On the spatial scales of a river plume

Authors


Abstract

[1] We report observations of the structure of the front that surrounds the plume of the Connecticut River in Long Island Sound (LIS). Salinity, temperature, and velocity in the near-surface waters were measured by both towed and ship-mounted sensors and an autonomous underwater vehicle. We find that the plume front extends south from the mouth of the river, normal to the direction of the tidal flow in LIS and then curves to the east to parallel the tidal current. The layer depth at the front and the cross-front jumps in salinity and near-surface velocity all tend to decrease as distance from the source increases. This is qualitatively consistent with the prediction of layer models. In the across-front direction, the plume layer depth increases from zero to the asymptotic value within a few times the plume depth (∼5 m). Vertical motion is generated in this zone, and there is evidence of overturning. Farther from the front, the high-frequency salinity standard deviation decays exponentially with a length scale of 30 m. Assuming that the salinity fluctuations are a consequence of turbulence, we find that the rate of turbulent kinetic energy dissipation decreases exponentially in the across-front direction with a decay scale LG ≈ 15 m. Estimates based on AUV-mounted shear probes are consistent with this estimate. We present an explanation of the physics that determines LG and provide a simple formula to guide the choice of resolution in models that are designed to resolve the frontal structure.

1. Introduction

[2] Since freshwater runoff transports particulates and dissolved material from land to estuaries and the coastal ocean, a quantitative understanding of the mechanisms of mixing and dispersion of this effluent is essential to improving our ability to predict and assess the consequences of human activity in the coastal ocean. Observations have made it clear that, during periods of high discharge, many rivers form large plumes of brackish water on the adjacent inner continental shelf that are frequently bounded by fronts. Examples are described by Garvine [1974], Stronach [1977], Ingram [1981], Freeman [1982], Lewis [1984], Luketina and Imberger [1987], Geyer et al. [1998] and Hickey et al. [1998]. A review of the earlier observations is given by O'Donnell [1993]. It is clear that the horizontal scales of variation at the fronts of river plumes can be as small as a few meters and that the density change can exceed 10 σT [see O'Donnell, 1997; O'Donnell et al., 1998; Trump and Marmorino, 2002, 2003]. Though three dimensional primitive equation models are now being widely employed to simulate the exchange between rivers and the ocean, as yet there have been none that resolve these small scales. The efficient design of models that are capable of effectively predicting the dispersion of terrestrial runoff in the coastal ocean requires that we establish the scales that must be resolved in the frontal boundaries and the processes that control the rate of vertical mixing.

[3] Recent technical advances in navigation and current measurement now allow a more detailed examination of the structure of plumes and plume fronts at the important spatial scales as shown by O'Donnell [1997], O'Donnell et al. [1998] and Trump and Marmorino [2002, 2003]. Here we describe the along-front variation of the pycnocline depth and the near-surface salinity and velocity on either side of the front. We also present the first quantitative estimates of the width of the frontal region in which mixing occurs and present estimates of the variation of the turbulent kinetic energy dissipation rate, ɛ, within the frontal zone.

2. Frontal Structure and Plume Theories

[4] Garvine [1974] developed a two dimensional (vertical and horizontal) model of the structure of the density and flow field in small-scale fronts. In this model “small” referred to the ratio of the horizontal length scale to the internal deformation radius, and justified the neglect of the Coriolis acceleration. Garvine assumed the dynamic balance was between the advection of momentum, the baroclinic pressure gradient and vertical eddy viscosity. He then prescribed the density field and the spatial structure of vertical mixing and friction across the base of the buoyant layer and predicted the vertical and horizontal variation in the velocity field. The magnitude of vertical mixing and friction was assumed to decay exponentially with distance from the front with a length scale, LG, that was unknown. The model allowed an exploration of the influence of LG on the structure of the frontal circulation and Garvine then estimated the value that allowed qualitative agreement between the predictions and the observations of Garvine and Monk [1974]. O'Donnell et al. [1998] obtained much higher resolution measurements of the density and velocity fields and demonstrated that LG had to be much smaller than Garvine [1974] reported. In this paper we present the first measurements that allow direct estimates of LG.

