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Sedimentation from buoyant fine-grained suspensions
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Continental Shelf Research 24 (2004) 1129–1142
Sedimentation from buoyant fine-grained suspensions Wayne W. McCool, Jeffrey D. Parsons* School of Oceanography, University of Washington, Box 357940, Seattle, WA 98195-7940, USA Received 27 March 2003; received in revised form 10 October 2003; accepted 12 March 2004
Abstract Laboratory experiments were performed to observe the sedimentation of natural sediment in buoyant turbulent suspensions. A series of experiments were conducted in a flume modified to investigate sedimentation from a steady, stratified shear layer. Ambient salinity stratification in the lower fluid allowed the upper layer to remain buoyant, while turbulence induced by free shear in the water column produced instabilities between the two fluids. These experiments showed that convective plumes dominated sedimentation. These convective plumes had vortex tips and vertical velocities of 1–2 cm/s. The velocities observed are two orders of magnitude larger than those predicted by Stokes settling of the constituent particles. Surface plume concentrations as low as 380 mg/l were documented to support robust mixing-induced convective sedimentation. At high concentrations (>6000 mg/l), the experiments produced a divergent plume with a considerable amount of the sediment-laden fluid being diverted along the bottom of the flume. Our observed vertical sediment fluxes demonstrated a 50% increase as compared to previous studies of double-diffusive sedimentation. A simple scaling analysis using the dissipation rate of turbulent energy and the surface plume sediment concentration was able to collapse the experimental data and indicated a positive correlation between turbulent energy and sedimentation. The empirical scaling relationship accurately predicted effective settling velocities measured on the Eel River margin in 1997–1998. The quality of the agreement between the laboratory and field measurements provides strong evidence that sedimentation by mixing-induced convection may be the dominant mode of sediment removal from energetic, highly concentrated, buoyant river plumes. r 2004 Elsevier Ltd. All rights reserved. Keywords: Eel River; River plume; Shelf sedimentation; Convective sedimentation; Cross-shelf transport
1. Introduction Many natural processes contribute to the fate of sedimentary particles on continental shelves and are essential in understanding the fate of terrestrial *Corresponding author. Tel.: +1-206-221-6627; fax: +1206-543-6073. E-mail address: [email protected] (J.D. Parsons).
carbon and constraining sediment budgets (Nittrouer and Kravitz, 1996). Milliman and Syvitski (1992) estimated that approximately 10 billion metric tons of sediment are transported annually by rivers to continental shelves. Small mountainous watersheds supply a large fraction of this global sediment supply. Due to their small drainage basins and intense precipitation events, these watersheds tend to have episodic floods which deliver pulses of sediment to the ocean (Hill et al., 2000).
0278-4343/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.csr.2004.03.009
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Periodic flooding events can produce hypopycnal river plumes that remain at the surface and transport fine material tens of kilometers from the river mouth. The fate of sediment within a buoyant river plume has been attributed to ambient ocean conditions, freshwater discharge, sediment load, and settling velocity of the sediment (Morehead and Syvitski, 1999; Hill et al., 2000). All of these factors contribute to the vertical flux of sediment, which controls sediment dispersal on continental margins. Understanding the dynamics of solid material involved in these intense oceanicflood events remains elusive due to the unpredictable nature of these environments (Wheatcroft et al., 1997). Settling of particles from buoyant river plumes will determine the initial transport of sediment to the bottom boundary layer prior to advection or diffusion by near-bed processes (Geyer et al., 2000). The development of sedimentation models for buoyant river plumes has been hindered by incomplete understanding of the processes that remove sediment from the base of the surface plumes. In some plume models, empirical relationships are used for sediment removal rates (Morehead and Syvitski, 1999), so that the models account for total removal, without capturing physical processes. Stokes settling of disaggregated constituent grains cannot account for the sediment flux out of most river plumes. Increased removal rates of fine-grained sediment have traditionally been linked to flocculation (Syvitski and Murray, 1981; Hill and Nowell, 1995; Hill et al., 2000). Flocculation of particles can increase effective settling velocities and is generally thought to account for the large sediment removal rates on river margins with buoyant plumes (Hill et al., 2000). The use of Stokes settling velocities for flocs or discrete particles is complicated by two problems. First, if the water column is stratified by salinity gradients (e.g., the Eel River in flood: Hill et al., 2000; Geyer et al., 2000), the ambient stratification can hinder the fall speed of a particle. As a result, the sediment will concentrate along the halocline, until the region becomes gravitationally unstable (Parsons et al., 2001). Recent laboratory studies
have suggested that convective motions associated with gravitational instability could contribute to the removal of sediment from surface plumes (Green, 1987; Chen, 1997; Hoyal et al., 1999; Parsons and Garcia, 2000). These earlier studies focused on a collection of particles above a pycnocline in a stable, stratified water column with temperature or salinity as the stabilizing property of the fluid. Inhomogeneities in the density field can eventually evolve into convective cells, initiating what has been called convective sedimentation (CS). A second problem in estimating the settling velocity of particles and flocs is the complex interaction between particles and turbulence. A turbulent flow field causes perturbations to the straight trajectory of a particle falling under gravity. Turbulence has been found to increase the effective settling speed of particles by 10–50% (Maxey and Corrsin, 1986; Maxey, 1987; Wang and Maxey, 1993; Aliseda et al., 2002). Assuming particle mixing by turbulence is a homogeneous process in which particles are uniformly dispersed without any bias can be grossly in error (Maxey, 1987; Aliseda et al., 2002). Parsons et al. (2001) and Maxworthy (1999) both found that turbulent mixing between a buoyant gravity current and the ambient denser fluid could produce non-uniform sedimentation associated with gravitational instability. The resulting convective plumes quickly remove sediment from the surface layer and deposit the sediment on the bottom. Hereafter, we will refer to these plumes as mixing-induced CS. These experiments indicate that mixing-induced CS dominates in the presence of strong stratification and intense mixing for laboratory-scale flows, but only for large sediment concentrations (generally o10,000 mg/l; Maxworthy, 1999). Unfortunately, these earlier studies did not measure turbulence properties or the vertical flux of sediment associated with convection. Therefore, they had difficulty speculating about the importance of these processes in environmental flows. We have performed laboratory experiments of a fresh, sediment-laden flow over ambient saltwater, which simulates a steady, buoyant river plume during flood. During these experiments, we
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a light-refraction salinometer. The system was initially stable (i.e., no sediment is transported directly into the basin). Maximum velocities in the surface layer varied between 7 and 15 cm/s. The velocity profiles indicated that shear was approximately constant throughout the water column (Fig. 2). A small return flow was observed consistently near the bottom of the basin. The return flow caused a slight counterclockwise circulation within the basin. Cored sediment with a median grain size of 20– 30 mm was used in all experiments reported in Table 1. The cored sediment used during this study was derived from samples taken from the Eel Canyon in November 2001. No dispersing agent was used on the supplied sediment, but turbulence supplied by the pump might have disaggregated flocs. By varying the pump speed, a wide range of sediment concentrations was possible. To perform an experiment, the sediment was mixed in a slurry head tank and pumped into the flume upstream of the flow confinement section and salt basin. The supply slurry was made by combining sediment and freshwater for the first 10 experiments and saltwater (5 ppt) for the last ten experiments. The basin salinity was consistently 15 ppt for the first ten experiments and changed to 20 ppt for the final 10 to maintain a consistent stratification throughout all experiments. The mixed-layer supporting the sediment-laden flow
measured sediment load, turbulent mixing, ambient stratification, and the net flux of sediment out of the buoyant flow. The goal of our study was to better understand sediment removal rates through stratification in the presence of shear-induced turbulence and the complex interaction between sedimentation and turbulence. Measurements from the Eel River margin were used to test the results of our experiments and analysis.
2. Methods 2.1. Experimental procedure Experiments were performed in the facility shown in Fig. 1. Water is circulated via motordriven propellers around the racetrack flume in a clockwise direction. Five flow straighteners are placed in both of the curved sides of the flume to reduce secondary circulation and a grid with 0.32cm straws is placed after the straighteners to homogenize the flow. Plexiglas placed in the flume confined the freshwater and sediment flow to 7 cm on the surface. A saltwater basin 90 cm long, 21 cm deep and 36 cm wide was formed in the lee of the Plexiglas constriction. The sediment-laden freshwater flowed over the salt basin, which contained a salinity of 15 ppt. All of the experiments were isothermal. The initial salinity was measured using
400 cm flow
Flume
propellers
Basin Supply Conductivity probe Impellor speedometer diffuser
MicroADV OBS (x2)
30 cm
Flume (fresh, mixed) flow barrier confines saline basin
mixed layer Basin (saline) 90 cm UFOB-7 (x2)
Supply
flow flow confinement 84 cm
honeycomb & flow straighteners
Fig. 1. Upper schematic shows the experimental facility in plan view. The lower schematic shows the side view of the test section. The flow was confined downstream of the sediment addition point.
