency of the near-surface convergence and transects where a convergence is apparent at both the the vertical velocity estimates can be evaluated by as- 1.3-m and 0.6-m levels. The maximum convergence rate suming the alongfront variations are small and vertically occurs at the 0.6-m level and reaches approximately integrating Eq. (7) from the interface, z ϭϪD, to the 0.05 sϪ1. surface, z ϭ 0, where the vertical component of the Since transect 16 had denser sample spacing in the velocity is zero. This yields uЈץ across-front coordinate than the other two transects, duЈ/ 0 dxЈ was also computed using velocity estimates aver- w ϭ dz. (8) xЈץ ͵ zϭϪD aged in 5-m bins (approximately four estimates per bin). ϪD xЈϭϪ0.09 m sϪ1 as an estimate of theץ/uЈץ The across front distribution is displayed in Fig. 9d. Taking With this averaging scale, the maximum convergence convergence over the upper 2 m of the water column, Ϫ1 Ϫ1 rate is 0.09 s . then we should expect wzϭϪ2 ഠ Ϫ0.18 m s . This is The convergence at the front must be associated with consistent with the ADCP observations shown in Figs. downwelling and this vertical velocity was also ob- 10c and 11. We conclude, therefore, that the spatial scale served by TOAD. Since the spatial resolution is limited of the velocity variations in the frontal zone is approx- by navigation uncertainties, the vertical velocity data imately 5 m and that the high-resolution transect (16) are presented using the salinity measured by TOAD to adequately resolved the horizontal variations. If the map the velocity observations to the hydrographic struc- front was of even smaller scale, the magnitude of the ture. Vertical velocity estimates observed in the front vertical velocity measured by the ADCP would have can then be separated from those obtained in the plume. been much larger than that estimated using the conti- On transect 16, between the points marked by the ``ϩ'' nuity argument.

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FIG. 10. Time series collected by TOAD on transect 16 showing (a) the salinity at 0.6 m, (b) the vertical structure of relative acoustic backscatter, and (c) the vertical structure of vertical velocity component. The intervals shaded gray in (a) indicate when TOAD entered and exited the region of the foam line.

Before proceeding to evaluate Garvine's (1974a) hy- Dw/Dt W 22/DD drostatic model, we estimate the magnitude of the con- ϭ O ϭ O . (11) zU΂΃΂΃/DLץ/pץvective acceleration in the vertical direction and the ver- ␳Ϫ122 tical derivative of the dynamic pressure, thereby as- 2 2 sessing the adequacy of the hydrostatic approximation Since for D ϭ 1 and L ϭ 5, D /L ϭ 0.04, the hydro- in the frontal zone. Assuming the ¯ow is steady in the static approximation is not unreasonable even in this frame of reference that moves with the front, then the abruptly changing ¯ow. material acceleration is With the combination of the data from SCUD and TOAD, the hydrography in the top 3 m of the water wUWW2 column and the velocity ®eld from 0.6 to 8.6 m belowץ wץ Dw ϭ u ϩ w ϭ O max , , (9) the surface are available to compare with the predictions zLDץ xץ Dt []΂΃ of the Garvine (1974a) model. The data acquired on where the scale of the horizontal and vertical velocity transect 16 are employed since they provide the highest components are taken to be U and W, respectively. As spatial resolution. Figure 12a shows the across-front pointed out above, continuity requires U/L ϭ O(W/D) section of density (␴T). Figure 12b shows the across- so that Dw/Dt ϭ O(W 2/D). Taking the scale for the front distribution of the across-front velocity component dynamic pressure p to be ␳U 2 then in the frame of reference moving with the front [i.e., Ϫ1 uЈ(x, z) Ϫ uf where uf ϭϪ0.28 m s ]. This ®gure was pU2 produced using the data measured by SCUD at 0.6 mץ 1 ϭ O . (10) zD and by TOAD from 1.1 to 8.6 m in 0.25-m bins. Bothץ ␳ ΂΃ datasets were averaged in 10-m bins in the across-front The relative magnitude of the pressure gradient and ac- coordinate. celeration is therefore To compute the velocity ®eld using the model of Gar-

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FIG. 11. The vertical structure of the mean vertical velocity in (a) the plume and (b) the frontal zone. In both ®gures the shaded band shows two standard deviations centered at the mean. vine (1974a), we must ®rst specify the parameters of this function and the data is shown in Fig. 13a. Since the density ®eld. We choose r(x) ϭ 1 Ϫ exp(x/bxb) with the data shown in Fig. 6 were acquired at much higher Ϫ3 b ϭ 0.005, xb ϭ 50 m, ␳ϱ ϭ 1022 kg m , and ␥ ϭ spatial resolution than in Fig. 1, the frontal slopes and 8.5 ϫ 10Ϫ3 to match the density observed by the SCUD other parameters must be different from those used by sensor at 0.15 m below the surface. A comparison of Garvine. We adopt the 24 psu contour, roughly equivalent to

the ␴T ϭ 19 contour, as the level of the bottom of the plume layer and estimate the slope of the contour at the front as 2.5/2 ϭ 1.25 and choose the plume layer depth