[5] The observations that fronts have much smaller spatial scale than plumes was exploited in the models of Garvine [1982] and O'Donnell [1988, 1990]. These models considered a plume to be a thin buoyant layer overlying a denser and much thicker ambient fluid layer. This allowed the dynamics of the buoyant layer to be simulated by the nonlinear long wave equations with weak frictional coupling at the interface. The lower layer, though in motion, was assumed to be unaffected by the upper layer. The frontal boundary was assumed to have a very small across-front scale (compared to that of horizontal variations in the plume) and modeled as a discrete line surrounding the plume layer. Exchange of mass and momentum was assumed to be significant in the frontal zone and weak elsewhere. For the special case of a straight linear front with no along-front velocity component, Garvine [1981] developed algebraic relationships between the layer thickness and velocity at the front and the rate of translation of the front relative to the ambient fluid. This approach is analogous to the use of shock patching in compressible gas dynamics. Garvine's frontal jump conditions, (the analog of the Rankin-Hugoniot shock conditions) included two parameters chosen with guidance from laboratory observations. Mathematically, the problem is to determine the position of the front and the solution to the long wave equations subject to specified inflow conditions and the frontal jump conditions.

[6] Garvine [1982] developed a technique to obtain a numerical solution when the discharge and ambient velocity were steady. The approach restricted the angle between the discharge and the ambient flow for which solutions could be obtained. An example of the predicted interface depth distribution is shown in Figure 1a. To reveal the structure most clearly, the layer depth is plotted upward. The maximum value occurs at the source where the layer depth and transport are prescribed. Elsewhere, the maximum occurs at the front and decreases in the offshore direction as the front bends toward the ambient flow vector. In contrast, the numerical technique employed by O'Donnell [1988, 1990] allowed unsteady behavior in both the source and ambient conditions but required cylindrical symmetry near the discharge. An example solution for the expansion of a plume and the evolution of the layer depth structure with a steady discharge and cross flow and no interfacial exchange in the interior is shown in Figures 1b1e. These solutions show the plume spreading into the ambient flow and becoming asymmetric as the cross flow arrests the front on the upstream side (with respect to the cross flow) and accelerates it on the downstream side. Consequently, the plume layer becomes thicker on the upstream side and thinner on the downstream side.

Figure 1.

(a) A-three dimensional projection of the layer depth (plotted as a positive upward) predicted by the model of Garvine [1982] for a plume discharged from a channel into a steady cross flow. Note that the depth at the front decreases with distance from the source as the front bends toward the direction of the along-coast flow velocity vector. (b–e) The evolution of the interfacial depth and horizontal transport vectors in a spreading plume from a cylindrically symmetric source in a uniform cross flow predicted by the model of O’Donnell [1988]. The initial condition, t = 0.45, is shown in Figure 1b, and solutions computed at times t = 1.04, 2.00 and t = 3.74 are presented in Figures 1c–1e. Though the discharge geometry is quite different, the front expands into and across the ambient flow with the depth at the front decreasing in the along front direction with distance from the source.

[7] The interior structure of the plume layer thickness is quite different in Figures 1a and 1e with a shallow trough evident between the source and the front in the radial discharge example. This difference results from the different source geometries chosen to circumvent limitations imposed by the numerical solution techniques adopted by Garvine [1982] and O'Donnell [1988]. More importantly, the two models display common features that are not sensitive to the choice of frontal parameters or source conditions including: (1) the angle between the frontal boundary and the ambient flow velocity vector decreases with distance along the front, and (2) the depth of the interface at the front decreases with distance along-front from the source. In Figures 1b1e, the front is almost normal to the ambient velocity near the discharge and curves to become almost parallel to the ambient flow further from the source. It is clear that this feature is consistent with Garvine's [1974] observations of the Connecticut River plume structure. However, observations are inadequate to conclude whether the predicted along front depth variation is also valid.

[8] Both models of Garvine [1982] and O'Donnell [1988] imbedded the Garvine [1981] frontal conditions that assumed that the front was straight and the magnitude of interfacial mixing and friction was proportional to the front-normal component of the velocity of the underlying water relative to the front. The neglect of the vertical shear in the along-front velocity in these models requires the front to spread across the ambient flow more rapidly than it would if the shear in the along front velocity enhanced vertical mixing and friction. These approximations were justified since no laboratory or field observations were available to guide the development of a more appropriate parameterization. However, the prediction of the along-front variation remains untested.

3. Observations

[9] The structure of the Connecticut River plume front was examined on the morning of 27 April 2000 using instruments deployed from the R/V Connecticut. The winds were less than 5 m/s and the river discharge at the USGS station at Thompsonville, CT, was 1,192 m3s−1, i.e., close to the long-term average for April and more than twice the mean annual discharge. The observations took place on the latter half of the ebb tide in Long Island Sound when the work of Garvine [1974] suggests that the plume should be to the east of the river mouth.

