Wind stress, bed roughness and sediment suspension on the inner shelf during an extreme storm event

ContinentalShelfResearch,Vol. 13, No. 11, pp. 1303-1324,1993.

0278-4343/93$6.00+ 0.00 PergamonPressLtd

Printed in Great Britain.

W i n d stress, bed roughness and sediment suspension on the inner shelf during an extreme storm event O. S. MADSEN,* L. D. WRIGnT,t J. D. BOONt and T. A. CHISHOLM* (Received 3 September 1992; accepted 2 February 1993) A b s t r a c t - - I n s t r u m e n t e d bottom boundary layer tripods were deployed on the inner shelf at depths of 13 and 8 m off the U.S. A r m y Corps of Engineers Field Research Facility at Duck, NC, U . S . A . , over a 2-week period that included the severe and prolonged "Halloween Storm" of late October 1991. The storm persisted for 5 days and generated waves with heights and periods of up to 6 m and 22 s. Although the instrumentation was destroyed, current profile and suspended sediment concentration profile data were recovered from the 13 m site. M e a n currents attained speeds of nearly 0.5 m s 1 at 0.29 m above the bed and were directed about 10° offshore from shore-parallel. These strong currents are shown to be wind driven and result in predictions of a wind-drag coefficient, C a = 4.7 × 10 -3. T h e currents were recorded simultaneously with root-mean-square (rms) wave orbital velocity amplitudes in the 0.6-1.0 m s 1 range. During the peak of the storm suspended sediment concentrations exceeded 1 kg m -3 throughout the lower 1 m of the water column. Analysis of current profiles, accounting for the presence of waves, is performed to obtain an equivalent bottom roughness, k n, of approximately 15 times the median sediment diameter, i.e. k, 15 ds0. Analysis of the suspended sediment concentration profiles, using the experimentally obtained hydrodynamic characteristics, results in a value of 4 × 10-4 for the resuspension parameter, 70, with the reference concentration taken 7 ds0 above the bed. From the severity of the storm condition it is inferred that our estimates of k n and 7o correspond to sheet flow conditions.

INTRODUCTION

THE importance of storms to coastal change has been abundantly documented. Stormdriven processes are also known to dominate sediment transport on the mid and outer regions of many continental shelves (e.g. SMITH and HOPKINS, 1 9 7 2 ; STERNBERG, 1986; VINCENT et al., 1981). The roles of storms in effecting shore-to-shelf coupling via offshore sand transport over the inner shelf have been inferred from indirect evidence (e.g. WRIGHT et al., 1986a, 1987). Earlier sets of field data from the inner shelf of the Middle Atlantic Bight (depth region of 7 - 10 m) showed that significant offshore transport of suspended sediment by downwelling benthic mean flows could occur during relatively commonplace northeasterly (extratropical) storms ( W R I G H T et al., 1986b, 1991). However, very little empirical information exists about the near-bottom currents, bed shear stresses, and sediment fluxes that operate during major storm events. * Ralph M. Parsons Laboratory, D e p a r t m e n t of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, M A 02139, U . S . A . tVirginia Institute of Marine Science, School of Marine Science, College of William and Mary, Gloucester Point, V A 23062, U . S . A . 1303

1304

O.S. MADSENet al.

Along the U.S. East Coast north of Cape Hatteras, it is extratropical storms rather than hurricanes that are responsible for most of the documented coastal erosion (DoLAN et al., 1988). For 5 days in late October and early November 1991 an extratropical storm of unusual size, duration and intensity prevailed in the western North Atlantic and affected the entire U.S. East Coast. In the southern part of the Middle Atlantic Bight, off the U.S. Army Corps of Engineers Field Research Facility at Duck, NC, this "Halloween Storm" generated exceptionally strong currents and extreme wave conditions. According to DOLAN and DAVIS (1992), this storm was the largest extratropical storm on record in this region; it surpassed the "Ash Wednesday Storm" of 1962. About 10 days prior to the storm we deployed two benthic boundary layer instrumentation systems (tripods) on the inner shelf off Duck at water depths of 8 and 13 m. We never found the 8-m tripod. Although the 13-m tripod and its instrumentation were destroyed by the storm, the data logging packages washed ashore and were retrieved shortly after the storm subsided. We recovered time-series data on near-bottom velocity and suspended sediment concentration profiles that extended from the time of initial deployment to a few hours prior to the peak of the storm. In this paper we report the data obtained from our serendipitous encounter with the "Halloween Storm" and present the details of how these data were used to obtain muchneeded empirical information on movable bed roughness and suspended sediment concentration corresponding to extreme hydrodynamic conditions.