FIG. 13. A comparison of across-front distribution of (a) ␴T observed by SCUD on transect 16 at 0.15 m (circles) and the functional representation used to evaluate the model of Garvine (1974a); (b)

FIG. 12. Across-front sections observed on transect 16 of (a) ␴t, the level of the ␴T ϭ 19 contour (dashed line) and the depth of the with the approximate level of the 19 contour shown by the thick line, plume layer predicted by Garvine (1974a); and (c) the model-pre- and (b) the across-front velocity component in a frame of reference dicted surface velocity (thick solid line), the model-predicted velocity moving at the frontal velocity with the depth of the ␴T ϭ 19 contour at 0.6 m (thick dashed line), and the corresponding velocity com- (thick line) to aid comparison with the density ®eld. ponent observed by SCUD at 0.6 m.

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TABLE 1. Frontal model parameter comparison. Param- Garvine 1994 eter Description (1974a) observations

xb frontal zone width (m) 118 50 b hydrography variation scale 0.055 0.005 Ϫ3 ␳a density scale (kg m ) 1020 1022 ␥ plume surface anomaly 0.0075 0.0085

Db plume layer thickness (m) 2 2.75 Ϫ1 uϱ ambient velocity (m s ) 0.5 0.45 ␤ mixing and friction distribution 0.10 0.13 a depth to length scale ratio 0.017 0.055 f friction and entrainment ratio 5.52 6.0

Rib Richardson number 0.60 1.13

as Db ϭ 2.75 m. The approximate level of the ␴T ϭ 19 contour is shown by the thick line on the contour map of the across-front velocity (Fig. 12b). Note that between x ϭ 3 and 17 m the ␴T ϭ 19 contour drops below SCUD's lowest conductivity temperature sensor (2.8 m) so that the level represented in the ®gure is only an upper bound in that interval. The average velocity below the ␴T ϭ 19 level is taken as the ambient ¯ow magnitude Ϫ1 (uϱ ϭ 0.45 m s ). These choices imply a ϭ 0.055 and FIG. 14. Across-front sections showing the structure of the pre- Rib ϭ 1.13. Equation (5) then requires f ϭ 6 and Eq. dictions of Garvine's (1974a) model. Parameter values were chosen (3) yields ␤ ϭ 0.13. to simulate the observations obtained on transect 16. (a) ␴t, with the Table 1 presents a summary to facilitate comparison observed level of the 19 contour shown by the thick line, and (b) the across-front velocity component. of the parameter choices adopted by Garvine and those used here. The most signi®cant differences are in the parameters, b and a, that describe the density ®eld vari- before rising abruptly to the surface at the front. This ation and the frontal zone length to layer depth ratio. suggests there is signi®cant, localized downwelling on These, together with the larger layer depth gradient at the buoyant side of the front. The model does not re- the front, require a slightly larger f and Rib. These produce this structure either. parameter values may be useful in providing the scale Similar comments can be made regarding the across- estimates in other circumstances. front velocity component distribution in Figs. 12b and Figure 13b displays a comparison of the depth of the 14b. Both the model and data show horizontal isotachs plume layer, D(x), computed using these parameters to in the interval x Ͼ 20 m. The model assumes a quadratic the level of the ␴T ϭ 19 contour. Though the behavior vertical structure with most of the shear in the lower at x ϭ 0 and xb is correct, the model underestimates the half of the plume layer. The data, in contrast, show frontal slope and the depth of the layer in the interval greatest shear above z ϭϪ1.5 m at the region of max- 0 Ͻ x Ͻ 20 m. The surface velocity predicted by the imum strati®cation. The model and velocity data also model is represented by the thick solid line in Fig. 13c disagree in the neighborhood of the front (0 Ͻ x Ͻ 20 and the distribution at 0.6 m by the thick dashed line. m). The model shows the isotachs converging and rising The SCUD velocity measurement at 0.6 m is shown by smoothly to the surface whereas the data show that they, the thin line for comparison. The model prediction is in fact, get deeper, a pattern similar to that of the iso- biased slightly and predicts 0.1 m sϪ1 more ¯ow toward pycnals. the front than is observed. The magnitude of the spatial The discrepancy between the vertical structure of the gradients is well represented however. density and velocity ®elds in the model and data could, The full two-dimensional structure of the model den- perhaps, be reduced by revising the functional forms sity and velocity ®eld is presented in Fig. 14 with the assumed. In fact, Garvine (1979a,b) has already gen- same scales as the data shown in Fig. 12. The density eralized his earlier model to include the effects of ro- ®elds are basically similar with horizontal isopycnals tation and examined more complex vertical structures. for x Ͼ 20 m. Figure 12 also shows that the strati®cation However, these structural changes, even together with above z ϭϪ1.5 m is signi®cantly greater than in the adjustments to model parameters do not yield regions x Ͼ 0 that are observed in (0 Ͻץ/uץ x Ͼ 0 andץ/␳ץ Ϫ3 Ͻ z ϽϪ1.5 interval. The model, which assumes of uniform vertical strati®cation above the pycnocline, x Ͻ 20, Ϫ2.8 Ͻ z Ͻ 1.5) m. The fundamental problem does not properly represent this detail. The second dis- with the model is the assumption that the vertical struc- crepancy is in the vicinity of the front. The data show ture of the ®elds is independent of x. This allows math- that the isopycnals slope downward toward the front ematical simplicity and is a good approximation away