[10] The velocity field and acoustic backscatter intensity were measured by an RD Instruments 1.2 MHz Broadband Acoustic Doppler current profiler (ADCP) mounted 0.7m below the surface on a vertical pipe attached to the side of the R/V Connecticut. The ship heading was acquired from a Trimble TANS Vector AGPS system at 10 Hz, filtered and decimated to 1 Hz. The ship position was acquired from a Trimble Differential Global Positioning System (DGPS). The ADCP water and ship velocity estimates were acquired at 1Hz and postprocessed to incorporate the AGPS heading data and correct for variations in the speed of sound, a less than 2% effect. The uncertainty of the ADCP velocity measurements were evaluated by comparing the ship velocity estimated using the ADCP bottom track velocity averaged in 20 s bins to that obtained from the DGPS positions at the beginning and end of the averaging interval. The root mean square difference in the estimates was 10 cm/s. This is consistent with the error expected from the navigation system when the ship is moving at approximately 1 m/s. The fundamental uncertainty in the relative horizontal velocity component estimates in 0.25 m vertical bins was 10 cm/s [RD Instruments, 1997].

[11] The pressure, salinity and temperature were measured at 1Hz by an Ocean Sensors OS200 mounted next to the ADCP transducers at 1 m below the surface on the port side of the vessel. The same variables were measured at 8 Hz by a Seabird 25 CTD mounted on a towed body (the BDF) and attached to a crane over the starboard side of the ship approximately 2 m below the surface and 5 m astern of the ADCP.

[12] The most relevant observations were acquired beginning at 10:30 EST when the tidal currents in LIS were near maximum ebb. At this time the river plume front was clearly delineated by a line of white foam (see Figure 2) which began at the southern end of the western breakwater at the river mouth. The photograph in Figure 2 was taken looking to the northwest and the front can be seen to trend southward from the breakwater and then curve to a more northeast-southwest alignment. The foam patch in the foreground is approximately 1 m in width, and the meanders in the front have a wavelength of approximately 10 m, in general agreement with the observations described by Trump and Marmorino [2002, 2003]. While sampling continuously, the R/V Connecticut steered a zig-zag track that crossed the front five times. Figure 3 shows a map of the coastline and bathymetry at the mouth of the Connecticut River with the ship track indicated by the thick gray line. The position of the ship when it crossed the front are shown by the plus symbols. Note that the tidal flow in LIS is to the east during the ebb which is to the right in Figure 3. This is not to be confused with the direction of the ambient cross flow assumed in the numerical solutions in Figures 1a and 1b1e. During the 1994 observation campaign described by O'Donnell et al. [1998] the Connecticut River discharge was approximately 1500 m3s−1 and the front was approximately 1 km to the west of the locations shown in Figure 3. Since it took almost an hour to complete the track the shape of the front in Figure 3 is not a synoptic view and no corrections have been applied to correct for the frontal velocity. The times that the ship crossed the front are listed in Table 1 with the transects numbered in order of increasing distance from the river mouth and not by time.

Figure 2.

Photograph of the river plume front at the mouth of the Connecticut River, taken on 27 April 2000, showing the front curving toward the western breakwater and short (∼10 m) along-front variations and foam patches in the center of small (∼1 m) cyclonic vortices.

Figure 3.

Ship track during sampling operations at the Connecticut River mouth on 27 April 2000. The dashed lines show bathymetric contours (m) and the location of the breakwaters at the mouth of the Connecticut River. The track of the R/V Connecticut is shown by the thick curving solid gray line. The locations where the ship crossed the foam line of the front is shown by the plus symbols. Times of the crossings are presented in Table 1. The orientation of the across- and along-front coordinate system used in the analysis is shown by the arrows. The short line between the “start” and “end” labels shows the transit of the turbulence measuring AUV.

Table 1. Times at Which the Ship Crossed the Front
SectionFront Crossing Time
109:53
210:17
309:46
409:42
509:38
609:33

[13] After the ship surveys were completed, a REMUS [von Alt et al., 1994] autonomous underwater vehicle (AUV) was deployed at the location labeled “Start” in Figure 3. The AUV then propelled itself at 1 m depth northeast at approximately 1 m/s along the track shown by the solid line using an array of four acoustic navigation beacons. While the AUV was being configured and readied for deployment, the front moved to the west and was oriented approximately north–south when the AUV crossed it. The bow of the AUV was instrumented with turbulence and fine structure sensors as described by Levine and Lueck [1999]. The instrument suite included two-axis small-scale velocity shear probes [Osborn and Crawford, 1982], ultra fast thermistors to measure small-scale temperature and vertical temperature gradient, and three orthogonal accelerometers for motion compensation. In addition, the REMUS vehicle measured the vertical gradient of horizontal velocity using an upward and downward looking 1200 kHz RDI ADCP, finescale temperature and salinity using a pair of FSI CTDs, and three-dimensional small-scale velocity using a Sontek Acoustic Doppler Velocimeter. The AUV-based instruments allowed the calculation of the horizontal distribution of the turbulent kinetic dissipation rate, horizontal velocity shear, and the fine-scale stratification following the approach described by Goodman et al. [2006]. A comprehensive discussion of the REMUS observations is provided by Levine et al. [2008]. In this report we only discuss the shear probe estimates of the distribution of the turbulent kinetic energy dissipation rate and compare them to the distribution inferred from the ship-mounted instruments.