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Height above basin bottom (cm)
25
20
15
Plume velocityU 15.0 cm/s 13.0 cm/s 11.3 cm/s 9.4 cm/s
10
5
0 20
15
10 5 Velocity (cm/s)
0
-5
Fig. 2. Profiles of mean velocity measured at 1 cm intervals within the saline basin. Profiles represent the four velocities used in the experiments to vary the turbulent mixing at the interface (B20 cm height) between the saltwater and the overlying lighter sediment-laden freshwater. The range between 25 and 18 cm above the bed shows a nearly linear free shear zone.
had a variable depth depending on the velocity of the surface layer. Faster surface layers had thicker mixed layers, while slower surface layers mixed less and had smaller mixed layers. Video and digital photography were used to visualize the vertical transport of sediment. Under normal room lighting, sedimentation was difficult to record, so the laboratory was completely darkened and a light sheet was reflected through the salt basin from below in the middle of the basin approximately 4 cm from the wall. All photos were taken in the initial 3 min of each experiment, as the water was clearest during this time. Later pictures show the same form of sedimentation, but were not as clear due to increased ambient turbidity in the saltwater basin. 2.2. Measurement of sediment concentration and vertical flux The instrumentation in the flume consisted of a high-speed conductivity probe (to measure salinity), two optical backscatter instruments (OBS),
two fiber-optic backscatter instruments (UFOB-7), and a current meter. In order to allow the flow to become steady, the instrumentation began sampling 2 min after the propellers initiated flow in the flume. The backscatter devices (i.e., all of the OBS and UFOB-7 instruments) measured sediment concentration at 20, 10, 8, and 4 cm above the bottom of the basin. The UFOB-7 has a fixed ellipsoid sampling volume of approximately 1 cm3, which is defined by the intersection of the offset transmit and receive beams. The sampling volume has a 1-cm vertical length. The OBS does not have fixed sampling volume, so the vertical length can be variable (approximately 0.5–5.0 cm). However, for the concentrations used in this study (300– 6000 mg/l), a vertical sampling volume length of 1 cm was appropriate for all experiments. At roughly 1000 mg/l, the UFOB-7 signal saturates. Therefore, any concentrations measured by the UFOB-7 exceeding 1000 mg/l have been excluded in this study. The vertical sediment flux through a horizontal plane in the saltwater basin Q was estimated from the time series of the backscatter instruments at 10, 8, and 4 cm above the bed. The sediment flux was calculated by taking the product of the temporal derivative of the mass concentration and the vertical length of the sampling volume of each instrument. This measurement is equivalent to the mass flux predicted by the effective settling velocity often calculated in field studies (Syvitski and Murray, 1981; Hill et al., 2000). The dominant source of variability in the flux measurements at the different instruments was found to be a result of small three-dimensional variations in the intensity of the convection. As a result, the flux used for our estimate of Q was obtained from the average flux measured with all three instruments. Spatial and temporal perturbations in the concentration associated with convective motions were removed during the averaging process. The final result is equal to the long-term removal rate of sediment from the plume, if the flow is in a steady state when the flux is calculated, the amount of sediment that leaves the water column (i.e., is deposited on the bed of the basin) is negligible, and the lower layer was turbulent. All of these
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Table 1 Experimental conditions Experiment
Cmass (mg/l)
Flux 10 ( 103 mg/cm2/s)
Flux8 ( 103 mg/cm2/s)
Flux 4 ( 103 mg/cm2/s)
Q ( 103 mg/cm2/s)
U (cm/s)
e (cm2/s3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6104 2029 1940 3272 1441 3736 769 2223 1234 2481 2420 660 380 990 864 1010 1930 1320 4080 2710
11.10 4.54 2.12 3.95 1.62 5.00 3.91 8.00 1.69 5.42 3.06 1.01 0.92 1.99 1.00 3.80 3.94 3.81 7.85 5.47
9.47 2.72 1.97 4.18 1.36 3.73 1.58 4.76 1.10 3.03 1.35 1.61 1.24 2.82 1.20 4.17 3.70 3.85 7.27 4.69
10.30 2.56 2.02 4.27 1.49 4.76 2.17 4.91 1.11 3.11 2.98 2.54 1.68 3.03 0.87 3.94 3.51 3.64 6.54 6.39
10.29 3.27 2.04 4.14 1.49 4.50 2.55 5.89 1.30 3.85 2.47 1.72 1.28 2.61 1.02 3.97 3.72 3.77 7.22 5.52
9 9 7 7 11 11 15 15 7 13 9 11 9 13 7 15 11 13 7 7
— — — — — — — — — — 0.60 1.03 0.51 1.55 0.44 1.63 0.83 1.22 0.54 0.57
Flux estimates were made from the backscatter instruments at 10 cm (Flux10), 8 cm (Flux8) and 4 cm (Flux4) above the bottom of basin. The average of these values for each experiment is used for the calculation of Q in Figs. 6 and 8. The first 10 experiments did not measure the dissipation rate of turbulent energy.
conditions appeared to be satisfied in all of the experiments reported. 2.3. Measurement of turbulence properties Plume speed was measured using an impeller speedometer within the surface flow. The speedometer ensemble averaged streamwise samples over 30 s to give the mean speed in the surface layer U. A micro-Acoustic Doppler Velocimeter (micro-ADV) was placed 20 cm above the bottom of the saltwater basin and in the mixing layer of the flow during the last 10 experiments. The microADV operating at 16 MHz was sampled at 25 Hz throughout this study and provided three orthogonal velocity components, signal-to-noise ratio (SNR), and correlation between successive samples. One velocity component represents the streamwise velocity in the tank, while the other two components represent the lateral and vertical velocity components. Data with an SNR below 15 dB (based on 25 Hz sampling rate) or a correlation
below 70% were removed from the time series, as per the manufacturer’s recommendation. An ADV has a low noise floor and fast sampling rate that makes it ideal for measuring turbulence (Voulgaris and Trowbridge, 1998). Five windowed bursts of 40 s were sampled and ensemble averaged in frequency space. A frequency band with 5/3 slope (associated with the inertial subrange) was identified for each experiment and used for calculations of the dissipation rate of turbulent energy. Using Kolmogorov’s turbulent spectra model (Tennekes and Lumley, 1972), a turbulentenergy dissipation rate for each experiment was calculated from the time series. According to this model, the spectrum of the streamwise velocity, Eu(k), in the inertial subrange is given by Eu ðkÞ ¼ 18=55aE2=3 k5=3 ;
ð1Þ
where the universal constant a ¼ 1:5; e is the dissipation rate of turbulent energy and k is the wavenumber. Frequency was changed to wavenumber by dividing by the mean velocity
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component for the experiment. The spectrum of the lateral velocity component is governed by Ev ðkÞ ¼ 4=3 Eu ðkÞ (Pope, 2000). We used the lateral spectra to estimate the error in our measurements.
3. Results The experiments were designed to investigate sedimentation from a steady-state hypopycnal (buoyant) plume. The mode of sedimentation from these experiments is similar to previous studies of mixing-induced CS in gravity currents (Maxworthy, 1999; Parsons et al., 2001). Discrete settling of individual particles (flocculated or disaggregated) was not observed in any of the experiments. The vertical propagation of the convective plumes was typified by the formation of a vortex tip, which was maintained during its fall (Fig. 3). These plumes travelled quickly (1.4 cm/s: Fig. 4). On average, initial fall velocities of the CS plumes were between 1 and 2 cm/s. These velocities are much larger than measured individual floc settling speeds (on the order of 0.1 cm/s: Sternberg et al., 1999; Hill et al., 2000) and disaggregated silt particles (25 mm) that settle at 0.05 cm/s estimated using Stokes Law. The range of concentrations observed within the surface plume ranged from 380 to 6000 mg/l (Table 1). In all experiments, the dominant form of sedimentation was mixing-induced CS. In Experiment 13, where the sediment concentration in the surface flow was 380 mg/l (Table 1), mixinginduced CS remained the dominant form of sedimentation from the surface flow (Fig. 4). In this study, concentrations lower than 300 mg/l were not possible due to the minimum speed of the supply pump. The small sampling volume of the UFOB-7 devices placed at 4 and 8 cm above the bed provided the unique opportunity to gain information on sediment concentrations within the convective plumes. From video, CS plumes were matched with the spikes in concentration shown in Fig. 5. These convective plumes had concentrations ranging from 500 to 700 mg/l for Experiment 4. For experiments with lower surface-plume
concentrations (o1000 mg/l), these plumes were somewhat obscured, but brief heightened concentrations ranging from 100 to 200 mg/l were identified in the time series. Because of the large sampling volume of the traditional OBSs, these spikes were not observed. Fig. 5 shows a plot of the excess fractional density for the duration of Experiment 4. Even though the supply of freshwater was kept constant, it is apparent that the mixed layer migrated downwards throughout the experiment. The downward propagation was a result of the finite volume of saltwater in the basin, eddy shedding into the mean flow, and mixing across the stratified interface. Turbulence production was dominated by a breaking internal wave that propagated along the pycnocline with a frequency between 0.08 to 0.25 Hz. Optical backscatter devices (all OBS and UFOB-7 probes) placed within the saline basin were used to provide an estimate of sediment flux. Table 1 shows the flux estimates for the devices placed at 10, 8, and 4 cm heights in the saline basin. The device at 20 cm was used to measure the sediment concentration in the surface plume. The time series from the backscatter instruments show a steady concentration of sediment in the surface plume and increasing sediment concentration within the basin below the mixed layer (Fig. 5). The experiments reported in Table 1 were for surface flow velocities of 7–15 cm/s. The surface plume concentration was positively correlated with the vertical sediment flux (Fig. 6a). A linear relationship existed between plume sediment concentration and the vertical sediment flux at plume velocities of 7 and 15 cm/s (Fig. 6b). Sediment flux was also linearly dependent on surface-plume velocity (Fig. 6c). Small surface velocities equate to a small Reynolds number and a transitional turbulent flow. For these flows (not the focus of this study), it is assumed that some other mode of sedimentation (e.g., disaggregated ballistic settling) would control the sediment flux. For the turbulent shear flows discussed herein, Reynolds numbers were of the order 104. Based upon the assumption of fully turbulent flow, the production and dissipation rates of turbulent energy should balance, and at small scales local
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Fig. 3. Photographs (a)–(f) show the progression of mixing-induced CS during Experiment 4. Photographs were taken using a light sheet from below. The scales are in cm. Time shown coincides with the elapsed time since sediment-laden fluid began flowing over saline basin. The plumes shown generally propagated downwards at speeds between 1 and 2 cm/s.
isotropy applies. With this in mind, Kolmogorov’s universal equilibrium theory was applied to the buoyant flows we observed. The assumption of a fully turbulent flow was supported in the experiments by the appearance of a well-defined inertial subrange (a spectrum with 5/3 slope: Fig. 7) in all of the spectra we observed. There was also a strong linear relationship between the dissipation rate of turbulent energy e and surface-plume velocity U. At higher velocities,
the turbulent production due to shear in the water column is more pronounced. Because turbulentenergy dissipation must be compensated by production in a steady flow, dissipation in a free shear flow is equal to the product of the shear and the negative of the turbulent Reynolds stress (Tennekes and Lumley, 1972; Pope, 2000). The Reynolds stress did not vary dramatically because the flow velocities in the mixed layer were nearly constant.