GENERAL DESCRIPTIONS The site The results presented here were obtained from the southern portion of the Middle Atlantic Bight off the coast of Duck, NC (Fig. 1). Diver-collected samples from the top 510 cm in 13-m depth show the bottom sediments to consist of 74% very fine to fine sands (0.06--0.18 mm diameter), 20% silts (0.004--0.06 mm), and 6% clay with a median diameter d5o = 0.10 mm. Samples collected from 8-m depth show a similar composition but have only a 10--15% silt and clay fraction. The inner shelf profile is concave upward over the region extending from the surf zone to about the 15-m isobath. Semi-diurnal tide range averages 1.2 m at the Duck Field Research Facility (FRF) pier (BIRgEMEmRet al., 1981) and shore-parallel near-bottom tidal currents typically have speeds of 10-20 cm s-1 (WRIGHT et al., 1991). The average significant height and peak period of the waves recorded by the FRF wave rider at a depth of 17 m are 0.88 m and 8.9 s, respectively, but extratropical storms often generate waves with significant heights in excess of 4 m during the period October-February (BIRKEMEIERet al., 1981). In this paper we present results using a coordinate system with a shore-parallel x-axis pointing in the southerly direction, 20° east of due south, and measure angles in the counterclockwise direction from this x-axis. The instrumentation Two bottom tripod instrumentation systems (detailed descriptions may be found in WRIGHT et al., 1991) were deployed from the R.V. Cape Hatteras on 17 October 1991.

1305

Wind stress, bed roughness and sediment suspension 76 °

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Fig. 1. The Middle Atlantic Bight and the field site.

Divers made elevation adjustments to sensors, checked orientations, and recorded bottom roughness conditions at the time of deployment. Additionally, an annular seabed flume (MAA, 1993) was deployed for a period of 12 h to determine the critical threshold shear stress at which resuspension of bed material begins. Both instrumentation systems consisted of a tripod frame supporting a Seadata Model 635 directional wave gauge

1306

o . s . MADSEN et al. 20

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Fig. 2. Wind speed (full line) and direction (squares) recorded by the U.S. Army Field Research Facility (FRF) during the "Halloween" storm. The record embraces the period 27 October-1 November 1991.

incorporating a pressure transducer and a single 3.8 cm-diameter Marsh-McBirney two-axis electromagnetic current meter, an array of five DOWNIN6 and ASSOCIATES(1985) Model OBS-2 optical backscatter sensors (OBS) for measuring suspended sediment concentration, and a digital sonar altimeter. One tripod was deployed on the 8-m isobath, the other, which in addition to the standard instrumentation also supported an array of three Marsh-McBirney current meters, was deployed at a depth of 13 m. The storm

A few days after the deployment, on 20 October, a typical autumn frontal system passed over the coast bringing northeasterly winds that generated a southerly setting current and waves with heights of 1.5 m and periods of 7-8 s. This typical storm was followed by a 3-day period of low wind and wave activity. Approximately 10 days into the deployment of the tripods, i.e. on 27 October, the storm, which has become known as the "Halloween Storm", began as Hurricane Grace migrated up the Atlantic. On 28 October, as the hurricane passed to the west of Bermuda, a cold front crossed the mid-Atlantic/New England coast and stalled offshore (DoLAN and DAvis, 1992). A very steep pressure gradient developed between the low over the North Atlantic and a high over the coast. According to DOLAN and DAVIS (1992; p. 8) "The low reached peak intensity at 1200 on the 30th some 340 nautical miles south of Halifax, Nova Scotia. At this time its central pressure had dipped to 972 mb with estimated maximum winds of 60 k n o t s . . , sustained winds persisted for 48 h o u r s . . . " To further put the severity of this storm in perspective, DOLAN and DAVIS (1992), using their storm classification system of wave height squared times duration, classified the storm as a class 5 event, i.e. the most severe, and concluded that the "Halloween Storm" was the largest extratropical storm on record in this region, surpassing the "Ash Wednesday Storm" of 1962 in severity. The local wind speed and direction (34-min averages) recorded by the FRF at 19.5 m above MSL are shown in Fig. 2 for the period covering the Halloween Storm (t = 0 at 0:00 hours EST on 27 October 1991). In our shore-parallel coordinate system wind directions between 0 and 180° indicate winds blowing over water towards land. Corresponding