[14] The six plots in Figure 4 show the variation of the salinity measured by the ship-mounted CTD at 0.7 m depth (thin lines) and, when available, the towed BDF (thick lines) as functions of the across-front distance. The stratified water of the river plume is on the right side of the plots and the higher-salinity, and less stratified, water of LIS is to the left. The location of the horizontal position origin in each section is the position recorded by the R/V Connecticut's navigation system at the time the ship mounted ADCP and CTD crossed the foam line. In Figures 4a and 4d the salinity jumps occur a few meters from the origin owing to small errors in recording the times the front was crossed and offsets between the position of the foam line and the salinity jump. At a survey speed of 2.5 m/s, a 2 second error in recording the crossing time results in an offset of 5 m.

Figure 4.

Salinity at 1m (labeled Su) and at the BDF depth (labeled SB), which we show in Figure 5. The distribution of the standard deviation of the salinity fluctuations measured by the BDF in 2-s time windows are shown by the lines labeled σB.

[15] To estimate and correct the horizontal offset of the ship-mounted and towed sensors we assume that the leading edge of the front is vertical and then compute the time lag between the salinity jumps in the two records. The BDF data is then offset to estimate the fields that would have been observed had the instruments been aligned in the vertical as in work by O'Donnell et al. [1998]. The spatial uncertainty introduced by this approach is to be a meter or two. Since the horizontal gradients are small, except in the immediate vicinity of the salinity jump, this error is insignificant.

[16] The central feature of the 0.7 m level salinity observations (labeled Su, in all six parts of Figure 4) is the abrupt decrease in salinity that occurs at x = 0 in all six transects. With the exception of section 2, Figure 4b, the abrupt decrease in salinity is followed by a slow rise to an intermediate value. The magnitude of the near surface salinity jump generally decreases in the offshore direction, i.e., from section 1 to 6.

[17] The salinity observations made by the BDF on sections 1, 3, 4 and 5 (labeled SB in Figures 4a, 4c, 4d, and 4e) show similar structure to the 0.7 m level measurements though the faster sampling rate reveals high wave number variability that appears to have large amplitude near the front and to decay toward the plume. The lines labeled σB in Figure 4 show the standard deviation of the BDF salinity in 2 s bins (16 samples) and demonstrate this point more clearly.

[18] An example of the ADCP horizontal velocity observations from section 2 is presented in Figure 5. To reduce the noise to 3 cm/s the observations at ∼1 Hz were averaged in 3 s time bins and 0.75 m vertical bins and are presented as functions of distance from the front in the local front-normal direction. The structure of the flow is very similar to that described by O'Donnell et al. [1998] with the across-front velocity in Figure 5 directed to the left near the surface and to the right (toward and under the plume) everywhere else. The mean-square shear, equation image, corrected for the noise bias, is approximately 0.15 s−2 at 2.25 m on sections 1 and 2.

Figure 5.

(a) Across-front and (b) along-front velocity components measured by the ship-mounted 1200-kHz ADCP on section 2 as a function of depth and across-front distance.

[19] Since the depth of the BDF is variable and the structure of the plume front changes in the along-front direction, further interpretation of these observations requires that the BDF location relative to plume structure be illustrated. It is well established theoretically and empirically [Seim, 1999] that the acoustic backscatter in the 1–103 kHz range is often dominated by salinity microstructure in estuarine waters. Deines [1999] outlined how ADCP measurements of backscatter signal strength can be corrected for losses due to absorption and beam spreading to obtain the vertical structure of backscatter intensity and this has been implemented to create the across-front distribution of backscatter from the ship-mounted ADCP shown in Figure 6. Prior work in at the Connecticut River plume front by O'Donnell et al. [1998] demonstrated the similarity of the structure of the acoustic backscatter distribution and the plume thickness observed by a rigid array of salinity sensors. In Figure 6a the track of the BDF (the solid black line) clearly goes through the high-backscatter region at the leading edge of the plume and then into the stratified layer. In section 2 the region of highest backscatter in the top 3 m (see Figure 6b) appears to be much wider than in section 1. Note that no BDF data was acquired on section 2. On sections 3 and 4 the BDF passed through the lower edge of the high-backscatter layer and the salinity observations in Figures 4c and 4d confirm that the LIS water was appreciably diluted by freshwater at the level of the BDF. In contrast, the salinity in Figures 4e and backscatter in Figure 6e agree that the BDF passed below the level of the plume on section 5. The 0.7 m salinity observations show that a very shallow, highly stratified plume layer was present at both sections 5 and 6 though the ADCP data and BDF measurements were too deep to resolve it.

