Marine Geology 175 (2001) 25±45
www.elsevier.nl/locate/margeo
Effects of ambient currents and waves on gravity-driven sediment
transport on continental shelves
L.D. Wright*, C.T. Friedrichs, S.C. Kim, M.E. Scully
Virginia Institute of Marine Science, College of William and Mary, Gloucester Point, VA 23062, USA
Received 4 July 2000; accepted 1 February 2001
Abstract
Observations from several shelf environments show that down-slope gravity-driven transport may constitute an important
mode of suspended sediment dispersal across shelves and highlight the in¯uence of ambient waves and currents on gravityinduced sediment ¯ux. The phenomena discussed here involve high concentrations of suspended sediment mixed with seawater
and thus differ in genesis from hyperpycnal plumes released directly from sediment-laden rivers. The ®eld sites examined are
the Gulf of Bohai off the mouth of the Yellow River (Huanghe), the northern California shelf off the mouth of the Eel River, and
the Louisiana shelf west of the mouths of the Mississippi River. Off the Yellow River, rapid down-slope transport over distances
of a few km occurred when frictional resistance, induced by strong along shelf currents, was temporarily relaxed. More
prolonged down-slope motion over longer distances occurred following ¯oods of the Eel River, when wave and current
agitation provided turbulence to sustain gravity-driven transport of ¯uid mud. On the Louisiana inner shelf, the down-slope
gravity force was much weaker, but observations suggest that thin gravity ¯ows may still have occurred in the presence of
waves. A simple analytical theory is developed that incorporates the in¯uence of ambient shelf currents on gravity-driven
transport of suspended sediment. This theory is quantitatively consistent with the observations from the three sites. If the supply
of easily suspended sediment is less than the capacity of ambient currents (including waves) to carry sediment, then intense
turbulence limits gravity-induced sediment transport by increasing the drag at the base of the ¯ow. When ambient currents
abruptly cease, rapid down-slope transport can then occur over short distances until the sediment settles. Such ¯ows do not
remain intensely turbulent because the slope of the continental shelf is too gentle to induce shear instability within the gravity
¯ow. The maximum sustained rate of gravity-induced sediment transport occurs when ambient currents are strong, but the
supply of easily suspended sediment exceeds the resuspension capacity of the ambient currents. Feedback then leads to values
of the gradient Richardson number (Ri) within the ¯ow that are near the critical value of 1/4. This partially damps bottom drag,
but still allows the generation of suf®cient turbulence to maintain sediment in suspension. Observations also indicate systematic
relationships among Ri, the supply of easily suspended sediment and the bottom drag coef®cient acting on the gravity ¯ow.
q 2001 Elsevier Science B.V. All rights reserved.
Keywords: Bed stress; Fluid mud; Bottom boundary layer; Wave boundary layer; Turbidity current; Hyperpycnal ¯ows
1. Introduction
* Corresponding author. Tel.: 11-804-684-7103; fax: 11-804684-7009.
E-mail address: [email protected] (L.D. Wright).
Advection of ®ne sediments by positively buoyant
river plumes in coastal and shelf environments is
widely appreciated and has been the subject of numerous studies (see reviews by Wright, 1985; Wright and
0025-3227/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.
PII: S 0025-322 7(01)00140-2
26
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
Nittrouer, 1995). Emphasis has been placed more
recently on negatively buoyant plumes that discharge
directly from extremely turbid rivers with suspended
sediment mass concentrations exceeding that of ocean
salinity (Mulder and Syvitski, 1995; Mulder et al.,
1998; Imran and Syvitski, 2000). This paper focuses
on a third type of buoyancy-driven transport of
riverine sediment across continental shelves. In this
third scenario, ®ne sediment freshly delivered by
positively buoyant river plumes settles and is mixed
with seawater by ambient waves and currents before
moving down-slope under the in¯uence of gravity.
Gravity-driven, down-slope transport of mud
suspended in seawater has been documented off the
mouths of the Zaire (Eisma and Kalf, 1984), Yellow
(Wright et al., 1988, 1990), Amazon (Kineke et al.,
1996; Sternberg et al., 1996) and Eel Rivers (Ogsten
et al., 2000; Traykovski et al., 2000). Traykovski et al.
(2000) recently observed offshore transport of ¯uid
mud within the wave boundary layer on the northern
California shelf, and suggest that gravity-driven transport of ¯uid mud is the dominant mechanism for
delivering ®ne sediment from the Eel River to the
middle shelf. Observations of thin ¯uid mud layers
have only recently been made possible by new sensor
developments, and it is likely that gravity-driven
transport of ¯uid mud may be more common than
previously believed.
Although high-density turbid layers can be
expected to move down-slope when forces other
than negative buoyancy are negligible, such layers
may also be advected along-slope or even up-slope
by ambient current stresses and regional pressure
gradients (Wright et al., 1997, 1999). Ambient
currents may also retard down-slope movement of
negatively buoyant turbid layers by enhancing eddy
viscosity (Kineke et al., 1996). Conversely, high
sediment concentrations can damp shear-generated
turbulence and accelerate deposition of plume-borne
sediment. Results from the AMASSEDS program off
of the mouth of the Amazon River demonstrated that
sediment-induced stable strati®cation can induce a feedback cycle which can maintain the Richardson number
at its critical value of 1/4 and thereby limit the capacity
of the ¯ow to carry additional sediment (Trowbridge
and Kineke, 1994). Wright et al. (1999) and Friedrichs
et al. (2000) report similar results from observations off
the mouth of the Eel River in northern California.
In this paper, we synthesize ®eld results from three
dissimilar shelf environments where gravity-driven,
sediment-laden ¯ows appear, at least episodically, to
be important modes of sediment transport and sources
of deposition. These environments are directly in¯uenced by the proximity of major river mouths and in
all three examples, ®ne, river-borne sediments are
actively accumulating on the shelf. The examples
reported here also involve superimposition of waves
and tidal or wind-driven currents on the gravity forces
acting on near-bed turbid layers. The observed in¯uence of ambient shelf currents on these ¯ows motivates our application of a simple analytical theory to
gravity-driven suspensions, which accounts for the
additional mixing and drag that ambient currents
produce. The results of this modeling suggest that
the gentle slopes of most continental shelves preclude
auto-suspending turbidity currents and that suspension by externally forced currents is required to
sustain gravity currents on the mid-shelf. The
presence of ambient currents will enhance gravity
currents, as long the supply of easily suspended ®ne
sediment is not limited. If the sediment supply is
limited, turbulence generated by ambient currents
will increase bottom drag and lower the potential
rate of gravity-induced sediment transport. Rapid
but short-lived gravity ¯ows may then occur if ambient currents abruptly cease.
2. Theory
The down-slope, depth-integrated momentum
equation for a gravity-driven ¯ow for which the
balance is between bottom friction and the ¯ow's
sediment-induced pressure gradient is given by (e.g.
Parker et al., 1986; van Kessel and Kranenburg, 1996)
gs…sin u†
Zh
0
c 0 dz ˆ
tx
:
r
…1†
In Eq. (1), u is the across-shelf slope of the seabed, g
the acceleration of gravity, h the thickness of the ¯ow,
s the submerged weight of the sediment (,1.6 for
siliceous material in seawater), c 0 the sediment
volume concentration, t x bottom stress, r the depthaveraged density of the gravity ¯ow, and all terms are
wave-averaged. The above relation assumes the
wave-averaged gravity ¯ow to be approximately
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
27
Fig. 1. Schematic diagram of a steady, uniform, sediment-induced gravity current of thickness h and depth-varying concentration c 0 moving
across a continental shelf of slope u . The velocity scale (Umax) most relevant to shear and frictional resistance acting on the turbid layer is due to
a combination of wave orbital velocity (Uw), along-shelf current magnitude (vc) and the speed of the gravity current (ug).
uniform and steady and neglects drag from the
overlying ¯uid (Fig. 1).