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necticut River plume front exhibits very short spatial scales in keeping with our expectations based on observations of the laboratory analogs, we have not yet made quantitative comparisons of frontal propagation and convergence rates between ®eld and laboratory. This will be the subject of future work.

6. Summary and conclusions In this paper we describe the application of a towed acoustic Doppler current pro®ler and a rigid array of FIG. 15. The dependence of the vertical velocity on across-front distance (solid curve) in the model of Garvine (1974a). The dotted electromagnetic current meters and conductivity±tem- line represents 5-m bin averages of the model predictions and the perature sensors to make the ®rst adequately resolved solid line shows vertical velocity estimates in the interval Ϫ4.75 m observations of the rates of convergence and consequent Ͻ z ϽϪ3.75 m obtained using TOAD averaged in 5-m bins. downwelling velocity at the front of a river plume. We report observations made along two front-normal and one front-tangential transects. The measurements reveal from the front, but in the region of strong vertical mix- that the near-surface convergence occurs in a narrow ing, and perhaps overturning, there are strong horizontal region of less than 5-m width near the surface foam variations in addition to the vertical gradients. line. The convergence, or strain rate, is of order 0.1 sϪ1. The vertical velocity in the ambient ¯uid (x Ͻ 0) and Direct observations of the vertical velocity obtained below the pycnocline (z ϽϪD) is predicted by Garvine from TOAD's ADCP are consistent with the estimates (1974a) to be independent of z since the lower layer is obtained using a simple continuity argument and the assumed to be in®nitely deep. The vertical pro®le of the convergence estimated from the SCUD data. Our esti- vertical velocity at the front, w(x ϭ 0), observed by mate is an order of magnitude larger than the Garvine TOAD is shown in Fig. 11 and suggests that the mag- and Monk (1974) estimates. We argue that these were nitude of w decreases toward the bottom. This com- biased because the horizontal scales were underre- parison reveals an important consequence of the neglect solved. of the ®nite depth of the lower layer and the kinematic It is interesting to note that even though the horizontal bottom boundary condition. scale is small, estimates of the magnitude of the con- The model-predicted maximum magnitude of w oc- vective acceleration terms in the vertical momentum curs at the front and can be computed using Eq. (6) and equation are an order of magnitude smaller than the the parameters listed in Table 1 to be Ϫ0.58 m sϪ1. Note vertical gradient in the dynamic pressure. This suggests that this is much larger that the Garvine estimate, prin- cipally because of the increased frontal slope. It is at that a hydrostatic model that resolves scales of order 1 least three times larger than that observed by TOAD. m could adequately represent the dynamics of these These observations are not inconsistent with the model, fronts. however, because the distribution of w is near-singular The Garvine (1974a) model is evaluated with the new at the front and could not possibly be resolved in our observations presented in section 4. Comparison of observations. This is demonstrated in Fig. 15, which model predictions and data show that though the layer shows the model predicted w at z ϭϪ4.5 m as a function depth dependence on distance from the front is quali- of across-front distance by the smooth curve. Vertical tatively correct, the internal structure of the density and variations under the plume at this level are predicted to velocity ®elds within 20 m of the front are not properly be very weak. If this pattern did exist and the instrument reproduced. We argue that the model is inadequate in used to measure it averaged in 5-m intervals, the ob- this region because of the assumptions about the vertical servations would reveal something like the dashed his- structure of the ®elds that are required to yield a trac- togram shown in Fig. 15. This spatially averaged pre- table model. diction is clearly much more consistent with the magnitude of the 5-m bin averaged vertical velocity obtained Acknowledgments. J. O'Donnell was supported by the by TOAD in the layer Ϫ4.75 m Ͻ z ϽϪ3.75 m, rep- State of Connecticut Department of Environmental Pro- resented by the solid lines in Fig. 15. The across-front tection through a grant from the Long Island Sound length scale for the decay of the observed magnitude Research Fund and by the University of Connecticut. (10 m) is also consistent with the model. We conclude, Marmorino and Trump were supported by the Of®ce of therefore, that though the vertical structure of the ver- Naval Research through the High Resolution Remote tical velocity below the front is not reproduced in the Sensing Accelerated Research Initiative. We are grateful model, the magnitude of the vertical velocity and the to Dave Andrews, David Cohen, Larry Burch, Red across-front length scale are adequately described. Banker, and Rick Morton who provided invaluable help Though we have shown that the structure of the Con- at sea. Rich Garvine and Kay Howard-Strobel carefully

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