Figure 6.

Acoustic backscatter (dB) at 1200 kHz measured by the ship-mounted ADCP on sections 1–6 as a function of depth and across-front distance.

4. Analysis

[20] The along front variation of the salinity in the plume is presented using measurements averaged in 2.5 m horizontal bins on either side of the front at both the level of the CTD and the BDF. Figure 7 displays the variation of these properties with along-front distance from the breakwater at the western side to the river mouth where the plume front first appears well-organized. Comparison of the dashed lines shows the salinity difference across the front at the 0.7 m level with the ‘O’ markers representing the salinity of the LIS water and the plus symbols showing the lower salinity of the plume water. The variations in the LIS water are relatively weak. In contrast, the near surface salinity of the plume increases offshore at a rate of approximately 5 km−1. At 1600 m from the breakwater the salinity jump across the front near the surface is only 25% of that near the breakwater but remains substantial with an across front gradient of at least 2 m−1.

Figure 7.

Along-front variation of the salinity at the 0.7 m (dashed lines) level average in 5-m bins on the plume side (plus symbols) and LIS side (circles) of the front. The solid lines show the averaged salinities at the BDF level in the plume side (squares) and LIS side (diamonds) of the front.

[21] The salinity measurements at the level of the BDF (2.5–2.8 m) are shown by the solid lines in Figure 7 with the squares indicating the salinity on the plume side of the front and the diamonds showing the salinity of the LIS water. At this level there is little offshore variation in the salinity of the LIS water, as is the case near the surface. The plume water salinity does increase with distance along the front at a rate comparable to that of the surface water so that the vertical gradient in salinity does not vary substantially. At section 5 (∼1300 m from the breakwater) the salinity difference across the front at the level of the BDF is very small since, as the acoustic backscatter distribution in Figure 6e indicates, the BDF passed underneath the plume layer. Note that though the depth of the BDF fluctuated in the range 2.5 to 2.8 m during the survey, the changes in salinity resulting from depth changes are not significant in this discussion. Comparison of the salinity measurements at 0.7 and 2.5 m on the LIS side of the front (solid line with diamonds and the dashed line with circles) demonstrates there is significant stratification near surface in the LIS water. The magnitude, ∼0.5/m, would be regarded as strong stratification in most environments but is small compared to that observed in the river plume (compare the lines with square and plus symbols) which is an order of magnitude larger.

[22] It has been well established by theoretical and experimental studies [e.g., Rohr et al., 1988; Smyth and Moum, 2000], that the gradient Richardson Number, Ri = N2/S2, where the buoyancy frequency equation image controls the rate of growth or decay of turbulence in stratified shear flows. The velocity and density observations we have acquired allow us to display the across-front distribution of Ri using the estimate of the shear squared discussed above, and the density gradient estimated in the same way as the salinity gradient, i.e., equation image. Figure 8 shows the results for sections 1 (plus symbol), 3 (circle), 4 (triangle) and 5 (asterisk). Though there is considerable scatter, it is clear that for x < 0, Ri is generally less than less than 0.1. In contrast, for observations made inside the plume (x > 0), Ri increases to values in excess of 0.3. The transition appears to occur in the interval within 20 m of the front (0 < x ≤ 20).

Figure 8.

Across-front distribution of the bulk shear Richardson number on sections; 1, plus symbol; 3, circle; 4, triangle; and 5, asterisk. The 0.25 level is shown by the thick solid line.

[23] It is clear in Figure 4 that the standard deviations of the BDF salinity measurements are very high close to the front and get smaller with distance into the plume. To make preliminary estimates of the across-front scale of vertical mixing rates we separated the 8 Hz salinity observations from the BDF into a high-frequency component s′ and a low-frequency signal, equation image, using a simple box-car filter of length of 2 s (16 samples). We then linear interpolated the 1 Hz, 0.7 m level measurements, equation image, to 8 Hz and computed the low-frequency vertical salinity gradient equation image. Assuming that the high-frequency salinity variations s′ are the result of vertical particle excursions in the gradient, equation image, then the displacement required is equation image. Defining mean square displacement scale LE2 = 〈l2〉, where the averaging is over 5 m wide bins in the across front direction, then LE is a convenient way to compare the distribution of the high-frequency variance in salinity between sections since it compensates for along front changes in the vertical salinity gradient. If we further assume that the fluctuations in salinity are a consequence of turbulence (and not internal waves), then LE can be interpreted as the Ellison [1957] overturning scale. Laboratory experiments [Rohr et al., 1984, 1988] have demonstrated that for Ri > Ricr ∼ 0.25, LE is proportional to LO, the Ozmidov [1965] scale, i.e., LE = aLo = a(ɛ/N3)1/2, where ɛ is the rate of dissipation of turbulent kinetic energy by viscosity and the proportionality constant a = 1.5. Rearranging this definition allows us to estimate the dissipation rate using ɛ = N3LE2/a2 . Note that this relationship is valid in the region of the plume front where the Richardson number is supercritical which, based on Figure 8, is in the interval x > 0.