A widely accepted formulation of wave-averaged
stress in a given direction, x, at the base of a bottom
boundary layer is the time-averaged quadratic formulation given by (e.g. Grant and Madsen, 1979; Feddersen et al., 2000)
D
E
…2†
tx ˆ r CD kul …u2 1 v2 †1=2 :
In Eq. (2), CD is a non-dimensional bottom drag
coef®cient, u and v are the instantaneous velocities
in x and y at the top of the bottom boundary layer,
and k l represents a time-average over many wave
periods. Combining Eqs. (1) and (2) yields
B sin u ˆ CD ug Umax ;
…3†
where ug ˆ kul; with x and ug positive down-slope,
B ˆ gs
Zh
0
c 0 dz
…4†
is the buoyancy anomaly integrated over the thickness
of the turbid layer (cf. Trowbridge and Kineke, 1994),
and
D
E
…5†
Umax ˆ …u2 1 v2 †1=2 :
If there are no waves or ambient currents other than
the gravity ¯ow itself contributing to Umax, then Eq.
(5) reduces to Umax ˆ ug, and Eq. (3) becomes the
classical Chezy equation
B sin u ˆ CD u2g
…6†
(e.g. Komar, 1977; van Kessel and Kranenburg,
1996; Traykovski et al., 2000). Applying Eq. (6),
Komar estimated that CD < 0.0035±0.0050 when
modeling auto-suspending turbidity currents in the
deep sea, while van Kessel and Kranenburg measured
CD < 0.003±0.006 in the laboratory for O(10 cm)
thick, turbulent gravity ¯ows. However, those formulations assume that gravity-induced ¯ow is the dominant source of near bed velocity and that gravity ¯ow
alone controls bottom drag and turbulence within the
gravity current.
Currents other than gravity ¯ows, such as tides,
waves and wind-driven ¯ows, are commonly the
dominant source of bottom stress on continental
shelves. In applying Eq. (3) to continental shelves, it
is appropriate to account for the contribution of the
total instantaneous velocity to Umax. It is important to
note that waves or an along-shore current can provide
the turbulence needed to support a gravity ¯ow
composed of suspended sediment (cf. Traykovski et
al., 2000) and simultaneously enhance the drag that
resists the down-slope movement of the turbid layer
(cf. Kineke et al., 1996). If waves are much stronger
than either ug or kvl; then Umax < Uw, where Uw is the
rms wave orbital velocity (cf. Grant and Madsen,
1979). If waves are insigni®cant, but along-shelf
28
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
currents are much stronger than ug, then Umax < vc,
where vc is the magnitude of the along-shelf current,
typically due to tides or wind. The simplest approximation for Umax that accounts for all three potential
contributions is then
Umax ù …Uw2 1 u2g 1 v2c †1=2
…7†
(see Fig. 1). Clearly a more sophisticated formulation
for Umax that accounts for the angle between currents
and waves would be slightly more accurate. (Note that
Umax will still be a scalar, whether or not one accounts
explicitly for wave angle.) However, the goal here is
to apply the simplest possible model that roughly
accounts for the lowest order physical processes.
The gradient Richardson number, Ri, is a key scale
for determining whether or not the shear within a
strati®ed layer will generate instabilities. Ri indicates
the importance of the buoyancy restoring force relative to the tendency of shear to increase the size of
interfacial waves. For the case of strati®cation
induced by suspended sediment, the gradient Richardson number is given by
Ri ù gs
…2c 0 =2z†
:
…2u=2z†2
…8†
Both theory (e.g. Howard, 1961; Turner, 1973) and
observations (e.g. Scotti and Corcos, 1972; Eriksen,
1978) indicate that in strati®ed shear with Ri & 1/4,
Kelvin±Helmholtz instabilities enhance turbulence,
whereas for Ri * 1/4, internal waves do not generally
become unstable. Additional work (e.g. Kundu, 1981;
Trowbridge, 1992) indicates that in strati®ed boundary layers, the overall level of turbulence is typically
dominated by the presence or absence of shear
instability, such that turbulent intensity is effectively
scaled by the gradient Richardson number rather than
the Reynolds number. Furthermore, the level of turbulence in strati®ed boundary layers often self-adjusts in
the presence of shear causing Ri to remain nearly
equal to a critical value, Ricr (Kranenburg, 1984;
Trowbridge, 1992; Trowbridge and Kineke, 1994).
Trowbridge and Kineke (1994) applied the
constraint of a constant Ri to ¯uid mud layers near
the mouth of the Amazon and showed that the gradient Richardson number throughout these highly turbid
boundary layers is scaled by
Ri ù gs
…2c 0 =2z†
…B=h2 †
B
ù
ù 2 :
…2u=2z†2
…Umax =h†2
Umax
…9†
The scaling applied in Eq. (9) will be a reasonable
representation of the gradient Richardson number
within a gravity-driven turbid ¯ow only if strati®cation extends through most of the layer thickness. This
implies that recent mixing has occurred between the
gravity ¯ow and the overlying water column. In other
words, this scaling may not hold for mud¯ows, which
originate from submarine slides and have not mixed
appreciably with the overlying water column (e.g.
Huang and Garcia, 1999).
For the case of strati®ed gravity ¯ows in which
Umax ˆ ug (i.e. with no signi®cant external source of
shear due to ambient currents such as tides or waves),Eqs. (6) and (9) can be combined to yield
Ri ù
CD
:
sin u
…10†
In other words, the gradient Richardson number of a
strati®ed, turbid gravity ¯ow (obeying the balance in
Eq. (1)) is, at lowest order, a function only of the
bottom drag coef®cient and the slope of the bottom
(van Kessel and Kranenburg, 1996, present a similar
asymptote). Assuming the gradient Richardson
number required for maintenance of shear-generated
turbulence is less than or equal to Ricr < 1/4 and
CD < 0.003, then sea beds with sin u . 0.012
(equivalent to 0.78) may be able to maintain intensely
turbulent gravity currents of this type through autosuspension, whereas sea beds with sin u , 0.012 will
not. Seaward of the shoreface, continental shelves
generally slope at angles less than 0.78. Thus, without
the existence of an external source of turbulence,
gravity-induced transport of suspended sediment on
most shelves should be short-lived and travel limited
distances.
Following the above logic, the maximum sustainable ¯ux of suspended sediment associated with
gravity-driven ¯ow across the continental shelf will
occur when there is an external source of turbulence
(Umax . ug), but on the condition suf®cient sediment is
available to allow Ri < Ricr. Rearranging Eq. (9)
yields the maximum sustainable (or `critical')
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
suspended sediment load
2
Bcr ù Ricr Umax
:
…11†
Combining Eqs. (3) and (11) yields
ugcr ù
…sin u†Ricr Umax
CD
…12†
and the maximum sustainable sediment ¯ux associated with the gravity-driven ¯ow is
Qcr ù
3
ucr rs Bcr
r …sin u†Ri2cr Umax
ù s
;
gs
gsCD
…13†
where r s < 2.65 is the density of siliceous sediment.
Gravity-driven sediment ¯ux will continue to grow
rapidly with Umax as long as the supply of easily
suspended sediment is not exhausted. This is because,
under conditions of unlimited sediment supply, the
down-slope pressure gradient in Eq. (3) associated
with greater suspension grows geometrically with
Umax, while frictional resistance to the down-slope
¯ow only increases linearly. Assuming easily
suspended sediment and Umax . ug, feedback will
keep Ri < Ricr (cf. Trowbridge and Kineke, 1994;
Friedrichs et al., 2000). If Umax increases, Ri will
drop below Ricr, and enhanced turbulence will
suspend more sediment, returning Ri to Ricr; if Umax
decreases, Ri will increase above Ricr, and damping of
turbulence will cause sediment to settle out of the
turbid layer, reducing Ri back towards Ricr.