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Fig. 4. Picture taken during Experiment 13, the lowest concentration experiment possible with the laboratory apparatus. The surface plume concentration was 380 mg/l and the surface velocity was approximately 9 cm/s. The scale is in cm. The plume shown fell with a speed of 1.4 cm/s.
4. Discussion 4.1. General comments Previously, it has been hypothesized that CS could not occur at sediment concentrations below 1000 mg/l (Parsons et al., 2001). Most rivers have suspended sediment concentrations less than 1000 mg/l. Therefore, it has been hypothesized that CS would be rare, with the only exception being active continental margins associated with small, steep coastal watersheds (Parsons et al., 2001). However, mixing-induced CS occurred at concentrations well below the 1000 mg/l concentration threshold set forth in earlier work (Fig. 5). Based upon these results, it is possible that mixinginduced CS might occur on many coasts, including those where the rivers are large and tectonic activity is diminished. During some experiments, a bottom nepheloid layer (BNL) began to form at the bed of the saline basin towards the end of the experiment (e.g., Fig. 6). In these cases, mixing-induced CS appeared to overload the bottom boundary layer quickly when plume fall rates exceeded 1 cm/s. In natural environments, this sediment could easily remain in suspension by turbulence induced by waves, as on the Eel margin (Traykovski et al., 2000), or flow
downslope as a gravity current, as on the northern Papua New Guinea margin (Kineke et al., 2000; Walsh and Nittrouer, 2003). The results reported in this paper were strictly from hypopycnal or surface flows where the initial condition and position of the two fluids were dynamically stable, so that the stratified interface was preserved. There were several experiments not reported in Table 1 where the incoming, sedimentladen flow became negatively buoyant or hyperpycnal. In general, sediment concentrations exceeding 6000 mg/l caused a large amount of sediment-laden fluid to enter the basin along the bed. These experiments produced divergent plumes with flows both on the surface and along the bottom of the saline basin. In the past, sediment concentrations greater than 35,000 mg/l have been expected to make a freshwater flow become hyperpycnal (Mulder and Syvitski, 1995). From a similar analysis of the static stability of our stratified layers, sediment loads near 12,000 mg/l would be required to form a hyperpycnal flow. Since our experiments only required half that amount, we speculate that intense turbulent mixing may lower the sediment concentration required to make a flow statically unstable. Further investigation is required to identify the quantitative limit of static stability. 4.2. Flow stability The flows modeled in the experiments were fully turbulent with respect to the Reynolds number calculations of the surface layer and by the presence of the 5/3 slope associated with the inertial subrange (Fig. 7). The shear-induced turbulence was produced by the confining geometry and the boundary layer generated by the flow constriction (Fig. 1). Internal waves often propagated along the pycnocline between the two fluids. These internal waves can be seen in the time series of density (Fig. 5a) and surface sediment concentration (Fig. 5b). Internal waves are an expected result of a free-shear flow between two fluids (Kundu, 1990), and are typical of estuaries and estuarine environments (Geyer and Smith, 1987). The Froude number throughout the water column
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(mg/L)
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0.012 0.008 0.004 0 0
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Excess fractional Cmass @ 20 cmab Cmass @ 10 cmab
density (ρsalt-ρ)/ρ
W.W. McCool, J.D. Parsons / Continental Shelf Research 24 (2004) 1129–1142
500 0
(mg/L)
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1000 (mg/L)
Cmass @ 4 cmab
Cmass@ 8 cmab
1000
BNL 500
CS plumes
0 0
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Fig. 5. The time series of conductivity and sediment concentrations for Experiment 4. Concentrations are at 20, 10, 8, and 4 cm above the bed of the basin (cmab). The average concentration in the surface plume is 3700 mg/l. Initial, discrete CS plumes can be seen in the bottom panel. The bottom panel also shows a bottom nepheloid layer (BNL) of 250–500 mg/l forming towards the end of the experiment. Time is synchronized as in Fig. 4. Conductivity time series has been converted to excess fractional density. r is the density of the freshwater and rsalt is the density of the saltwater.
was always sub-critical (no hydraulic jumps or perturbations were observed). The bulk Richardson number of a mixed layer, a useful tool for the assessment of mixing and
dynamic stability, is typically defined by Ri ¼
g0 L ; DU 2
ð2Þ
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1138 14
100
10 8 6 4 2 0 1000
(a)
2000 3000 4000 5000 6000 Mass concentration Cmass (mg/l)
7000
14 Sediment mass flux Q (x 10-3 mg cm-2 sec-1)
10
slope = -5/3
10-3
10-4
10-1 100 101 Wavenumber k (radians/cm)
102
6 4
0 1000 2000 3000 4000 Mass concentration Cmass (mg/l)
(b)
5000
7 Cmass ~ 2000 mg/l Cmass ~ 1000 mg/l
6 Sediment mass flux Q (x 10-3 mg cm-2 sec-1)
10-2
Fig. 7. Spectrum of turbulent motions in wavenumber space for Experiment 11.
8
2
5 4 3 2 1 0 0
(c)
10-1
10-5 -2 10
U = 7 cm/s U = 15 cm/s
12
Power density Eu(k) (cm3/sec2)
(x 10-3 mg cm-2 sec-1)
Sediment mass flux Q
12
4 8 12 Surface plume velocity U (cm/s)
16
Fig. 6. (a) Plume mass concentration versus sediment flux. (b) Plume mass concentration versus sediment flux for both 7 and 15 cm/s plume velocities. (c) Surface-plume velocity U versus vertical sediment flux Q for two different sediment concentrations.
where L is the depth of the mixed layer, g0 is the reduced gravitational acceleration and DU is the velocity gradient across the mixed layer. The reduced gravitational acceleration was not varied in the experiments, while DU was proportional to the surface-layer velocity U. L was not measured directly; however, it can be estimated using the
measurement of the dissipation rate of turbulent energy e. Ivey and Imberger (1991) note that epU3/L, if production and dissipation approximately balance. The dissipation rate was linearly proportional to U, so therefore LpU2. If this proportionality is substituted into Eq. (2), we find that the Richardson number was most likely the same near-critical value for all of the experiments, which is consistent with areas of active mixing in natural environments (e.g., Geyer and Smith, 1987). Based upon the visual observations of the mixed-layer depth and the estimation of the bulk Richardson number cited above, the Richardson number for these flows (0.3–0.5) indicates that Kelvin–Hemholtz instabilities should not be present. From visual observation, it was evident that Kelvin–Hemholtz instabilities did occur intermittently along the pycnoline between the two fluids, and calculations of gradient Richardson numbers within the mixed layer must be at least temporarily below critical. Cuspate-shaped instabilities originating from Holmboe waves in the mixed layer were also identified in all experiments. Holmboe waves propagate along isopycnal surfaces and can be found in any fully turbulent flow with finite bulk Richardson number greater than the critical value (Smyth and Peltier, 1991). This is consistent with observations of natural systems dominated by
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4.3. Dimensional analysis Many processes contribute to the vertical flux of sediment from buoyant river plumes. It is intuitive that vertical sediment flux increase with increasing plume concentration (Figs. 7 and 8), but when mixing is taken into account this relation is not trivial. Dimensional analysis is useful in observing the relationship between many variables. There are nine dimensional variables associated with the experiments (in addition to the volumetric concentration, which is dimensionless). These variables are the density of the fluid (r), the density of the sediment (rs), gravity (g), the kinematic viscosity of the fluid (v), the surface plume velocity (U), the sediment-grain diameter (D), the buoyancy frequency (N), the sediment flux (Q), and the dissipation rate of turbulent energy (e). Using plume velocity, fluid density and viscosity as the repeating variables in the Buckingham Pi theorem, six dimensionless variables are capable of describing the flow. Among the six dimensionless variables obtained from the scale analysis are the relative density of the sediment, two Reynolds numbers (one defining the mixed-layer, the other relating to the particles) and a Grashof number (the product of a mixed1.4 1.2
Q ρU
106
1.0
Q Cεν 1.5x105 4 10-7 U ρU
r2=.85
0.8 0.6
layer Reynolds and a Richardson number). Because of Reynolds similarity, the near-critical nature of the mixed layer, and the use of natural sediment, the remaining two dimensionless parameters should be related to one another and useful in predicting environmental sedimentation rates. The two remaining dimensionless variables are the dimensionless dissipation ev/U4 and the dimensionless vertical flux of sediment Q/rU . After an examination of the laboratory data, it was realized that the product of dimensionless dissipation and volumetric concentration were proportional to the dimensionless flux (Fig. 9). A simple model resulting from this relationship can be formed: Q CEv ¼ A 4 þ B; rU U
.14 .12
Model Observations (Hill et al., 2000)
.10 .08 .06 Disaggregated settling velocity
.04 .02 0 10-14
0.4
ð3Þ
where A and B are empirical coefficients. In the limit of small sediment concentration (i.e., C-0), the vertical flux of sediment should vanish. In Eq. (3), this would suggest that the y-intercept should be zero (i.e, BE0). This common-sense limit is also consistent with our data.
Effective settling velocity (mm/s)
internal waves along isopycnal surfaces, which often exhibit Richardson numbers slightly above the critical value (Geyer and Smith, 1987).