[24] The random errors in the estimates of LE and ɛ arise from the errors in the measurement of salinity and temperature and from the uncertainty in the estimate of a. Lorke and Wűest's [2002] discussion of the variability of the ratio of the Thorpe overturning scale to LO suggest that it may vary by a factor of two and it seems reasonable to assume this may also apply to a. However, since we are primarily interested in the spatial scale of variation within the plume in this paper, we are less concerned about the accuracy of the absolute value than the resolution threshold.

[25] The SBE25 has salinity and temperature uncertainties (standard deviations) of σS = 0.003 and σT = 0.001 in the range of values observed in the study area [see Sea-Bird Electronics, 2007]. Assuming that equation image, the uncertainty in the vertical gradient of the bin averaged salinity, equation image, is dominated by the salinity uncertainty and that there are M (generally ∼30) independent salinity measurement in each estimate of the average gradient, then equation image, where Δz is the vertical separation of the sensors. For the observations reported in this paper equation image. The fractional uncertainty in LE2 can be expressed as the sum of the squares of the relative errors in the two factors in its definition and written as equation image. This can be shown to simplify to equation image where the second term on the right represents the error associated with the estimation of the vertical gradient. Since turbulent eddies are confined by the presence of the free surface then equation image and, since the second term decreases with 1/M , it can be neglected. The first term is simply the apparent displacement scale that results from instrument noise. Taking equation image as a representative value of the vertical salinity gradient squared in the plume then we find σL2 = 3 × 10−5 m2 or σL = 5 mm. Since the physical size of the conductivity-temperature sensors are a factor of two larger, we take σL2 = 10−4 m2 as a more appropriate estimate of the noise floor for LE. A representative value of the buoyancy frequency in the plume is N2 ≈ 2 × 10−2 s−2 and so the minimum dissipation rate that can be observed is 2 × 10−7 W/m3. Though this would normally be regarded as large, it is small compared to the values in the plume front. Recall that the approach is inappropriate in the LIS water since the Richardson Number is not supercritical there.

[26] As with all measures of turbulence, there is substantial variability in the estimates of LE and ɛ within across-front averaging bins and this variability dwarfs the effect of instrument noise. Since the probability density functions of l2 is not normal, we use the median of the distribution to estimate 〈l2〉 = LE2 rather than the mean, and estimate the 68% confidence interval by the bootstrap approach (see Efron and Gong [1983] or Willmott et al. [1985]).

[27] Figure 9 (top) shows the across-front distribution of LE for sections 1 (plus sign), 3 (circle), 4 (triangle), and 5 (asterisk). It is evident from this graph that LE estimates are distributed asymmetrically about the front (x = 0) with small values (LE ≤ 0.05 m) in the LIS water, maxima (LE ≈ 1 m) close to the front, and values in the plume rapidly decreasing with distance from the front. The data from section 5 are anomalous in that there is no peak in LE at the front. However, this is consistent with our interpretation of Figures 4 and 6 which show that the offshore reduction in the plume layer thickness had caused the BDF to pass below the level of the plume during section 5.

Figure 9.

(top) The across-front distribution of the square root of the squared Ellison scale, LE, averaged in 5-m across-front bins. Sections 1, 3, 4, and 5 are represented using the same symbols as Figure 8. (bottom) To reveal the across-front and along-front variation of salinity fluctuations the dependence of LE on the across-front distance from the front is shown on a logarithmic axis. The thick solid line illustrates an exponential decay with a decay length scale of 30 m.

[28] To reveal the across-front variation in LE on the plume side (x > 0) of the front more clearly, Figure 9 (bottom) shows LE observed on sections 1, 3, 4 and 5 in a semilog plot. Note that all the values exceed the estimated noise level. The straight dashed line represents an exponential decay with distance from the front with a decay scale of 30 m. Clearly, the observations in sections 1, 3 and 4 show that the Ellison scale decays exponentially with decay scale of approximately 30 m.