Stronger ambient currents will eventually cause
gravity-induced sediment ¯ux to decrease under
conditions of limited sediment supply. If B increases
more slowly than Umax, Eq. (3) indicates that enhanced
quadratic drag will cause ug to decrease. Ri will drop
according to Eq. (9), causing turbulence within the
turbid boundary layer to become more intense. CD is
then expected to rise, further decreasing ug and Q.
Under conditions of limited sediment supply, rapid
(but short-lived) down-slope movement of suspended
sediment may then occur when ambient currents
abruptly cease. An example would be the relaxation
of wave energy or the arrival of tidal slack water. As
Umax drops to ug, B may temporarily remain large
since high concentrations of ®ne sediment can take
several hours to settle. Then Ri will increase to B/ug2
and CD will decrease following Eq. (10). The classical
relation given by Eq. (6) would then apply, but with a
29
depressed drag coef®cient. The gentle slope of the
continental shelf would prevent intense shear-induced
turbulence within the gravity ¯ow, and the bulk of the
suspension would presumably settle within a few
hours or less, depending on the initial thickness of
the layer. The above arguments regarding the drag
coef®cient assume that the effective viscosity of the
suspension decreases as turbulence is damped. At
suf®ciently high concentrations (,300 kg m 23),
molecular viscosity under laminar ¯ow can exceed
the eddy viscosity of lower concentration gravity
¯ows (van Kessel and Kranenburg, 1996).
The theoretical discussion to this point has assumed
the lowest order across-shelf momentum balance
within the gravity ¯ow to be between bottom friction
and the down-slope pressure gradient associated with
the turbid layer itself. For this to be the case, the
sediment-induced pressure gradient must overwhelm
the across-shelf acceleration of the wave-averaged
current, the Coriolis response to the along-shelf
current, across-shelf frictional drag at the top of the
turbid layer, and larger scale across-shelf pressure
gradients caused by tides, wind set-up or regional
density gradients. If depth-integrated buoyancy is
held constant, these other forces are more likely to
overwhelm gravity-induced motion as the slope of
the shelf decreases or the thickness of the turbid
layer increases.
3. Field examples
The observations on which this paper is based were
obtained over the last 15 years from contrasting ®eld
sites. Except in the Gulf of Bohai, ®eld observations
were made using instrumented tripod systems. The
bottom-boundary-layer instrumentation consisted of
tetrapod or tripod frames supporting sonar altimeters,
arrays of electromagnetic Marsh McBirney current
sensors and optical backscatter (OBS) sensors to
obtain measurements of suspended sediment concentration. In addition, the tripod data reported by Traykovski et al. (2000) included transducers that recorded
acoustic backscatter (ABS) at 1 cm intervals over the
lowest meter of the water column. OBS and ABS
sensors were calibrated using either local bed sediment or, if possible, local suspended material captured
in sediment traps.
30
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
Fig. 2. Location map of Gulf of Bohai and Yellow River (Huanghe) mouth.
3.1. The Yellow River subaqueous Delta/Gulf of Bohai
The Yellow (Huanghe) River mouth in the Gulf of
Bohai (Fig. 2) is widely recognized for discharging
high suspended sediment concentrations, and this
system is presented here as a benchmark example of
suspension-induced gravity ¯ow.Wright et al. (1988,
1990) have discussed the behavior of highly turbid
benthic layers observed off the mouth of the Yellow
River over three ®eld seasons in 1985, 1986 and 1987.
This system has been amply described in the literature
(e.g. Prior et al., 1986; Wiseman et al., 1986; Wright
et al., 1990) so the details are omitted here. From the
perspective of this paper, the important characteristics
are listed in Table 1 and summarized below.
Within the weakly con®ned mouths of the Yellow
River, high suspended concentrations are known to
occur; these concentrations can reach 200 kg m 23
during river ¯oods. However, our data were obtained
from sites upcoast and downcoast from the point
sources. Redistribution of moderately concentrated
suspended sediment along the coast was affected by
strong reversing semidiurnal tidal currents, which
attained speeds on the order of 1 m s 21.Wright et al.
(1988, 1990) credited these same currents with mixing
river and Bohai waters and maintaining sediment in
suspension. The currents must also be a major source
of eddy viscosity and enhanced bottom drag. As a
result of the mixing, the sediment suspension surrounding the delta had a salinity-induced density anomaly of
14±15 kg m 23. Under fair-weather (i.e. tide-dominated) conditions during summer high-river-¯ow
conditions, suspended sediment contributed another
5±10 kg m 23 to the suspension's bulk density, thereby
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
31
Table 1
Benthic turbid layer characteristics, Gulf of Bohai summer 1986, depth ˆ 5 m, sin u ˆ 0.005
ug (cm s 21)
vc (cm s 21)
Uw (cm s 21)
Umax (cm s 21)
B (m 2 s 22)
H (m)
Ri
CD
C (kg m 23)
Q (kg m 21 s 21)
Maximum ¯ood tide
Slack water after ¯ood
Maximum ebb tide
10
70
0
71
0.021
3.0
0.15
0.0052
4.0
1.2
40
15
0
43
0.033
1.5
0.40
0.0021
8.0
4.8
10
75
0
76
0.092
2.0
0.11
0.0040
5.0
1.0
creating the observed negative buoyancy relative to the
surrounding low-turbidity water, which had a typical
density of 1016±1017 kg m 23.
Fig. 3 shows time series of suspended sediment
concentration pro®les, isobath-parallel ¯uxes and
across-isobath ¯uxes as observed in summer 1986
(Wright et al., 1990). Fig. 3 is particularly instructive
with regard to the relationship between along-isobath
currents and gravity-induced sediment transport.
Speci®cally, down-slope transport was suppressed
during times of maximum tidal currents, which ¯owed
parallel to isobaths. The thickest and most turbid
layers were observed after the maximum ¯ood-tide
currents. The maximum gravity-induced down-slope
sediment ¯uxes were centered on the slack after ¯ood.
No corresponding gravity ¯ows prevailed at the slack
after ebb.
The higher total eddy viscosity and drag associated
with the strong tidal ¯ows would have retarded downslope response to the sediment-induced pressuregradient force even though that force and the stresses
induced by tidal currents were mutually orthogonal
and not in direct opposition. We can infer that,
through resuspension, strong tidal ¯ows near high
tide added sediment to highly turbid layers overlying
tidal ¯ats, and these turbid layers then pulsed down
slope at the ensuing slack water when Umax was at a
minimum, consistent with Eq. (3). Currents near low
tide would not have impinged directly on the ¯ats, and
this is presumably why we did not observe turbid
conditions at the slack after low water. Thus, the
sediment-induced gravity ¯ows pulsed at diurnal
rather than semi-diurnal frequencies. Time-series
observations over the 5 m isobath in summer 1986
revealed that down-slope ¯ow velocities, ug,
associated with the turbid layers ranged from 5 to
40 cm s 21 and averaged 15 cm s 21.
Wright et al. (1986, 1988, 1990) showed that, when
operating, the gravity ¯ows exhibited internal waves
at frequencies close to the Brunt-Vaisala frequency
and concluded that these waves enhanced momentum
exchange between the turbid ¯ows and ambient
waters and contributed to extinction of the under¯ows. Based on the theory presented here, we also
conclude that the slack water gravity ¯ows were
constrained to have Ri , 1/4 because of the slope of
the shelf. Therefore, the gravity ¯ows would have
been unable to sustain themselves through autosuspension brought about by shear-generated
turbulence. Wright et al. (1988) showed a downslope acoustic pro®le of a turbid layer measured in
summer 1986 with a 200 kHz echo sounder. The
layer became progressively thinner seaward, until
vanishing altogether, over a cross-slope distance of
about 8 km.