1139
Model µ= 0.81 Field µ= 0.80 Floc settling speed ~ 1 mm/s
10-13
10-12
10-11
Cεν
0.2
U4
0 1
2
3
4
Cεν U4
1012
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6
7
Fig. 8. Dimensionless flux versus the product of the volumetric concentration and the dimensionless dissipation rate of turbulent energy for Experiments 11–20.
Fig. 9. Effective settling velocity versus the product of the dimensionless dissipation and the volumetric sediment concentration for conditions observed on the Eel River margin. Measured effective settling velocities were obtained from Table 2 of Hill et al. (2000). Modeled effective settling velocities are based upon Eq. (2) using the data (C, e, U) reported by Hill et al. (2000) and dividing Q by Cmass.
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4.4. Application to the Eel River margin The conditions of our experiments were designed to closely match the geometry of the Eel River plume. These conditions (e.g., isothermal, salinity differences on the order of 5–15 ppt, etc.) are typical of energetic continental margins. Surface-layer sediment concentrations in the experiments ranged from 400 to 6000 mg/l and represent realistic concentrations for oceanic flood conditions in small mountainous rivers. During the period of observations, the Eel River plume concentrations ranged from 900 to 2600 mg/l for winter storms in 1998 (Hill et al., 2000). Other rivers, like the Salinas River in Northern California have higher sediment loads (6000 mg/l: Johnson et al., 2001), while still others can have slightly lower concentrations (e.g., the Sepik River in Papua New Guinea, 300–400 mg/l: Kineke et al., 2000). Qualitative comparison of our experiments with the conditions observed indicate that mixinginduced CS might be important on all of these margins. Although our experiments are small compared to the mixed layers present in large river systems, the characteristic turbulence and velocities are realistic. In fact, the surface velocities reported in this paper correspond well with other natural flows. For instance, Ivey and Imberger (1991) reported wind-driven surface plumes that propagated at 12 cm/s. These natural stratified flows had measured dissipation rates that ranged from 103 to 104 cm2/s3, within the range of our experiments. It is important to note that the fluxes observed in the experiments were 10–50% higher than the flux estimates measured by Chen (1997) for double-diffusive sedimentation at the same sediment concentrations. At slower flow speeds, the flux estimates became more similar to the quiescent conditions examined in earlier studies (e.g., Parsons et al., 2001). The ability of turbulence to enhance the removal rate of sediment is a counterintuitive, but powerful finding. Hill et al. (2000) implicitly assumed that mixing within the plume was dominated by surface gravity waves in order to calculate dissipation rates within the Eel River plume. Using a simple drag law
(Large and Pond, 1981), they found that dissipation rates varied between 100 and 101 cm2/s3 in the Eel River plume. Using the plume sediment concentrations, dissipation rates and surface velocities reported by Hill et al. (2000), the sediment flux near the Eel River mouth based on our simple relationship varied between 7–50 103 mg/cm2/s. These flux calculations are roughly five times larger than those reported in our study due to the increased turbulent energy found on the continental margin. As a result, the increased turbulence found in oceanic surface layers may account for large sediment flux estimates observed in a variety of environments (e.g., Eel River margin, but also northern Papua New Guinea: Kineke et al., 2000; Walsh and Nittrouer, 2003). Effective settling velocities are usually reported in field studies to estimate clearance rates from surface plumes. The effective settling velocity of the sediment load in a river plume can be calculated by dividing the mass flux per unit area Q by the mass concentration in the plume Cmass. Using the flux Q calculated by Eq. (3), the mean effective settling velocities for oceanic-flood conditions on the Eel River during 1998 are found to be 0.085 mm/s with a range of 0.06–0.13 mm/s. The average effective settling velocity measured on the Eel River during this time period is 0.08 mm/s (Hill et al., 2000), with a range of 0.07 to 0.12 mm/s (Fig. 9). The Stokes settling velocity of disaggregated particles was significantly lower (0.04 mm/s). Hill et al. (2000) explained the enhanced flux (over and above Stokes settling of disaggregated particles) by a packaging of flocs, which was dependent on sediment concentration and floc-formation rates. Flocculated particles near the seabed on the Eel River margin generally settle at speeds on the order of 1 mm/s (Sternberg et al., 1999). More recently, a well-mixed and flocculated plume with disaggregated sediment resupply from the inner shelf or surf zone has also been proposed to account for the mix of flocs and disaggregated particles in the plume (Curran et al., 2002). However, in the absence of evidence to the contrary, mixing-induced convective sedimentation explains the removal rates observed, without appealing to external, unmeasured processes.
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5. Summary and conclusions There remains a controversy about what controls the sediment dynamics in a buoyant river plume. Our observations and analysis argue that sediment flux out of a buoyant river plume is predominately controlled by convective processes generated by shear-induced turbulence when the sediment load is significant and fine-grained. Our experiments used natural sediment, so that if flocculation were important (or present), it would be apparent in the experiments. The similarity of the results from the natural material used in this study (Table 1) and earlier investigations that used inorganic particles (carborundum powder: Maxworthy, 1999; crushed silica: Parsons et al., 2001) argues that, at least when concentrations are high, removal of sediment from buoyant plumes is not dependent on particle characteristics. Rather, on the time scale of all of the experiments, turbulent mixing and the convective plumes it generated regulated the transport of sediment out of the buoyant, sediment-laden flow. The vertical flux of sediment from buoyant river plumes is important for understanding sediment dispersal on continental margins. Mixing-induced CS was found to occur for surface plume concentrations smaller than previously observed (51000 mg/l). In addition, concentrations lower than expected (7000 mg/l) developed a divergent plume due to wholesale removal of sediment-laden fluid by local, intense areas of turbulent mixing. In all of these cases, the vertical flux of sediment from these flows is related predominantly to the dissipation rate of turbulent energy and volumetric sediment concentration. A simple scaling relationship is able to predict effective settling velocities observed in oceanic-flood events. In energetic environments, mixing-induced CS dominates the sediment transport in the vertical. In quiescent locales, less efficient modes of CS (e.g., leaking convection: Parsons et al., 2001) or individual particle settling may be more common. These results do not imply other processes are not important in natural river plumes. On the contrary, we conclude only that mixing-induced CS transports sediment from the mixed layer of a plume to the saline fluid below. Flocs can take part in this
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transport (i.e., transport is not particle dependent), as it is well known that sediment becomes flocculated by the time it reaches the seabed (Sternberg et al., 1999). It is possible that mixinginduced CS enhances floc formation by keeping fine particles together in vertically falling plumes. This increases the potential for particle collisions, while incorporating saline water, and ultimately forming larger flocs. Recent evidence would suggest that flocs would leave the vertically falling plume when the individual settling velocity of the floc exceeds the fall velocity of the plume (Bush et al., 2003); therefore leaving floc settling rates as a function of water-column turbulence rather than lithology. Existing models of river-plume sedimentation do not consider the interaction between particles and fluid turbulence. Jet models, common to most standard numerical studies, assume fully turbulent flow and the diffusion of fresh water and sediment is laterally dispersed through turbulent mixing with the surrounding fluid (e.g., Morehead and Syvitski, 1999). Settling velocity of individual particles is typically the only means by which material is transported in the vertical (i.e., turbulent mixing in the vertical is not incorporated into models). The interaction between sediment load and turbulent forcing is very dynamic. This study has incorporated the dynamics associated with these two forcing mechanisms to formulate a simple model based on sediment concentration and turbulent energy dissipation rate for typical oceanic-plume stratifications. These results may begin to explain the increased sediment flux found on many margins and should aid future sedimentdispersal modeling efforts.
Acknowledgements This research was supported by the US Office of Naval Research through the National Science and Education Graduate Fellowship and contracts N000140110922 and N000140110922. Sincere thanks are given to C. Nittrouer and A. Ogston for their assistance obtaining the cored sediments and comments improving an early draft of the manuscript. P. Hill, K. Curran, and M. Pehrup provided productive and valuable reviews.
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References Aliseda, A., Cartellier, A., Hainaux, F., Lasheras, J.C., 2002. Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. Journal of Fluid Mechanics 468, 77–105. Bush, J.W.M., Thurber, B.A., Blanchette, F., 2003. Particle clouds in homogeneous and stratified environments. Journal of Fluid Mechanics 489, 29–54. Chen, C.F., 1997. Particle flux through sediment fingers. DeepSea Research Part I—oceanographic Research Papers 44 (9–10), 1645–1654. Curran, K.J., Hill, P.S., Milligan, T.G., 2002. Fine-grained suspended sediment dynamics in the Eel River flood plume. Continental Shelf Research 22 (17), 2537–2550. Geyer, W.R., Smith, J.D., 1987. Shear instability in a highly stratified estuary. Journal of Physical Oceanography 17 (10), 1668–1679. Geyer, W.R., Hill, P., Milligan, T., Traykovski, P., 2000. The structure of the Eel River plume during floods. Continental Shelf Research 20 (16), 2067–2093. Green, T., 1987. The importance of double diffusion to the settling of suspended material. Sedimentology 34 (2), 319–331. Hill, P.S., Nowell, A.R.M., 1995. Comparison of 2 models of aggregation in continental-shelf bottom boundary-layers. Journal of Geophysical Research-Oceans 100 (C11), 22749–22763. Hill, P.S., Milligan, T.G., Geyer, W.R., 2000. Controls on effective settling velocity of suspended sediment in the Eel River flood plume. Continental Shelf Research 20 (16), 2095–2111. Hoyal, D.C.J.D., Bursik, M.I., Atkinson, J.F., 1999. The influence of diffusive convection on sedimentation from buoyant plumes. Marine Geology 159 (1–4), 205–220. Ivey, G.N., Imberger, J., 1991. On the nature of turbulence in a stratified fluid.1. The energetics of mixing. Journal of Physical Oceanography 21 (5), 650–658. Johnson, K.S., Paull, C.K., Barry, J.P., Chavez, F.P., 2001. A decadal record of underflows from a coastal river into the deep sea. Geology 29 (11), 1019–1022. Kineke, G.C., Woolfe, K.J., Kuehl, S.A., Milliman, J.D., Dellapenna, T.M., Purdon, R.G., 2000. Sediment export from the Sepik River, Papua New Guinea: evidence for a divergent sediment plume. Continental Shelf Research 20 (16), 2239–2266. Kundu, P., 1990. Fluid Mechanics. Academic Press, San Diego. Large, W.G., Pond, S., 1981. Open ocean momentum flux measurements in moderate to strong winds. Journal of Physical Oceanography 11, 324–336. Maxey, M.R., 1987. The motion of small spherical-particles in a cellular-flow field. Physics of Fluids 30 (7), 1915–1928. Maxey, M.R., Corrsin, S., 1986. Gravitational settling of aerosol-particles in randomly oriented cellular-flow fields. Journal of the Atmospheric Sciences 43 (11), 1112–1134.