[29] Figure 10 shows the distribution of the frontal zone dissipation rate computed using equation image for sections 1, 3, 4 and 5. The linear regression trends for log LEsections 1, 3 and 4 using estimates in the interval 10 ≤ x ≤ 100 are also shown to assist comparison between observations and to quantitatively estimate the decay length scale. The thin dotted lines show ɛ = 16νN2, the dissipation rate required to sustain active overturning in a stratified shear flow with Ri > Ricr as reported by Itsweire et al. [1986] and Rohr et al. [1988]. Close to the front dissipation rates reach 10−3 W/kg and decrease exponentially to 10−6 W/kg 100 m from the front. This is approximately equivalent to ɛ(x) = ɛ0 exp(−x/LG) with LG = 15 m which is illustrated in Figure 10 by the thick dashed line. The length scales derived from regression through the data obtained on each section are listed in Table 2 and the trends are shown by the solid lines in Figure 10. Though dissipation rate estimates suggest that the maximum decreases with distance from the source and that LG increases, these differences are not statistically significant and additional observations are required to address these issues.

Figure 10.

Across-front distribution of the turbulent kinetic energy dissipation rate for sections 1, 3, 4, and 5. The symbol code is the same as used in Figure 8. The thick solid lines illustrate the best-fit exponential decay of the dissipation rate in the across-front direction for sections 1, 3, and 4. The dotted lines show the Rohr et al. [1988] estimate of the level of dissipation at which mixing ceases.

Table 2. Estimates for the Width of the Zone of Active Mixing
 Section
1345Mean
LG (m)11.416.722.6 16.9
LI (m)23.526.738.626.928.9

[30] Though the measurements by the REMUS AUV were acquired more than an hour after the ship measurements and, as is clear in Figure 3, approximately 300 m west of the frontal crossing on section 3, they provide an independent and more precise estimate of the dissipation rate distribution. Figure 11 displays the dissipation rate estimate assuming isotropy at viscous dissipation scales. These were computed from micro-scale velocity gradients measured by the shear probes following the processing approach detailed by Goodman et al. [2006] and averaged in 10 m across-front bins. A maximum value of ɛ = 7 × 10−5 W kg−1 occurs near the front and ɛ decreases with distance from the front. The maxima is somewhat lower than those shown in Figure 10 (though it is still very large). This difference is partially due to the larger spatial averaging window employed. However, the across-front decay rate is entirely consistent with the ship-based measurements. This is demonstrated by comparison of the measurements in Figure 11 with the straight dashed line which shows an ɛ(x) ∝ exp (−x/LG) with a length scale LG = 15 m.

Figure 11.

Across-front distribution of the turbulent kinetic energy dissipation rate computed from the shear probe measurements by the REMUS AUV.

5. Summary and Discussion

[31] Though river plumes like that of the Connecticut have been reported in many locations [e.g., Wright and Coleman, 1971; Stronach, 1977; Ingram, 1981; Freeman, 1982; Lewis, 1984; Luketina and Imberger, 1987; Geyer et al., 1998; Hickey et al., 1998] there have been few systematic observations of the along front variation of the plume characteristics. We believe this report is the first quasi-synoptic, high-resolution view of the along-front variation in plume layer thickness and salinity. We find that the plume layer at the front thins in the offshore direction while the salinity increases. At 1 km from the source, the across-front salinity jump is half of that at the source. This behavior is largely consistent with the predictions of the models of Garvine [1982] and O'Donnell [1988, 1990]. The mechanisms that control the relative importance of the vertical exchange with the deeper water and the horizontal exchange with the plume to the rate of the reduction of the along-front freshwater flux remain unresolved. With the data available we are unable to adequately resolve the terms in the salt budget in the frontal zone. An observation campaign with more vertical resolution of the salinity field together with ADCP data that resolves the near surface advection flux toward the front is required.

[32] Establishing the mechanisms that control the width of river plume fronts is likely to be critical to the accurate prediction of the dispersion of terrestrial effluent in the coastal ocean since a significant amount of mixing occurs in its vicinity. A scale estimate can be developed by consideration of a simple conceptual gravity current model and laboratory experiments. There is considerable literature in which this approach has been used to model the spreading of buoyant fluids and much of it is coherently summarized at an introductory level by Simpson [1987]. The analytic work of Benjamin [1968] was extended in a semi-empirical analysis and a series of laboratory experiments by Britter and Simpson [1978] and Simpson and Britter [1979] to model the spreading of negatively buoyant fluids. Subsequently, Simpson and Nunes [1981] and Garvine [1981] based their interpretation of the dynamics of a small-scale river plume fronts on this literature. Underlying these models is the idea that the Kelvin-Helmholtz instabilities at the leading edge of the gravity current lead to the generation of three-dimensional turbulence in the stratified shear layer between the buoyant and ambient fluids. In both the analysis of Britter and Simpson [1978] and the model of Garvine [1974] the magnitude and spatial rate of decay of mixing between the layers is prescribed in order to match observed density field structure. Our observations that the magnitude of ɛ and, by extension, the vertical eddy diffusivity, decays across the frontal zone confirm that their assumptions were well founded.