Table 1 summarizes properties of the highly turbid
layers in Fig. 3 evaluated at maximum ¯ood tide,
slack after ¯ood, and maximum ebb tide, where ug
and vc are the across- and along-shelf components of
velocity near the top of the turbid layer, Uw is wave
orbital velocity, Umax ˆ …u2g 1 v2c 1 Uw2 †1=2 ; C is
observed mass concentration averaged over the layer
thickness (h), and Q is across-shelf sediment ¯ux
integrated over h. B and Ri are calculated directly
from observations using Eqs. (4) and (9), while CD
is estimated indirectly based on Eq. (3). The slope
(sin u ) of the Bohai shelf in the vicinity of the
observed gravity currents was 0.005. From the
32
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
`classical' Chezy approach (i.e. Eq. (6)) with
CD < 0.004, one would expect ug < 16 cm s 21 at
peak ¯ood tide, ug < 20 cm s 21 at slack, and
ug < 30 cm s 21 at peak ebb. For the Gulf of Bohai
data set, this over-predicts observed ug during peak
tidal currents and under-predicts ug at slack. This is
because the classical approach misrepresents
sediment-induced gravity ¯ows on shelves in two
ways: (1) it does not account for the role of the
along-shelf current in increasing bottom drag on
the across-shelf ¯ow; and (2) it does not account for
the effect of varying Ri on turbulence and CD.
Based on the analytical theory presented in the
Section 3, we interpret the dynamics of the gravity
¯ows in Fig. 3 as follows. During peak ¯ood and
peak ebb, the capacity of the strong along-shelf tidal
currents to suspend sediment was greater than the
available supply of easily suspended ®ne sediment.
Thus Ri within the turbid layer was below 1/4,
velocities within the layer were intensely turbulent,
and CD was ,0.004±0.005, similar to the value of
CD used in modeling highly turbulent gravity currents
in the deep sea (Komar, 1977). The strong along-shelf
velocity, intense turbulence and relatively high CD
value caused a large quadratic drag to be associated
with a relatively weak down-slope gravity ¯ow. At
slack after ¯ood, the ambient current dropped more
quickly than B, causing Ri to climb above 1/4, damp
turbulence, and reduce CD by 50%. The decrease in
quadratic stress allowed the negatively buoyant layer
to move rapidly down slope. The gentle slope of the
continental shelf combined with strong strati®cation
in the lower layer severely damped turbulence, and
the suspension settled as it moved offshore.
3.2. The Eel River Shelf, northern California
Fig. 3. Time series of (a) current speed; (b) suspended sediment
concentration; and (c) suspended sediment ¯ux as observed off
the mouth of the Yellow River (Huanghe) in summer of 1986
(Wright et al., 1990).
The Eel River drains a relatively small (9500 km 2)
basin in the northern California Coastal Range. It has
the largest annual yield of any river of comparable or
larger basin-size in the conterminous United States
(Brown and Ritter, 1971). Its discharge is episodic
on both inter- and intra-annual time scales, with
nearly all of the discharge occurring in association
with large winter storms and thus coinciding with
high waves and strong wind-driven currents. Wheatcroft (2000) describes such ¯ood situations as
`oceanic ¯oods'. The continental shelf adjacent to
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
33
Fig. 4. Map of Eel River site showing location of tripod data from deployment 1 (VIMS, Wright et al., 1999), deployment 2 (UW, Ogston et al.,
2000), and deployment 3 (WHOI, Traykovski et al., 2000).
the Eel River (Fig. 4) is rapidly accumulating ®ne
sediment in the presence of strong and frequent
agitation by waves (Nittrouer, 1999; Sommer®eld
and Nittrouer, 1999). Geological investigations as
part of the STRATAFORM program (Wheatcroft et
al., 1996, 1997; Drake, 1999; Sommer®eld and
Nittrouer, 1999) reveal that following signi®cant
¯oods, ®ne grained sediment accumulates in a distinct
¯ood deposit centered near the 70 m isobath and
extending over 30 km along-shelf and 8 km acrossshelf. Recent work suggests that much of the sediment
from the plume initially settles near shore before
moving offshore to the region of the ¯ood deposit
(Traykovski et al., 2000; Ogsten et al., 2000; Geyer
et al., 2000).
Bottom-boundary layer velocity and suspended
sediment concentration pro®les were measured with
instrumented tripods in the vicinity of the 60 m
isobath on this shelf (where sin u < 0.005) during
winter 1995±1996 (Wright et al., 1999), winter
1996±1997 (Ogston et al., 2000), and winter 1997±
1998 (Traykovski et al., 2000). These observation
periods are hereafter referred to as deployments 1, 2
and 3. Peak Eel River discharge was 2000 m 3 s 21
during deployment 1, 10,000 m 3 s 21 during deployment 2 and 5000 m 3 s s 21 during deployment 3,
qualifying the latter two as `¯ood years'. Maximum
rms wave orbital velocities at the 60 m isobath during
storms that coincided with the ¯oods during deployments 2 and 3 were on the order of 40 cm s 21 and
75 cm s 21, respectively. During the ®rst deployment,
the value at 60 m was about 40 cm s 21. (Near-bed
orbital velocity during deployments 2 and 3 is based
on a frequency- and depth-dependent transformation
34
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
Table 2
Benthic turbid layer characteristics, Eel River Shelf, 1996, 1997 and 1998, depth ˆ 60 m, sin u ˆ 0.005
ug (cm s 21)
vc (cm s 21)
Uw (cm s 21)
Umax (cm s 21)
B (m 2 s 22)
h (m)
Ri
CD
C (kg m 23)
Q (kg m 21 s 21)
Deployment #1
February 1996
S60
Deployment #2
1 January 1997
S60
Deployment #3
19-20 January 1998
K60
6
12
37
39
0.028
0.07
0.18
0.0057
75
0.29
17
13
29
36
0.033
0.05
0.25
0.0026
110
0.93
20
16
55
61
0.092
0.10
0.25
0.0038
150
3.0
of coincident NOS surface buoy data. Orbital velocities during deployment 1 were reported by Wright et
al., 1999.) During all three years, net offshore
transport of ®ne sediment was observed at 60 m
during storm events, consistent with geological
observations. Additional characteristics of these
storm events are summarized in Table 2.
During the two ¯ood years, Ogston et al. (2000) and
Traykovski et al. (2000) concluded that the majority
of across-shelf sediment ¯ux occurred in near-bed
gravity ¯ows of ¯uid mud (.10 kg m 23). Evidence
for near-bed gravity-driven transport in each of the
¯ood years included an increase in the down-slope
component of wave-averaged velocity toward the
bed (Fig. 5a). During both of these winters, a clear
increase in offshore ¯ow between the lowest two
current meters coincided with the period of strongest
waves within the duration of the ¯ood, suggesting that
waves played a key role in both suspending and
sustaining the thin gravity ¯ows (Traykovski et al.,
2000). In addition to measuring offshore ¯ow,
Traykovski et al. (2000) deployed acoustic backscatter sensors that documented the simultaneous
presence of a near-bed ¯uid mud layer about 10 cm
thick which scaled with the height of the wave boundary layer.