Maxworthy, T., 1999. The dynamics of sedimenting surface gravity currents. Journal of Fluid Mechanics 392, 27–44. Milliman, J.D., Syvitski, J.P.M., 1992. Geomorphic tectonic control of sediment discharge to the ocean—the importance of small mountainous rivers. Journal of Geology 100 (5), 525–544. Morehead, M.D., Syvitski, J.P., 1999. River-plume sedimentation modeling for sequence stratigraphy: application to the Eel margin, northern California. Marine Geology 154 (1–4), 29–41. Mulder, T., Syvitski, J.P.M., 1995. Turbidity currents generated at river mouths during exceptional discharges to the world oceans. Journal of Geology 103 (3), 285–299. Nittrouer, C.A., Kravitz, J.H., 1996. STRATAFORM: A program to study the creation and interpretation of sedimentary strata on continental margins. Oceanography 9, 146–152. Parsons, J.D., Garcia, M.H., 2000. Enhanced sediment scavenging due to double-diffusive convection. Journal of Sedimentary Research 70 (1), 47–52. Parsons, J.D., Bush, J.W.M., Syvitski, J.P.M., 2001. Hyperpycnal plume formation from riverine outflows with small sediment concentrations. Sedimentology 48 (2), 465–478. Pope, S.B., 2000. Turbulent Flows. Cambridge University Press, Cambridge, MA. Smyth, W.D., Peltier, W.R., 1991. Instability and transition in finite-amplitude kelvin-helmholtz and holmboe waves. Journal of Fluid Mechanics 228, 387–415. Sternberg, R.W., Berhane, I., Ogston, A.S., 1999. Measurement of size and settling velocity of suspended aggregates on the northern California continental shelf. Marine Geology 154 (1–4), 43–53. Syvitski, J.P.M., Murray, J.W., 1981. Particle interaction in fjord suspended sediment. Marine Geology 39 (3–4), 215–242. Tennekes, H., Lumley, J.L., 1972. A First Course in Turbulence. MIT Press, Cambridge, MA. Traykovski, P., Geyer, W.R., Irish, J.D., Lynch, J.F., 2000. The role of wave-induced density-driven fluid mud flows for cross-shelf transport on the Eel River continental shelf. Continental Shelf Research 20 (16), 2113–2140. Voulgaris, G., Trowbridge, J.H., 1998. Evaluation of the acoustic doppler velocimeter (adv) for turbulence measurements. Journal of Atmospheric and Oceanic Technology 15 (1), 272–289. Walsh, J.P., Nittrouer, C.A., 2003. Contrasting styles of offshelf sediment accumulation in New Guinea. Marine Geology 196 (3–4), 105–125. Wang, L.P., Maxey, M.R., 1993. Settling velocity and concentration distribution of heavy-particles in homogeneous isotropic turbulence. Journal of Fluid Mechanics 256, 27–68. Wheatcroft, R.A., Sommerfield, C.K., Drake, D.E., Borgeld, J.C., Nittrouer, C.A., 1997. Rapid and widespread dispersal of flood sediment on the Northern California margin. Geology 25 (2), 163–166.
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Sedimentation from buoyant fine-grained suspensions Wayne W. McCool, Jeffrey D. Parsons* School of Oceanography, University of Washington, Box 357940, Seattle, WA 98195-7940, USA Received 27 March 2003; received in revised form 10 October 2003; accepted 12 March 2004
Abstract Laboratory experiments were performed to observe the sedimentation of natural sediment in buoyant turbulent suspensions. A series of experiments were conducted in a flume modified to investigate sedimentation from a steady, stratified shear layer. Ambient salinity stratification in the lower fluid allowed the upper layer to remain buoyant, while turbulence induced by free shear in the water column produced instabilities between the two fluids. These experiments showed that convective plumes dominated sedimentation. These convective plumes had vortex tips and vertical velocities of 1–2 cm/s. The velocities observed are two orders of magnitude larger than those predicted by Stokes settling of the constituent particles. Surface plume concentrations as low as 380 mg/l were documented to support robust mixing-induced convective sedimentation. At high concentrations (>6000 mg/l), the experiments produced a divergent plume with a considerable amount of the sediment-laden fluid being diverted along the bottom of the flume. Our observed vertical sediment fluxes demonstrated a 50% increase as compared to previous studies of double-diffusive sedimentation. A simple scaling analysis using the dissipation rate of turbulent energy and the surface plume sediment concentration was able to collapse the experimental data and indicated a positive correlation between turbulent energy and sedimentation. The empirical scaling relationship accurately predicted effective settling velocities measured on the Eel River margin in 1997–1998. The quality of the agreement between the laboratory and field measurements provides strong evidence that sedimentation by mixing-induced convection may be the dominant mode of sediment removal from energetic, highly concentrated, buoyant river plumes. r 2004 Elsevier Ltd. All rights reserved. Keywords: Eel River; River plume; Shelf sedimentation; Convective sedimentation; Cross-shelf transport
1. Introduction Many natural processes contribute to the fate of sedimentary particles on continental shelves and are essential in understanding the fate of terrestrial *Corresponding author. Tel.: +1-206-221-6627; fax: +1206-543-6073. E-mail address: [email protected] (J.D. Parsons).
carbon and constraining sediment budgets (Nittrouer and Kravitz, 1996). Milliman and Syvitski (1992) estimated that approximately 10 billion metric tons of sediment are transported annually by rivers to continental shelves. Small mountainous watersheds supply a large fraction of this global sediment supply. Due to their small drainage basins and intense precipitation events, these watersheds tend to have episodic floods which deliver pulses of sediment to the ocean (Hill et al., 2000).
0278-4343/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.csr.2004.03.009
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Periodic flooding events can produce hypopycnal river plumes that remain at the surface and transport fine material tens of kilometers from the river mouth. The fate of sediment within a buoyant river plume has been attributed to ambient ocean conditions, freshwater discharge, sediment load, and settling velocity of the sediment (Morehead and Syvitski, 1999; Hill et al., 2000). All of these factors contribute to the vertical flux of sediment, which controls sediment dispersal on continental margins. Understanding the dynamics of solid material involved in these intense oceanicflood events remains elusive due to the unpredictable nature of these environments (Wheatcroft et al., 1997). Settling of particles from buoyant river plumes will determine the initial transport of sediment to the bottom boundary layer prior to advection or diffusion by near-bed processes (Geyer et al., 2000). The development of sedimentation models for buoyant river plumes has been hindered by incomplete understanding of the processes that remove sediment from the base of the surface plumes. In some plume models, empirical relationships are used for sediment removal rates (Morehead and Syvitski, 1999), so that the models account for total removal, without capturing physical processes. Stokes settling of disaggregated constituent grains cannot account for the sediment flux out of most river plumes. Increased removal rates of fine-grained sediment have traditionally been linked to flocculation (Syvitski and Murray, 1981; Hill and Nowell, 1995; Hill et al., 2000). Flocculation of particles can increase effective settling velocities and is generally thought to account for the large sediment removal rates on river margins with buoyant plumes (Hill et al., 2000). The use of Stokes settling velocities for flocs or discrete particles is complicated by two problems. First, if the water column is stratified by salinity gradients (e.g., the Eel River in flood: Hill et al., 2000; Geyer et al., 2000), the ambient stratification can hinder the fall speed of a particle. As a result, the sediment will concentrate along the halocline, until the region becomes gravitationally unstable (Parsons et al., 2001). Recent laboratory studies
have suggested that convective motions associated with gravitational instability could contribute to the removal of sediment from surface plumes (Green, 1987; Chen, 1997; Hoyal et al., 1999; Parsons and Garcia, 2000). These earlier studies focused on a collection of particles above a pycnocline in a stable, stratified water column with temperature or salinity as the stabilizing property of the fluid. Inhomogeneities in the density field can eventually evolve into convective cells, initiating what has been called convective sedimentation (CS). A second problem in estimating the settling velocity of particles and flocs is the complex interaction between particles and turbulence. A turbulent flow field causes perturbations to the straight trajectory of a particle falling under gravity. Turbulence has been found to increase the effective settling speed of particles by 10–50% (Maxey and Corrsin, 1986; Maxey, 1987; Wang and Maxey, 1993; Aliseda et al., 2002). Assuming particle mixing by turbulence is a homogeneous process in which particles are uniformly dispersed without any bias can be grossly in error (Maxey, 1987; Aliseda et al., 2002). Parsons et al. (2001) and Maxworthy (1999) both found that turbulent mixing between a buoyant gravity current and the ambient denser fluid could produce non-uniform sedimentation associated with gravitational instability. The resulting convective plumes quickly remove sediment from the surface layer and deposit the sediment on the bottom. Hereafter, we will refer to these plumes as mixing-induced CS. These experiments indicate that mixing-induced CS dominates in the presence of strong stratification and intense mixing for laboratory-scale flows, but only for large sediment concentrations (generally o10,000 mg/l; Maxworthy, 1999). Unfortunately, these earlier studies did not measure turbulence properties or the vertical flux of sediment associated with convection. Therefore, they had difficulty speculating about the importance of these processes in environmental flows. We have performed laboratory experiments of a fresh, sediment-laden flow over ambient saltwater, which simulates a steady, buoyant river plume during flood. During these experiments, we
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a light-refraction salinometer. The system was initially stable (i.e., no sediment is transported directly into the basin). Maximum velocities in the surface layer varied between 7 and 15 cm/s. The velocity profiles indicated that shear was approximately constant throughout the water column (Fig. 2). A small return flow was observed consistently near the bottom of the basin. The return flow caused a slight counterclockwise circulation within the basin. Cored sediment with a median grain size of 20– 30 mm was used in all experiments reported in Table 1. The cored sediment used during this study was derived from samples taken from the Eel Canyon in November 2001. No dispersing agent was used on the supplied sediment, but turbulence supplied by the pump might have disaggregated flocs. By varying the pump speed, a wide range of sediment concentrations was possible. To perform an experiment, the sediment was mixed in a slurry head tank and pumped into the flume upstream of the flow confinement section and salt basin. The supply slurry was made by combining sediment and freshwater for the first 10 experiments and saltwater (5 ppt) for the last ten experiments. The basin salinity was consistently 15 ppt for the first ten experiments and changed to 20 ppt for the final 10 to maintain a consistent stratification throughout all experiments. The mixed-layer supporting the sediment-laden flow
measured sediment load, turbulent mixing, ambient stratification, and the net flux of sediment out of the buoyant flow. The goal of our study was to better understand sediment removal rates through stratification in the presence of shear-induced turbulence and the complex interaction between sedimentation and turbulence. Measurements from the Eel River margin were used to test the results of our experiments and analysis.