[33] Rohr et al. [1988] and Itsweire et al. [1993] performed careful and extensive lab experiments on the growth and decay of grid generated turbulence in stratified shear flows. One of the important results was the demonstration that in experiments with gradient Richardson number, Ri > Ricr = 0.25, turbulence and vertical mixing was suppressed. Further, for values of the dissipation rate, ɛ < 16vN2, where N is the buoyancy frequency and v is the molecular viscosity, the vertical turbulent buoyancy flux was effectively zero. In experiments with a mean flow in the shear layer, U, and Ri > Ricr, Itsweire et al. [1993] concluded that the vertical buoyancy flux went to zero within 5 buoyancy periods of passing through the grid, or equivalently after a distance LI = 5U/N from the generation location.

[34] If we accept that lab and field observations of the decay of turbulence should be in agreement once the effects of stratification begin to dominate and then assume, on the basis of the flow visualizations of gravity currents of Simpson and Britter [1979], that any coherent structures at the leading edge of the front break up into turbulence within a few buoyant layer depths from the leading edge, then the scale LI should provide a guide to the width of the active mixing zone in plume fronts with Ri > Ricr. Note, however, that the flow field in the Connecticut River is not a two dimensional flow. There is a significant along-front velocity component that has shear in both the horizontal and vertical directions. Visual observations (see photograph in Figure 2) and the analysis of ADCP observations in the same area by Trump and Marmorino [2002, 2003] strongly suggest that coherent vortices with vertical vorticity components of magnitude ∼0.1 s−1 are present at the frontal boundary. Such structures likely enhance the production of turbulent kinetic energy and modify the distribution of the dissipation rate even where stratification dominates.

[35] Computed values for LI using the data from Connecticut River plume sections in which N can be estimated (1, 3, 4, and 5) are presented in Table 2. Estimated LI are approximately 1.5–2 times larger than LG, the decay scale for ɛ and shown in Figure 10. Since the vertical gradients were only minimally resolved by our measurements the estimates of LE2 and N2 are likely to be underestimated. Despite the weakness of the instrumentation, it is clear that the spatial decay scale, LG, is the same order of magnitude as LI and, therefore, we conclude that LI should provide a useful guide for the scale of river plume fronts.

[36] An analysis of the frontal zone mechanical energy budget would be a useful check on the magnitudes of the dissipation rates we estimate but, unfortunately, the near surface flow toward the front is unresolved causing the budget to be too uncertain to provide a constraint on the dissipation rate. Only two previous observational programs in similar environments have been reported with which we can compare our estimates. Note that the spatial resolution of those was significantly less than our measurements. Luketina and Imberger [1989] made the first estimates using a moored profiler and found a maximum value of 10−6 W/kg near a thermal plume front. More recently Orton and Jay [2005] presented estimates of the variation of ɛ with distance from the Columbia River plume front using Thorpe sorting [see Thorpe, 1977; Galbraith and Kelley, 1996] of measurements by an undulating towed CTD. They reported that ɛ varied from 10−3 W/kg at 100 m from the front to 10−6 W/kg at 1000 m. This is equivalent to a spatial decay scale of 130 m. Using the reported frontal propagation speed uf = 0.60 m/s as the mean velocity in the shear layer and a buoyancy frequency value N = 0.05 based on the salinity distribution, we obtain the estimate LI = 5uf/N = 60 m for the scale of the frontal zone width. Again, this is approximately a factor of 2 less than the observed spatial decay rate but the correct order of magnitude.

[37] Though more detailed measurements of both the velocity field and density gradients need to be obtained to further evaluate the approach to estimating dissipation rate, and more consideration needs to be given to the role of the shear in the along front velocity gradients, the scale estimate for the width of the region of active mixing presented here can provide guidance to both observation campaigns and numerical model formulations to determine the scale of variations that need to be resolved in studies of river plumes.

Acknowledgments

[38] This work was supported by the National Science Foundation through grant 0096551 and by the University of Connecticut. We thank the reviewers of the manuscript and acknowledge that their criticism led to a clearer presentation of our work. J. O'Donnell is also grateful to the faculty and staff of the School of Ocean Sciences, University of Wales, Bangor, and the people of Ynys Môn for their advice and hospitality during the drafting of this manuscript.

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