Fig. 5a shows the average across shelf current
reported by Ogston et al. (2000) and Traykovski et
al. (2000) as recorded at their lowest two current
meters during periods of presumed gravity ¯ow within
the wave boundary layer. Based on a spline-®t,
Traykovski et al. (2000) estimated the change in
velocity between the top of the wave boundary layer
and the current meter at 50 cm to be about the same as
that observed between 50 and 110 cm. This yields an
average offshore velocity of ug < 20 cm s 21 at the top
of the wave boundary layer for the most sustained
gravity current during deployment 3 (which occurred
between Julian day 19±20-7-1998). Using the results
of Traykovski et al. (2000) to scale the hyperpycnal
layer thickness proportional to Uw suggests h < 5 cm
during the deployment 2 event. A proportional shear
applied to the gravity current associated with deployment 2 (which occurred throughout 1 January 1997)
then yields an average offshore velocity at the top of
the wave boundary layer of about 17 cm s 21. The drag
coef®cient during each of these events can then be
estimated by setting Umax ˆ …u2g 1 v2c 1 Uw2 †1=2 and
assuming that the wave boundary layer is holding its
maximum sustainable load (Table 2). With Ricr ˆ 1/4,
Eq. (12) then gives CD ˆ 0.0026 and 0.0038 for the
deployment 2 and 3 gravity ¯ows, respectively
(utilizing event-averaged values for ug, Uw, vc, etc.).
Acoustic backscatter data indicate that the ¯uid
mud, which was con®ned to the wave boundary
layer during the deployment 3 event, was about
10 cm thick (Traykovski et al., 2000). Above the
wave boundary layer, suspended sediment concentration was observed to rapidly decrease with elevation.
Fig. 5b displays average concentrations at 30 and
100 cm above the bed for 1 January 1997 from Ogston
et al. (2000) and an example ABS pro®le observed on
20 January 1998 by Traykovski et al. (2000).
Traykovski et al. could not precisely resolve the
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
35
Fig. 5. Pro®les of (a) across-shelf velocity and (b) suspended sediment concentration at the 60 m isobath on the northern California shelf under
high waves during Eel River ¯oods on 1 January 1997 (Ogston et al., 2000) and 20 January 1998 (Traykovski et al., 2000). January 1998
concentrations are near continuous ABS measurements; otherwise o is the data from sensors and x is the extrapolation to top of wave boundary
layer.
concentration within the wave boundary layer because
of attenuation of the acoustic signal. The depth-averaged concentration for the wave boundary layer is
predicted by Eq. (11) to have been about 110 and
150 kg m 23 for these two cases, respectively.
Thus a consistent story is emerging: sustained
gravity ¯ows can occur on continental shelves when
the supply of ®ne sediment exceeds the suspension
capacity of ambient currents. Under these conditions,
feedback among turbulence, resuspension and
sediment-induced strati®cation favors a gradient
Richardson number of 1/4. This allows the velocity
36
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
within the gravity current to remain near the transition
to intense shear-generated turbulence. The resulting
drag coef®cient is then intermediate between the
weakly and intensely turbulent cases observed off
the Yellow River. Proper estimation of the buoyancy
anomaly within the wave boundary layer requires
inclusion of ambient currents in the drag formulation.
Ogston et al. (2000) and Traykovski et al. (2000) used
the classical relation of Eq. (6) to infer B within the
wave boundary layer, neglecting Umax. The smaller
drag based on consideration of ug alone only requires
a weaker balancing pressure gradient and results in
lower estimates of suspended sediment concentration.
With CD < 0.003, ug < 20 cm s 21 and h < 10 cm, the
classical approach in Eq. (6) predicts a depthaveraged concentration in the wave boundary layer
of 40 kg m 23, which is similar to the results of Ogston
et al. (2000) and Traykovski et al. (2000), but signi®cantly less than the concentrations inferred here. As a
consequence, the theory applied here predicts higher
overall rates of sediment ¯ux and a more rapid
accumulation of mid-shelf ¯ood deposits.
Re-examination of our data from non-¯ood conditions in deployment 1 suggests that near-bed gravity
¯ows may also have occurred at that time. The tripod
used in deployment 1 had a ®ner near-bed resolution
of the velocity pro®le than the 60 m tripods in deployment 2 or 3, with current meters and OBSs paired at
heights of approximately 10, 40, 70 and 100 cm.
Based on those data, Friedrichs et al. (2000) showed
that strong waves during deployment 1 caused the
wave-averaged gradient Richardson number at
elevations between 10 and 40 cm to be close to the
critical value of 1/4 and also caused the pro®le of the
mean current (which was predominantly along-shelf)
to be nearly logarithmic. Friedrichs et al. (2000)
hypothesized that waves during deployment 1 resuspended ®ne sediment within the wave boundary layer
to concentrations approaching ¯uid mud, and the
strong concentration gradient at the top of the wave
boundary layer provided the boundary condition
needed to maintain Ri < 1/4 at the base of the
overlying current boundary layer. Fig. 6 displays
wave-averaged pro®les of across-shelf velocity and
suspended sediment concentration during deployment
1 for the four bursts with strongest wave orbital velocities, which also exhibited Ri < 1/4 between 10 and
40 cm above the bed. For these bursts, wave-averaged
velocity at the top of the wave boundary layer is
estimated by logarithmically extrapolating the shear
observed between 10 and 40 cm down to 6 cm. (A
logarithmic extrapolation was not possible using the
deployment 2 and 3 velocity data because the higher
elevation, more widely spaced current meters did not
resolve a log-layer immediately above the wave
boundary layer.)
Extrapolations of the high wave cases with Ri < 1/4
in the current boundary layer during deployment 1
suggest that offshore directed ¯ow at the top of the
wave boundary layer was consistent with thin near
bed gravity ¯ows. However, the average velocity of
about 5 cm s 21 is signi®cantly less than that estimated
for weaker waves during the ¯ood of deployment 2. A
limited supply of easily suspended sediment would
explain the weaker offshore velocity during deployment 1. During this non-¯ood year, the muddy
sediment on the Eel shelf was presumably more
consolidated and bed stresses were too weak to
erode a suf®cient amount to overwhelm the suspension capacity of the wave boundary layer. Under these
conditions, the wave boundary layer should have
remained intensely turbulent and the enhanced
viscosity and drag of intensely turbulent ambient
currents should have limited the velocity of the gravity current. To maintain consistency with the results
from deployments 2 and 3 as well as data from the
Gulf of Bohai, we also expect to ®nd Ri , 1/4 and
CD $ 0.004.
A reasonable estimate of CD during deployment 1
can be derived from the literature by assuming the
wave boundary layer to have been only weakly strati®ed. Under these conditions, the wave friction factor
( fw) of Swart (1974) can be applied:
CD ˆ fw =2 ˆ 0:5 exp‰5:213…kb v=Uw †0:194 2 5:977Š;
…14†
where v is wave radian frequency and kb is bottom
roughness. Based on photographic pro®les of the sediment water interface, Cutter and Diaz (2000) reported
a mean rms roughness of 3.2 mm for the muddy Eel
Shelf between the 60 and 64 m isobaths in late fall
1995. Because those images were taken before the
onset of winter storms, Cutter and Diaz (2000)
suggested that roughness would likely diminish as
wave action ®lled in the O(3 mm) biogenic pits. In
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
37
Fig. 6. Pro®les of (a) across-shelf velocity and (b) suspended sediment concentration at the 60 m isobath on the northern California shelf under
high waves during an Eel River non-¯ood year, February 1996 (Wright et al., 1999). o is the data from sensors and x is the extrapolation to top
of wave boundary layer.
the absence of these pits, the sand-sized (,0.3 mm),
biologically cemented aggregates forming the surface
layer at this depth (Cutter and Diaz, 2000) are a
logical lower-limit for bottom roughness. With an
upper limit of 3.2 mm and a lower limit of 0.3 mm,
the average drag coef®cient resulting from Eq. (14)
for 14 s waves is 0.0057. B and Ri within the wave
boundary layer are then given by Eqs. (3) and (9) to be
about 0.028 m 2 s 22 and 0.18. The above value for CD
is somewhat higher than that inferred for lower Ri
values on the Bohai shelf and re¯ects the expected,
albeit weak, inverse relationship between CD and total
layer thickness.