2. Methods 2.1. Experimental procedure Experiments were performed in the facility shown in Fig. 1. Water is circulated via motordriven propellers around the racetrack flume in a clockwise direction. Five flow straighteners are placed in both of the curved sides of the flume to reduce secondary circulation and a grid with 0.32cm straws is placed after the straighteners to homogenize the flow. Plexiglas placed in the flume confined the freshwater and sediment flow to 7 cm on the surface. A saltwater basin 90 cm long, 21 cm deep and 36 cm wide was formed in the lee of the Plexiglas constriction. The sediment-laden freshwater flowed over the salt basin, which contained a salinity of 15 ppt. All of the experiments were isothermal. The initial salinity was measured using
400 cm flow
Flume
propellers
Basin Supply Conductivity probe Impellor speedometer diffuser
MicroADV OBS (x2)
30 cm
Flume (fresh, mixed) flow barrier confines saline basin
mixed layer Basin (saline) 90 cm UFOB-7 (x2)
Supply
flow flow confinement 84 cm
honeycomb & flow straighteners
Fig. 1. Upper schematic shows the experimental facility in plan view. The lower schematic shows the side view of the test section. The flow was confined downstream of the sediment addition point.
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Height above basin bottom (cm)
25
20
15
Plume velocityU 15.0 cm/s 13.0 cm/s 11.3 cm/s 9.4 cm/s
10
5
0 20
15
10 5 Velocity (cm/s)
0
-5
Fig. 2. Profiles of mean velocity measured at 1 cm intervals within the saline basin. Profiles represent the four velocities used in the experiments to vary the turbulent mixing at the interface (B20 cm height) between the saltwater and the overlying lighter sediment-laden freshwater. The range between 25 and 18 cm above the bed shows a nearly linear free shear zone.
had a variable depth depending on the velocity of the surface layer. Faster surface layers had thicker mixed layers, while slower surface layers mixed less and had smaller mixed layers. Video and digital photography were used to visualize the vertical transport of sediment. Under normal room lighting, sedimentation was difficult to record, so the laboratory was completely darkened and a light sheet was reflected through the salt basin from below in the middle of the basin approximately 4 cm from the wall. All photos were taken in the initial 3 min of each experiment, as the water was clearest during this time. Later pictures show the same form of sedimentation, but were not as clear due to increased ambient turbidity in the saltwater basin. 2.2. Measurement of sediment concentration and vertical flux The instrumentation in the flume consisted of a high-speed conductivity probe (to measure salinity), two optical backscatter instruments (OBS),
two fiber-optic backscatter instruments (UFOB-7), and a current meter. In order to allow the flow to become steady, the instrumentation began sampling 2 min after the propellers initiated flow in the flume. The backscatter devices (i.e., all of the OBS and UFOB-7 instruments) measured sediment concentration at 20, 10, 8, and 4 cm above the bottom of the basin. The UFOB-7 has a fixed ellipsoid sampling volume of approximately 1 cm3, which is defined by the intersection of the offset transmit and receive beams. The sampling volume has a 1-cm vertical length. The OBS does not have fixed sampling volume, so the vertical length can be variable (approximately 0.5–5.0 cm). However, for the concentrations used in this study (300– 6000 mg/l), a vertical sampling volume length of 1 cm was appropriate for all experiments. At roughly 1000 mg/l, the UFOB-7 signal saturates. Therefore, any concentrations measured by the UFOB-7 exceeding 1000 mg/l have been excluded in this study. The vertical sediment flux through a horizontal plane in the saltwater basin Q was estimated from the time series of the backscatter instruments at 10, 8, and 4 cm above the bed. The sediment flux was calculated by taking the product of the temporal derivative of the mass concentration and the vertical length of the sampling volume of each instrument. This measurement is equivalent to the mass flux predicted by the effective settling velocity often calculated in field studies (Syvitski and Murray, 1981; Hill et al., 2000). The dominant source of variability in the flux measurements at the different instruments was found to be a result of small three-dimensional variations in the intensity of the convection. As a result, the flux used for our estimate of Q was obtained from the average flux measured with all three instruments. Spatial and temporal perturbations in the concentration associated with convective motions were removed during the averaging process. The final result is equal to the long-term removal rate of sediment from the plume, if the flow is in a steady state when the flux is calculated, the amount of sediment that leaves the water column (i.e., is deposited on the bed of the basin) is negligible, and the lower layer was turbulent. All of these
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Table 1 Experimental conditions Experiment
Cmass (mg/l)
Flux 10 ( 103 mg/cm2/s)
Flux8 ( 103 mg/cm2/s)
Flux 4 ( 103 mg/cm2/s)
Q ( 103 mg/cm2/s)
U (cm/s)
e (cm2/s3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6104 2029 1940 3272 1441 3736 769 2223 1234 2481 2420 660 380 990 864 1010 1930 1320 4080 2710
11.10 4.54 2.12 3.95 1.62 5.00 3.91 8.00 1.69 5.42 3.06 1.01 0.92 1.99 1.00 3.80 3.94 3.81 7.85 5.47
9.47 2.72 1.97 4.18 1.36 3.73 1.58 4.76 1.10 3.03 1.35 1.61 1.24 2.82 1.20 4.17 3.70 3.85 7.27 4.69
10.30 2.56 2.02 4.27 1.49 4.76 2.17 4.91 1.11 3.11 2.98 2.54 1.68 3.03 0.87 3.94 3.51 3.64 6.54 6.39
10.29 3.27 2.04 4.14 1.49 4.50 2.55 5.89 1.30 3.85 2.47 1.72 1.28 2.61 1.02 3.97 3.72 3.77 7.22 5.52
9 9 7 7 11 11 15 15 7 13 9 11 9 13 7 15 11 13 7 7
— — — — — — — — — — 0.60 1.03 0.51 1.55 0.44 1.63 0.83 1.22 0.54 0.57
Flux estimates were made from the backscatter instruments at 10 cm (Flux10), 8 cm (Flux8) and 4 cm (Flux4) above the bottom of basin. The average of these values for each experiment is used for the calculation of Q in Figs. 6 and 8. The first 10 experiments did not measure the dissipation rate of turbulent energy.
conditions appeared to be satisfied in all of the experiments reported. 2.3. Measurement of turbulence properties Plume speed was measured using an impeller speedometer within the surface flow. The speedometer ensemble averaged streamwise samples over 30 s to give the mean speed in the surface layer U. A micro-Acoustic Doppler Velocimeter (micro-ADV) was placed 20 cm above the bottom of the saltwater basin and in the mixing layer of the flow during the last 10 experiments. The microADV operating at 16 MHz was sampled at 25 Hz throughout this study and provided three orthogonal velocity components, signal-to-noise ratio (SNR), and correlation between successive samples. One velocity component represents the streamwise velocity in the tank, while the other two components represent the lateral and vertical velocity components. Data with an SNR below 15 dB (based on 25 Hz sampling rate) or a correlation
below 70% were removed from the time series, as per the manufacturer’s recommendation. An ADV has a low noise floor and fast sampling rate that makes it ideal for measuring turbulence (Voulgaris and Trowbridge, 1998). Five windowed bursts of 40 s were sampled and ensemble averaged in frequency space. A frequency band with 5/3 slope (associated with the inertial subrange) was identified for each experiment and used for calculations of the dissipation rate of turbulent energy. Using Kolmogorov’s turbulent spectra model (Tennekes and Lumley, 1972), a turbulentenergy dissipation rate for each experiment was calculated from the time series. According to this model, the spectrum of the streamwise velocity, Eu(k), in the inertial subrange is given by Eu ðkÞ ¼ 18=55aE2=3 k5=3 ;
ð1Þ
where the universal constant a ¼ 1:5; e is the dissipation rate of turbulent energy and k is the wavenumber. Frequency was changed to wavenumber by dividing by the mean velocity
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component for the experiment. The spectrum of the lateral velocity component is governed by Ev ðkÞ ¼ 4=3 Eu ðkÞ (Pope, 2000). We used the lateral spectra to estimate the error in our measurements.
3. Results The experiments were designed to investigate sedimentation from a steady-state hypopycnal (buoyant) plume. The mode of sedimentation from these experiments is similar to previous studies of mixing-induced CS in gravity currents (Maxworthy, 1999; Parsons et al., 2001). Discrete settling of individual particles (flocculated or disaggregated) was not observed in any of the experiments. The vertical propagation of the convective plumes was typified by the formation of a vortex tip, which was maintained during its fall (Fig. 3). These plumes travelled quickly (1.4 cm/s: Fig. 4). On average, initial fall velocities of the CS plumes were between 1 and 2 cm/s. These velocities are much larger than measured individual floc settling speeds (on the order of 0.1 cm/s: Sternberg et al., 1999; Hill et al., 2000) and disaggregated silt particles (25 mm) that settle at 0.05 cm/s estimated using Stokes Law. The range of concentrations observed within the surface plume ranged from 380 to 6000 mg/l (Table 1). In all experiments, the dominant form of sedimentation was mixing-induced CS. In Experiment 13, where the sediment concentration in the surface flow was 380 mg/l (Table 1), mixinginduced CS remained the dominant form of sedimentation from the surface flow (Fig. 4). In this study, concentrations lower than 300 mg/l were not possible due to the minimum speed of the supply pump. The small sampling volume of the UFOB-7 devices placed at 4 and 8 cm above the bed provided the unique opportunity to gain information on sediment concentrations within the convective plumes. From video, CS plumes were matched with the spikes in concentration shown in Fig. 5. These convective plumes had concentrations ranging from 500 to 700 mg/l for Experiment 4. For experiments with lower surface-plume
concentrations (o1000 mg/l), these plumes were somewhat obscured, but brief heightened concentrations ranging from 100 to 200 mg/l were identified in the time series. Because of the large sampling volume of the traditional OBSs, these spikes were not observed. Fig. 5 shows a plot of the excess fractional density for the duration of Experiment 4. Even though the supply of freshwater was kept constant, it is apparent that the mixed layer migrated downwards throughout the experiment. The downward propagation was a result of the finite volume of saltwater in the basin, eddy shedding into the mean flow, and mixing across the stratified interface. Turbulence production was dominated by a breaking internal wave that propagated along the pycnocline with a frequency between 0.08 to 0.25 Hz. Optical backscatter devices (all OBS and UFOB-7 probes) placed within the saline basin were used to provide an estimate of sediment flux. Table 1 shows the flux estimates for the devices placed at 10, 8, and 4 cm heights in the saline basin. The device at 20 cm was used to measure the sediment concentration in the surface plume. The time series from the backscatter instruments show a steady concentration of sediment in the surface plume and increasing sediment concentration within the basin below the mixed layer (Fig. 5). The experiments reported in Table 1 were for surface flow velocities of 7–15 cm/s. The surface plume concentration was positively correlated with the vertical sediment flux (Fig. 6a). A linear relationship existed between plume sediment concentration and the vertical sediment flux at plume velocities of 7 and 15 cm/s (Fig. 6b). Sediment flux was also linearly dependent on surface-plume velocity (Fig. 6c). Small surface velocities equate to a small Reynolds number and a transitional turbulent flow. For these flows (not the focus of this study), it is assumed that some other mode of sedimentation (e.g., disaggregated ballistic settling) would control the sediment flux. For the turbulent shear flows discussed herein, Reynolds numbers were of the order 104. Based upon the assumption of fully turbulent flow, the production and dissipation rates of turbulent energy should balance, and at small scales local
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Fig. 3. Photographs (a)–(f) show the progression of mixing-induced CS during Experiment 4. Photographs were taken using a light sheet from below. The scales are in cm. Time shown coincides with the elapsed time since sediment-laden fluid began flowing over saline basin. The plumes shown generally propagated downwards at speeds between 1 and 2 cm/s.
isotropy applies. With this in mind, Kolmogorov’s universal equilibrium theory was applied to the buoyant flows we observed. The assumption of a fully turbulent flow was supported in the experiments by the appearance of a well-defined inertial subrange (a spectrum with 5/3 slope: Fig. 7) in all of the spectra we observed. There was also a strong linear relationship between the dissipation rate of turbulent energy e and surface-plume velocity U. At higher velocities,
the turbulent production due to shear in the water column is more pronounced. Because turbulentenergy dissipation must be compensated by production in a steady flow, dissipation in a free shear flow is equal to the product of the shear and the negative of the turbulent Reynolds stress (Tennekes and Lumley, 1972; Pope, 2000). The Reynolds stress did not vary dramatically because the flow velocities in the mixed layer were nearly constant.
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Fig. 4. Picture taken during Experiment 13, the lowest concentration experiment possible with the laboratory apparatus. The surface plume concentration was 380 mg/l and the surface velocity was approximately 9 cm/s. The scale is in cm. The plume shown fell with a speed of 1.4 cm/s.
4. Discussion 4.1. General comments Previously, it has been hypothesized that CS could not occur at sediment concentrations below 1000 mg/l (Parsons et al., 2001). Most rivers have suspended sediment concentrations less than 1000 mg/l. Therefore, it has been hypothesized that CS would be rare, with the only exception being active continental margins associated with small, steep coastal watersheds (Parsons et al., 2001). However, mixing-induced CS occurred at concentrations well below the 1000 mg/l concentration threshold set forth in earlier work (Fig. 5). Based upon these results, it is possible that mixinginduced CS might occur on many coasts, including those where the rivers are large and tectonic activity is diminished. During some experiments, a bottom nepheloid layer (BNL) began to form at the bed of the saline basin towards the end of the experiment (e.g., Fig. 6). In these cases, mixing-induced CS appeared to overload the bottom boundary layer quickly when plume fall rates exceeded 1 cm/s. In natural environments, this sediment could easily remain in suspension by turbulence induced by waves, as on the Eel margin (Traykovski et al., 2000), or flow
downslope as a gravity current, as on the northern Papua New Guinea margin (Kineke et al., 2000; Walsh and Nittrouer, 2003). The results reported in this paper were strictly from hypopycnal or surface flows where the initial condition and position of the two fluids were dynamically stable, so that the stratified interface was preserved. There were several experiments not reported in Table 1 where the incoming, sedimentladen flow became negatively buoyant or hyperpycnal. In general, sediment concentrations exceeding 6000 mg/l caused a large amount of sediment-laden fluid to enter the basin along the bed. These experiments produced divergent plumes with flows both on the surface and along the bottom of the saline basin. In the past, sediment concentrations greater than 35,000 mg/l have been expected to make a freshwater flow become hyperpycnal (Mulder and Syvitski, 1995). From a similar analysis of the static stability of our stratified layers, sediment loads near 12,000 mg/l would be required to form a hyperpycnal flow. Since our experiments only required half that amount, we speculate that intense turbulent mixing may lower the sediment concentration required to make a flow statically unstable. Further investigation is required to identify the quantitative limit of static stability. 4.2. Flow stability The flows modeled in the experiments were fully turbulent with respect to the Reynolds number calculations of the surface layer and by the presence of the 5/3 slope associated with the inertial subrange (Fig. 7). The shear-induced turbulence was produced by the confining geometry and the boundary layer generated by the flow constriction (Fig. 1). Internal waves often propagated along the pycnocline between the two fluids. These internal waves can be seen in the time series of density (Fig. 5a) and surface sediment concentration (Fig. 5b). Internal waves are an expected result of a free-shear flow between two fluids (Kundu, 1990), and are typical of estuaries and estuarine environments (Geyer and Smith, 1987). The Froude number throughout the water column
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Fig. 5. The time series of conductivity and sediment concentrations for Experiment 4. Concentrations are at 20, 10, 8, and 4 cm above the bed of the basin (cmab). The average concentration in the surface plume is 3700 mg/l. Initial, discrete CS plumes can be seen in the bottom panel. The bottom panel also shows a bottom nepheloid layer (BNL) of 250–500 mg/l forming towards the end of the experiment. Time is synchronized as in Fig. 4. Conductivity time series has been converted to excess fractional density. r is the density of the freshwater and rsalt is the density of the saltwater.
was always sub-critical (no hydraulic jumps or perturbations were observed). The bulk Richardson number of a mixed layer, a useful tool for the assessment of mixing and
dynamic stability, is typically defined by Ri ¼
g0 L ; DU 2
ð2Þ
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Fig. 6. (a) Plume mass concentration versus sediment flux. (b) Plume mass concentration versus sediment flux for both 7 and 15 cm/s plume velocities. (c) Surface-plume velocity U versus vertical sediment flux Q for two different sediment concentrations.