For unstrati®ed conditions, wave boundary layer
thickness is given by
dw ˆ
fw
8
1=2
Uw
v
…15†
38
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
Fig. 7. Location map showing instrument sites on the Louisiana shelf.
(e.g. Wiberg and Smith, 1983). Parameters for strong
wave events during deployment 1 then predict
dw ˆ 3 cm which seems surprisingly thin given the
acoustic backscatter observations of Traykovski et al.
(2000). Further inspection reveals that Eqs. (14) and
(15) are inconsistent with the gravity ¯ows which
Traykovski et al. simultaneously characterized using
relatively small CD and relatively large d w. Traykovski
et al. used Eqs. (14) and (15) with kb < 6 cm to characterize d w < 10 cm as observed during deployment 3.
However, doing so requires CD < 0.02, which is much
too large to allow rapid gravity ¯ows. If one applies an
appropriate value for CD, wave action must be capable of
suspending ¯uid mud signi®cantly higher than the thickness of the wave boundary layer as predicted by Eq.
(15). Scaling d w , Uw consistent with d w < 10 cm for
Uw < 55 cm s 21 yields d w < 7 cm during deployment 1
at which time the depth-averaged concentration in the
wave boundary layer wave would have been about
75 kg m 23.
3.3. The Louisiana inner shelf
Fine sediments discharged from the Mississippi and
Atchafalaya River mouths are rapidly accumulating
on the inner continental shelf off coastal Louisiana
(Wright and Nittrouer, 1995). The slope of the inner
shelf here is very gentle, with sin u < 0.0005 an order
of magnitude smaller than that off the Yellow or Eel
Rivers. Wave energy off Louisiana is low most of the
time and currents associated with the 40 cm diurnal
tides are weak. Mud accumulation is thus favored by
the combination of nearby major ¯uvial sediment
sources and low benthic energy; near-bottom currents
are usually too weak to resuspend sediments (Wright
and Nittrouer, 1995; Wright et al., 1997). Wright et al.
(1997) measured bottom boundary layer processes in
spring and summer 1993 at the site shown in Fig. 7.
During the spring 1993 deployment, a two-phase
event of high turbidity was observed (Wright et al.,
1997; Friedrichs et al., 2000). The ®rst `thin layer'
phase was characterized by moderate waves and
suspended sediment concentration pro®les that
decreased rapidly with elevation from ,1 kg m 23 at
z ˆ 23 cm to ,0.1 kg m 23 at z ˆ 113 cm (Fig. 8). The
second phase was marked by a decrease in wave orbital velocity and a pronounced increase in suspended
sediment concentration, which exceeded 1 kg m 23 at
each of the OBS sensors (Fig. 9).
The rms orbital velocity of 13 cm s 21 documented
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
39
Fig. 8. Pro®les of (a) across-shelf velocity and (b) suspended sediment concentration at the 20 m isobath on the Louisiana shelf during the
moderate wave, thin turbid layer event, summer 1993 (Wright et al., 1997; Friedrichs et al., 2000). o is the data from sensors and x is the
extrapolation to top of wave boundary layer. In (b), the upper two OBS sensors returned minimal response during these bursts, and concentrations were set to an assumed background of 0.020 kg m 23.
during the thin layer phase was the highest observed
during any of the deployments on the Louisiana shelf.
The rapid decrease in concentration with elevation at
this time was qualitatively similar to that above the
wave boundary layer during storms on the Eel River
shelf. This suggests the possibility that ¯uid mud was
also present in the wave boundary layer of the Louisiana shelf. Fig. 8a displays across-shelf velocity
40
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
Fig. 9. Pro®les of (a) across-shelf velocity and (b) suspended sediment concentration at the 20 m isobath on the Louisiana shelf during the low
wave, thick turbid layer event, summer 1993 (Wright et al., 1997; Friedrichs et al., 2000). o is the data from sensors and x is the extrapolation to
top of wave boundary layer. In (b), the OBS sensor at 30 cm may have been poorly calibrated for high concentrations.
pro®les from the ®rst four bursts within the thin layer
event de®ned by Friedrichs et al. (2000), which
included the strongest waves during the entire deployment. The across-shelf current in Fig. 8a is extrapolated down to the top of the wave boundary layer as in
Fig. 6a. (Friedrichs et al. (2000) found the overall
speed of the predominantly along-shelf current to be
generally logarithmic during this event.) This
extrapolation is highly speculative given the accuracy
of EMCMs and the questionable logarithmic assumption. Nevertheless, this extrapolation yields an
average down-slope velocity at the top of the wave
boundary layer of ,0.5 cm s 21. Friedrichs et al.
(2000) found Ri in the current boundary layer to be
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
above critical during this event, suggesting that
settling occurred in the current boundary layer and
thus an abundant supply of easily suspended sediment
was probably available in the wave boundary layer. If
one assumes that the wave boundary layer was carrying suspended sediment at maximum capacity and
that Ri < 1/4, then with Umax < 12 cm s 21, Eq. (6)
gives B < 0.0036. Assuming d w to be proportional
to Uw, it is inferred that h < 2 cm and the depthaveraged concentration within the wave boundary
layer was ,30 kg m 23. With sin u < 0.0005 and
ug < 0.6 cm s 21, Eq. (4) gives CD < 0.0031; this
falls between the two critical Ri cases from the Eel
River shelf.
During the `thick' phase of the turbidity event,
which occurred after the wave height decreased, the
high concentration layer extended vertically beyond
the uppermost OBS located at 113 cm (Fig. 9b). A linear
extrapolation of the concentration decrease between the
two uppermost OBS (corresponding to the thick-layer
period examined by Friedrichs et al., 2000) for the four
bursts with the highest concentration suggests a lower
limit of h < 3 m. This extrapolation allows the buoyancy anomaly of B<0.022 m 2 s 22 to be estimated from
the observed concentration pro®le. The average acrossshelf velocity over this period was directed up-slope at
all depths (Fig. 9a) and was much less logarithmic than
during the thin phase (Friedrichs et al., 2000). Considering the poor log-®t and absence of a wave boundary
layer, extrapolation of velocity to the bed is not
warranted. By means of ®nite difference estimates
within the thick layer, Friedrichs et al. found Ri < 8.
With Umax ˆ 7 cm s 21 and B ˆ 0.022 m 2 s 22, Eq. (9)
gives Ri < 4.7. In either case, the high concentrations
during the thick layer phase cannot be explained in terms
of local resuspension (Wright et al., 1997; Friedrichs et
al., 2000). The inference is that sediment initially delivered via a surface plume in the upper water column was
subsequently concentrated by persistent regional upwelling as it settled. This high turbidity layer caused 5 cm of
deposition over the 1 month observation period of spring
1993 (Wright et al., 1997). As discussed earlier, rapid
deposition from highly turbid layers is expected in the
absence of ambient currents because there is no source
of shear-induced turbulence to keep the sediment in
suspension.
The thick turbid layer presumably did not move
down-slope as it settled because the same regional
41
pressure gradients that drove upwelling overcame
the down-slope gravity force on the layer. Since B
increased between the thin and thick phases, it
initially seems counterintuitive that the down-slope
gravity force no longer overcame regional upwelling.
To compare the strength of regional pressure gradients to the down-slope gravity force, however, the
regional pressure gradient must also be depthintegrated. The down-slope gravity force acting on
the turbid layer increased six-fold in the thick phase;
but because of the increase in h, the upwelling force
acting on the layer became 150 times greater. It is also
useful to compare the strength of the down-slope
gravity force during the thick stage to that observed
on the Bohai shelf. Because of lower sediment
concentrations and a much lower bottom slope, the
down-slope gravity force acting on the Louisiana
thick turbid layer was 20 times smaller than the
gravity force acting on the Bohai suspensions.