where L is the depth of the mixed layer, g0 is the reduced gravitational acceleration and DU is the velocity gradient across the mixed layer. The reduced gravitational acceleration was not varied in the experiments, while DU was proportional to the surface-layer velocity U. L was not measured directly; however, it can be estimated using the
measurement of the dissipation rate of turbulent energy e. Ivey and Imberger (1991) note that epU3/L, if production and dissipation approximately balance. The dissipation rate was linearly proportional to U, so therefore LpU2. If this proportionality is substituted into Eq. (2), we find that the Richardson number was most likely the same near-critical value for all of the experiments, which is consistent with areas of active mixing in natural environments (e.g., Geyer and Smith, 1987). Based upon the visual observations of the mixed-layer depth and the estimation of the bulk Richardson number cited above, the Richardson number for these flows (0.3–0.5) indicates that Kelvin–Hemholtz instabilities should not be present. From visual observation, it was evident that Kelvin–Hemholtz instabilities did occur intermittently along the pycnoline between the two fluids, and calculations of gradient Richardson numbers within the mixed layer must be at least temporarily below critical. Cuspate-shaped instabilities originating from Holmboe waves in the mixed layer were also identified in all experiments. Holmboe waves propagate along isopycnal surfaces and can be found in any fully turbulent flow with finite bulk Richardson number greater than the critical value (Smyth and Peltier, 1991). This is consistent with observations of natural systems dominated by
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4.3. Dimensional analysis Many processes contribute to the vertical flux of sediment from buoyant river plumes. It is intuitive that vertical sediment flux increase with increasing plume concentration (Figs. 7 and 8), but when mixing is taken into account this relation is not trivial. Dimensional analysis is useful in observing the relationship between many variables. There are nine dimensional variables associated with the experiments (in addition to the volumetric concentration, which is dimensionless). These variables are the density of the fluid (r), the density of the sediment (rs), gravity (g), the kinematic viscosity of the fluid (v), the surface plume velocity (U), the sediment-grain diameter (D), the buoyancy frequency (N), the sediment flux (Q), and the dissipation rate of turbulent energy (e). Using plume velocity, fluid density and viscosity as the repeating variables in the Buckingham Pi theorem, six dimensionless variables are capable of describing the flow. Among the six dimensionless variables obtained from the scale analysis are the relative density of the sediment, two Reynolds numbers (one defining the mixed-layer, the other relating to the particles) and a Grashof number (the product of a mixed1.4 1.2
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layer Reynolds and a Richardson number). Because of Reynolds similarity, the near-critical nature of the mixed layer, and the use of natural sediment, the remaining two dimensionless parameters should be related to one another and useful in predicting environmental sedimentation rates. The two remaining dimensionless variables are the dimensionless dissipation ev/U4 and the dimensionless vertical flux of sediment Q/rU . After an examination of the laboratory data, it was realized that the product of dimensionless dissipation and volumetric concentration were proportional to the dimensionless flux (Fig. 9). A simple model resulting from this relationship can be formed: Q CEv ¼ A 4 þ B; rU U
.14 .12
Model Observations (Hill et al., 2000)
.10 .08 .06 Disaggregated settling velocity
.04 .02 0 10-14
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ð3Þ
where A and B are empirical coefficients. In the limit of small sediment concentration (i.e., C-0), the vertical flux of sediment should vanish. In Eq. (3), this would suggest that the y-intercept should be zero (i.e, BE0). This common-sense limit is also consistent with our data.
Effective settling velocity (mm/s)
internal waves along isopycnal surfaces, which often exhibit Richardson numbers slightly above the critical value (Geyer and Smith, 1987).
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Model µ= 0.81 Field µ= 0.80 Floc settling speed ~ 1 mm/s
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Fig. 8. Dimensionless flux versus the product of the volumetric concentration and the dimensionless dissipation rate of turbulent energy for Experiments 11–20.
Fig. 9. Effective settling velocity versus the product of the dimensionless dissipation and the volumetric sediment concentration for conditions observed on the Eel River margin. Measured effective settling velocities were obtained from Table 2 of Hill et al. (2000). Modeled effective settling velocities are based upon Eq. (2) using the data (C, e, U) reported by Hill et al. (2000) and dividing Q by Cmass.
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4.4. Application to the Eel River margin The conditions of our experiments were designed to closely match the geometry of the Eel River plume. These conditions (e.g., isothermal, salinity differences on the order of 5–15 ppt, etc.) are typical of energetic continental margins. Surface-layer sediment concentrations in the experiments ranged from 400 to 6000 mg/l and represent realistic concentrations for oceanic flood conditions in small mountainous rivers. During the period of observations, the Eel River plume concentrations ranged from 900 to 2600 mg/l for winter storms in 1998 (Hill et al., 2000). Other rivers, like the Salinas River in Northern California have higher sediment loads (6000 mg/l: Johnson et al., 2001), while still others can have slightly lower concentrations (e.g., the Sepik River in Papua New Guinea, 300–400 mg/l: Kineke et al., 2000). Qualitative comparison of our experiments with the conditions observed indicate that mixinginduced CS might be important on all of these margins. Although our experiments are small compared to the mixed layers present in large river systems, the characteristic turbulence and velocities are realistic. In fact, the surface velocities reported in this paper correspond well with other natural flows. For instance, Ivey and Imberger (1991) reported wind-driven surface plumes that propagated at 12 cm/s. These natural stratified flows had measured dissipation rates that ranged from 103 to 104 cm2/s3, within the range of our experiments. It is important to note that the fluxes observed in the experiments were 10–50% higher than the flux estimates measured by Chen (1997) for double-diffusive sedimentation at the same sediment concentrations. At slower flow speeds, the flux estimates became more similar to the quiescent conditions examined in earlier studies (e.g., Parsons et al., 2001). The ability of turbulence to enhance the removal rate of sediment is a counterintuitive, but powerful finding. Hill et al. (2000) implicitly assumed that mixing within the plume was dominated by surface gravity waves in order to calculate dissipation rates within the Eel River plume. Using a simple drag law
(Large and Pond, 1981), they found that dissipation rates varied between 100 and 101 cm2/s3 in the Eel River plume. Using the plume sediment concentrations, dissipation rates and surface velocities reported by Hill et al. (2000), the sediment flux near the Eel River mouth based on our simple relationship varied between 7–50 103 mg/cm2/s. These flux calculations are roughly five times larger than those reported in our study due to the increased turbulent energy found on the continental margin. As a result, the increased turbulence found in oceanic surface layers may account for large sediment flux estimates observed in a variety of environments (e.g., Eel River margin, but also northern Papua New Guinea: Kineke et al., 2000; Walsh and Nittrouer, 2003). Effective settling velocities are usually reported in field studies to estimate clearance rates from surface plumes. The effective settling velocity of the sediment load in a river plume can be calculated by dividing the mass flux per unit area Q by the mass concentration in the plume Cmass. Using the flux Q calculated by Eq. (3), the mean effective settling velocities for oceanic-flood conditions on the Eel River during 1998 are found to be 0.085 mm/s with a range of 0.06–0.13 mm/s. The average effective settling velocity measured on the Eel River during this time period is 0.08 mm/s (Hill et al., 2000), with a range of 0.07 to 0.12 mm/s (Fig. 9). The Stokes settling velocity of disaggregated particles was significantly lower (0.04 mm/s). Hill et al. (2000) explained the enhanced flux (over and above Stokes settling of disaggregated particles) by a packaging of flocs, which was dependent on sediment concentration and floc-formation rates. Flocculated particles near the seabed on the Eel River margin generally settle at speeds on the order of 1 mm/s (Sternberg et al., 1999). More recently, a well-mixed and flocculated plume with disaggregated sediment resupply from the inner shelf or surf zone has also been proposed to account for the mix of flocs and disaggregated particles in the plume (Curran et al., 2002). However, in the absence of evidence to the contrary, mixing-induced convective sedimentation explains the removal rates observed, without appealing to external, unmeasured processes.
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5. Summary and conclusions There remains a controversy about what controls the sediment dynamics in a buoyant river plume. Our observations and analysis argue that sediment flux out of a buoyant river plume is predominately controlled by convective processes generated by shear-induced turbulence when the sediment load is significant and fine-grained. Our experiments used natural sediment, so that if flocculation were important (or present), it would be apparent in the experiments. The similarity of the results from the natural material used in this study (Table 1) and earlier investigations that used inorganic particles (carborundum powder: Maxworthy, 1999; crushed silica: Parsons et al., 2001) argues that, at least when concentrations are high, removal of sediment from buoyant plumes is not dependent on particle characteristics. Rather, on the time scale of all of the experiments, turbulent mixing and the convective plumes it generated regulated the transport of sediment out of the buoyant, sediment-laden flow. The vertical flux of sediment from buoyant river plumes is important for understanding sediment dispersal on continental margins. Mixing-induced CS was found to occur for surface plume concentrations smaller than previously observed (51000 mg/l). In addition, concentrations lower than expected (7000 mg/l) developed a divergent plume due to wholesale removal of sediment-laden fluid by local, intense areas of turbulent mixing. In all of these cases, the vertical flux of sediment from these flows is related predominantly to the dissipation rate of turbulent energy and volumetric sediment concentration. A simple scaling relationship is able to predict effective settling velocities observed in oceanic-flood events. In energetic environments, mixing-induced CS dominates the sediment transport in the vertical. In quiescent locales, less efficient modes of CS (e.g., leaking convection: Parsons et al., 2001) or individual particle settling may be more common. These results do not imply other processes are not important in natural river plumes. On the contrary, we conclude only that mixing-induced CS transports sediment from the mixed layer of a plume to the saline fluid below. Flocs can take part in this
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transport (i.e., transport is not particle dependent), as it is well known that sediment becomes flocculated by the time it reaches the seabed (Sternberg et al., 1999). It is possible that mixinginduced CS enhances floc formation by keeping fine particles together in vertically falling plumes. This increases the potential for particle collisions, while incorporating saline water, and ultimately forming larger flocs. Recent evidence would suggest that flocs would leave the vertically falling plume when the individual settling velocity of the floc exceeds the fall velocity of the plume (Bush et al., 2003); therefore leaving floc settling rates as a function of water-column turbulence rather than lithology. Existing models of river-plume sedimentation do not consider the interaction between particles and fluid turbulence. Jet models, common to most standard numerical studies, assume fully turbulent flow and the diffusion of fresh water and sediment is laterally dispersed through turbulent mixing with the surrounding fluid (e.g., Morehead and Syvitski, 1999). Settling velocity of individual particles is typically the only means by which material is transported in the vertical (i.e., turbulent mixing in the vertical is not incorporated into models). The interaction between sediment load and turbulent forcing is very dynamic. This study has incorporated the dynamics associated with these two forcing mechanisms to formulate a simple model based on sediment concentration and turbulent energy dissipation rate for typical oceanic-plume stratifications. These results may begin to explain the increased sediment flux found on many margins and should aid future sedimentdispersal modeling efforts.
Acknowledgements This research was supported by the US Office of Naval Research through the National Science and Education Graduate Fellowship and contracts N000140110922 and N000140110922. Sincere thanks are given to C. Nittrouer and A. Ogston for their assistance obtaining the cored sediments and comments improving an early draft of the manuscript. P. Hill, K. Curran, and M. Pehrup provided productive and valuable reviews.
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