4. Discussion and conclusions
In this paper, we have offered ®eld illustrations and
simple analytical theory to address the diverse
outcomes that can result on continental shelves
when turbid, negatively buoyant layers move over
sloping seabeds. Sometimes, as in the archetypal
example of the Yellow River-mouth system, the
simple expectation of down-slope sediment ¯ux is
realized for several hours at a time. However, less
obvious modi®cations of current-driven or wavedriven transport processes may be more common. In
the cases we have examined, tidal and wind-driven
currents, together with waves, often made dominant
contributions to the total eddy viscosity and bottom
drag. Therefore, the frictional resistance acting on the
gravity current was often greater, and hence, downslope velocity was lower, than would be implied by
the classical Chezy equation. At the same time,
however, the increased bed stress caused by imposed
¯ows increased sediment suspension and therefore the
negative buoyancy anomaly. Thus, waves and ambient currents simultaneously enhance negative buoyancy and retard down-slope ¯ow.
It is important to recognize the limitations of the
relatively small data sets examined in this paper.
Among the ®eld deployments considered here, only
42
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
eight distinct sediment-induced gravity ¯ow `events'
were documented. The gravity ¯ows directly observed
on the Bohai shelf each lasted only a few hours, and
the events on the California and Louisiana shelves are
each documented by less direct measurement via
remote benthic tripods over periods of a single day.
Thus the results presented here do not conclusively
demonstrate the dominant role or precise nature of
sediment-induced gravity ¯ows on continental shelves
that accumulate ®ne sediment. Rather, this paper illustrates that recent observations of across-shelf ®ne
sediment transport are, in many circumstances,
consistent with the potential existence of high concentration, often very thin, near-bed gravity currents. As
advances in instrumentation continue to improve our
ability to observe ®ne sediment transport very near the
seabed, we anticipate that thin, highly turbid gravitydriven ¯ows will be shown to play an important role in
across-shelf sediment ¯ux in a wide variety of shelf
environments worldwide.
Some important points to summarize are:
1. Gravity-driven sediment transport across shelves
does not require direct release of a hyperpycnal
plume from a sediment-laden river. Sedimentladen gravity currents also come about, perhaps
more often, from subsequent mixing with ambient
seawater on the continental shelf. Resuspension
involving mixing with ambient seawater was the
source of all the observed gravity ¯ows considered in this paper.
2. None of the gravity ¯ows considered here were
auto-suspending, nor are sediment-induced gravity ¯ows on shelves in general. The slope, u , of
most shelves is too gentle for shear-induced
turbulence to be generated within gravity currents
without additional velocity shear being provided
by ambient waves and currents.
3. To model sediment-induced gravity currents on
shelves properly, the effect of ambient waves
and currents must be included in the quadratic
formulation of bottom stress. Application of the
classical Chezy equation to gravity currents
observed here without consideration of ambient
currents and waves yielded consistently erroneous
results.
4. If the supply of easily suspended sediment is less
than the maximum capacity of ambient waves and
5.
6.
7.
8.
9.
currents, intense turbulence generated by these
waves and currents limits gravity-induced sediment transport by increasing both the near-bed
velocity and the drag coef®cient and therefore
the quadratic bed stress. This scenario applies to
the Bohai shelf during peak tidal ¯ow and to the
Eel Shelf in non-¯ood years.
When ambient currents abruptly cease, bottom
drag lessens as both quadratic velocity and the
drag coef®cient are reduced, and rapid downslope ¯ow can occur as the sediment settles.
This occurs on the Bohai shelf at slack after
¯ood tide.
The gradient Richardson number (Ri) within a
highly turbid layer can be approximated by its
buoyancy anomaly (B) divided by its total velocity (Umax) squared, where Umax includes ambient
waves and currents. Based on observations, an
inverse relationship then exists between Ri and
the bottom drag coef®cient, CD (Fig. 10).
The maximum sustained rate of gravity-induced
sediment transport occurs when ambient currents
are strong, but the supply of easily suspended
sediment still exceeds the capacity of the ¯ow.
This scenario was seen during ¯ood-year wave
events on the Eel Shelf and possibly also on the
Louisiana shelf during wave events.
Feedback then favors Ri within the turbid layer to
be near its critical value of Ricr ˆ 1/4. This
subdues bottom drag somewhat (CD < 0.003),
but simultaneously provides suf®cient turbulence
to maintain sediment in suspension.
The maximum sustained gravity ¯ow velocity
Table 3
Benthic turbid layer characteristics, Louisiana Inner Shelf, Spring
1993, depth ˆ 20 m, sin u ˆ 0.0005
ug (cm s 21)
vc (cm s 21)
Uw (cm s 21)
Umax (cm s 21)
B (m 2 s 22)
h (m)
Ri
CD
C (kg m 23)
Q (kg m 21 s 21)
Thin Layer
Thick Layer
0.5
5
11
12
0.0036
0.02
0.25
0.0031
30
0.0028
24
5
2
7
0.022
3.0
4.7
±
1.2
20.15
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
43
Fig. 10. Bottom drag coef®cients from Tables 1±3 plotted as a function of the gradient Richardson number within the gravity ¯ow.
then equals RicrUmax(sin u )/CD. The maximum
sustainable buoyancy anomaly is B ˆ Ricr(Umax) 2.
The maximum gravity-induced sediment ¯ux is
easily calculated from the product of the above
relations.
10. Finally, for constant B, the likelihood of strong
gravity-induced transport on shelves decreases
as the slope of the bed decreases or the thickness
of the turbid layer increases. This is because
the down-slope gravity force decreases with
decreased bed slope, while the contribution
of regional pressure gradients increases with
increased layer thickness. This scenario explains
the behavior of the thick turbid layer on the gently
sloping Louisiana shelf.
from Bohai and the Eel River shelf were made
possible by the vision and sustained support provided
by Joseph Kravitz through the Of®ce of Naval
Research. Field measurements on the Louisiana
shelf were supported by the Mineral Management
Service in connection with the LATEX-B study via
a subcontract from Louisiana State University. This
work builds directly on the previous work by, and
insightful discussions with, P. Traykovski, W.R.
Geyer, and A.S. Ogston. We thank John Wells, J.P.
Syvitski, and a third anonymous reviewer for
constructive comments that improved the original
manuscript. R.A. Gammisch provided essential
support of VIMS ®eldwork at all three sites. We
also thank C.A. Nittrouer, R.W. Sternberg, W.J. Wiseman, S.P. Murray and T. Nelson for collaboration and
assistance with different facets of the ®eld studies.
Acknowledgements
The analyses reported in this paper were supported
by the Of®ce of Naval Research, Marine Geology and
Geophysics (Grant N00014-95-1-0391), as a component of the STRATAFORM Program. The results
References
Brown, W.M., Ritter, J.R., 1971. Sediment transport and turbidity in
the Eel River basin, California. US Geol. Surv. Water-Supply
Paper, 70.
44
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
Cutter Jr, G.R., Diaz, R.J., 2000. Biological alteration of physically
structured ¯ood deposits on the Eel margin, northern California.
Cont. Shelf Res. 20, 235±253.
Drake, D.A., 1999. Temporal and spatial variability of the sediment
grain-size distribution on the Eel shelf: the ¯ood layer of 1995.
Mar. Geol. 154, 169±182.
Eisma, D., Kalf, J., 1984. Dispersal of Zaire River suspended matter
in the estuary and the Angola Basin. Neth. J. Sea Res. 17,
385±411.
Eriksen, C.C., 1978. Measurements and models of ®ne structure,
internal gravity waves, and wave breaking in the deep ocean. J.
Geophys. Res. 83, 2989±3009.
Feddersen, F., Guza, R.T., Elgar, S., Herbers, T.H.C., 2000. Velocity moments in alongshore bottom stress parameterizations. J.
Geophys. Res. 105, 8673±8686.
Friedrichs, C.T., Wright, L.D., Hepworth, D.A., Kim, S.C., 2000.
Bottom boundary layer processes associated with ®ne sediment
accumulation in coastal seas and bays. Cont. Shelf Res. 20,
807±841.
Geyer, W.R., Hill, P.S., Milligan, T., Traykovski, P., 2000. The
structure of the Eel River plume during ¯oods. Cont. Shelf
Res. 20, 2067±2093.
Grant, W.D., Madsen, O.S., 1979. Combined wave and current
interaction with a rough bottom. J. Geophys. Res. 84,
1797±1808.
Howard, L.N., 1961. Note on a paper of John W. Miles. J. Fluid
Mech. 13, 158±160.
Huang, X., Garcia, M.H., 1999. Modeling of non-hydroplaning
mud¯ows on continental slopes. Mar. Geol. 154, 131±142.
Imram, J., Syvitski, J.P.M., 2000. Impact of extreme river events on
the coastal ocean. Oceanography 13, 85±92.
van Kessel, T., Kranenburg, C., 1996. Gravity current of ¯uid mud
on sloping bed. J. Hydraul. Engng. 122, 710±717.
Kineke, G.C., Sternberg, R.W., Trowbridge, J.H., Geyer, W.R.,
1996. Fluid mud processes on the Amazon continental shelf.
Cont. Shelf Res. 16, 667±696.
Komar, P.D., 1977. Computer simulation of turbidity current ¯ow
and the study of deep-sea channels and fan sedimentation. In:
Goldberg, E.D., McCave, I.N., O'Brian, J.J., Steele, J.H. (Eds.),
Marine Modeling (The Sea), vol. 6. Wiley, New York, pp.
603±621.
Kranenberg, C., 1984. The in¯uence of side-wall friction on shearstress driven entrainment experiments. J. Hydraul. Res. 21,
99±117.
Kundu, P.K., 1981. Self-similarity in stress-driven entrainment
experiments. J. Geophys. Res. 86, 1979±1988.
Mulder, T., Syvitski, J.P.M., 1995. Turbidity currents generated
at river mouths during exceptional discharges to the ocean:
the importance of small mountainous rivers. J. Geol. 100,
525±544.
Mulder, T., Syvitski, J.P.M., Skene, K.I., 1998. Modeling of erosion
and deposition by turbidity currents generated at river mouths. J.
Sediment. Res. 68, 124±137.
Nittrouer, C.A., 1999. STRATAFORM: overview of its design and
synthesis of its results. Mar. Geol. 154, 3±12.
Ogston, A.S., Cacchione, D.A., Sternberg, R.W., Kineke, G.C.,
2000. Observations of storm and river ¯ood-driven sediment
transport on the northern California continental shelf. Cont.
Shelf Res. 20, 2141±2162.
Parker, G., Fukushima, Y., Pantin, H.M., 1986. Self-accelerating
turbidity currents. J. Fluid Mech. 171, 145±181.
Prior, D.B., Yang, Z.-S., Bornhold, B.D., Keller, G.H., Wiseman,
W.J., Wright, L.D., 1986. Active slope failure, sediment
collapse, and silt ¯ows on the modern subaqueous Huanghe
Delta. Geo-Mar. Lett. 6, 85±95.
Scotti, R.S., Corcos, G.M., 1972. An experiment on the stability of
small disturbances in a strati®ed free shear layer. J. Fluid Mech.
52, 499±528.
Sommer®eld, C.K., Nittrouer, C.A., 1999. Modern accumulation
rates and a sediment budget for the Eel shelf: a ¯ood-dominated
depositional environment. Mar. Geol. 154, 227±242.
Sternberg, R.W., Cacchione, D.A., Paulson, B., Kineke, G.C.,
Drake, D.E., 1996. Observations of sediment transport on the
Amazon subaqueous delta. Cont. Shelf Res. 16, 697±715.
Swart, D.H., 1974. Offshore sediment transport and equilibrium
beach pro®les. Publ. 131, Delft Hydr. Laboratory, Delft,
Netherlands.
Traykovski, P., Geyer, W.R., Irish, J.D., Lynch, J.F., 2000. The role
of wave-induced density-driven ¯uid mud ¯ows for cross-shelf
transport on the Eel River continental shelf. Cont. Shelf Res. 20,
2113±2140.
Trowbridge, J.H., 1992. A simple description of the deepening and
structure of a stably strati®ed ¯ow driven by a surface stress. J.
Geophys. Res. 97, 15,529±15,543.
Trowbridge, J.H., Kineke, G.C., 1994. Structure and dynamics of
¯uid muds on the Amazon continental shelf. J. Geophys. Res.
99, 865±874.
Turner, J.S., 1973. Buoyancy Effects in Fluids. Cambridge University Press, Cambridge, UK.
Wheatcroft, R.A., 2000. Oceanic ¯ood sedimentation: a new
perspective. Cont. Shelf Res. 20, 2059±2066.
Wheatcroft, R.A., Borgeld, J.C., Born, R.S., Drake, D.E., Leithold,
E.L., Nittrouer, C.A., Sommer®eld, C.K., 1996. The anatomy of
an oceanic ¯ood deposit. Oceanography 9, 158±162.
Wheatcroft, R.A., Sommer®eld, C.K., Drake, D.E., Borgeld, J.C.,
Nittrouer, C.A., 1997. Rapid and widespread dispersal of ¯ood
sediment on the northern California margin. Geology 25,
163±166.
Wiberg, P.L., Smith, J.D., 1983. A comparison of ®eld data and
theoretical models for wave-current interactions at the bed on
the continental shelf. Cont. Shelf Res. 2, 147±162.
Wiseman, W.J., Yang, Z.-S., Bornhold, B.D., Keller, G.H., Prior,
D.B., Wright, L.D., 1986. Suspended sediment advection by
tidal currents off the Huanghe (Yellow River) Delta. GeoMar.
Lett. 6, 107±113.
Wright, L.D., 1985. River deltas. In: Davis, R.A. (Ed.), Coastal
Sedimentary Environments. Springer, New York, pp. 1±76.
Wright, L.D., Nittrouer, C.A., 1995. Dispersal of river sediments in
coastal seas: six contrasting cases. Estuaries 18, 494±508.
Wright, L.D., Yang, Z.-S., Bornhold, B.D., Keller, G.H., Prior,
D.B., Wiseman, W.J., 1986. Short period internal waves over
the Huanghe (Yellow River) Delta Front (PRC). Geo-Mar. Lett.
6, 115±120.
Wright, L.D., Wiseman, W.J., Prior, D.B., Suhayda, J.N., Keller,
L.D. Wright et al. / Marine Geology 175 (2001) 25±45
G.H., Yang, Z.-S., Fan, Y.B., 1988. Marine dispersal and
deposition of Yellow River silts by gravity driven under¯ows.
Nature 332, 629±632.
Wright, L.D., Wiseman, W.J., Yang, Z.-S., Bornhold, B.D., Keller,
G.H., Prior, D.B., Suhayda, J.M., 1990. Processes of marine
dispersal and deposition of suspended silts off the modern
mouth of the Huanghe (Yellow River). Cont. Shelf Res. 10,
1±40.
45
Wright, L.D., Sherwood, C.R., Sternberg, R.W., 1997. Field
measurements of fairweather bottom boundary layer processes
and sediment suspension on the Louisiana inner continental
shelf. Mar. Geol. 140, 329±345.
Wright, L.D., Kim, S.-C., Friedrichs, C.T., 1999. Across-shelf
Variations in bed roughness bed stress and sediment transport
on the northern California Shelf. Mar. Geol. 154, 99±115.