1307

Wind stress, bed roughness and sediment suspension

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Fig. 3. Significant wave heights (full line) and peak periods (squares) recorded by the FRF at Duck during the Halloween storm. The record embraces the period 27 October-1 November 1991. (a) Waves measured by the offshore waverider in 17-m depth. (b) Waves measured by a pressure gauge off the end of the research pier at a depth of 8 m,

significant wave heights and peak periods measured by FRF's offshore wave rider at a depth of 17 m and their (puv)-gauge, consisting of a pressure transducer and a two-axis electromagnetic current meter, in 8-m depth are shown in Fig. 3(a) and (b), respectively. The initial increase in wind velocity from the north-northeast (Fig. 2) and rise in wave height to about 2 m [Fig. 3(a) and (b)] began on 27 October with the northward passage of Hurricane Grace offshore of Duck. Although Grace passed out of the area rather quickly, the passage of a cold front across the coast on the 28th resulted in intensification of local winds from the northeast and the appearance of locally generated wind waves in addition to distant swell in the wave record [note the sudden drop in peak period at t -~ 36 h in Fig. 3(a) and (b)]. By the evening of the 28th, northeasterly winds at the Duck pier had speeds of nearly 18 m s -1 (Fig. 2) and waves at the offshore wave rider were over 4 m high. With the exception of a brief period around t = 78 h, the local winds retained an onshore component and speeds in the 13 ___2 m s -1 range for the ensuing 2 days while wave heights remained above 3 m.

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O.S. MADSENet al.

Although the storm itself remained very intense until 3 November (DOLAN and DAVIS, 1992), the highest winds prevailed well out to sea. Local winds at Duck turned to the northwest, losing the onshore component, and began to slacken considerably on 30 October. However, despite the diminution of local wind stress, wave heights and period continued to increase. The largest waves occurred in the late evening hours of the 30th and early morning of the 31st. As recorded by the offshore wave rider, these waves had significant heights of about 6 m and peak periods of 22 s [Fig. 3(a)]. The significant height recorded by the (puv)-gauge in 8 m water depth never exceeded 4.5 m [Fig. 3(b)]. We conclude from this that the wave gauge at 8 m and consequently also our 8 m tripod were located in the surf zone at the time of maximum wave intensity. It is of some interest to note the high correlation between wind speeds and directions (lower speeds for offshore winds) recorded at the FRF pier and shown in Fig. 2. This onoffshore wind speed correlation is clearly evident in the wind record from noon on 30 October to noon 1 November (t -- 84-132 h in Fig. 2) and is most dramatically demonstrated by the rapid variation in recorded wind speeds around t = 78 h. We infer from this that actual over-water wind speeds of offshore winds were larger than those indicated in Fig. 2. The data

Although hoping to capture a severe autumn storm event(s) during the deployment of our tripods, we had not anticipated the magnitude of the Halloween Storm, which placed our 8-m tripod within the surf zone. The 8-m tripod was lost. The storm also destroyed our 13-m tripod. However, the uppermost portion of this tripod including broken sensors and cylinders containing data loggers washed ashore 3 km to the south of the deployment site on or before 2 November. The data from the Seadata Model 635 system were too badly corrupted to be usable and the digital sonar altimeter and its recorder were missing. However, the tape containing data from the other three electromagnetic current meters was intact and nearly full of high-quality data. In addition, after treatment to remove a corrosive film caused by flooding of the OBS data logging canister, the magnetic disc containing the OBS data was made readable and all the data were recovered. We therefore recovered data obtained in 13-m depth from the three two-axis current meters, located at heights of 29, 88 and 124 cm above the bottom, and from the fiveelement OBS array with sensors situated at elevations 27, 54, 87, 120 and 147 cm. The current meter data were logged by means of a Seadata Model 626 electronic package and were sampled at 1 Hz with a burst interval of 4 h and a burst duration of 17 min. The OBS array data were recorded at 5 Hz with a burst interval of 8 h and a burst duration of 6.8 min by an ONSET Tattletale solid state logging system. The last burst of recovered current meter data was recorded at 18:00 h on 30 October, i.e. slightly before peak wave conditions were recorded by the FRF wave rider [Fig. 3(a)]. Although no evidence of rocking of the tripod prior to its failure was found in the current meter records, the erratic behavior of the results obtained from analysis of the last two bursts of current meter data suggest that the system ceased to operate reliably around noon on 30 October. Despite the absence of evidence of tripod rocking it is possible that the tripod legs became partially buried during deployment. Unfortunately the sonar altimeter record which could have resolved this problem was lost. We are therefore forced to accept the instrument heights given above, which were obtained at the time of deployment.

Wind stress, bed roughness and sediment suspension

1309

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Direction of Wave Velocity (deg)

Fig. 4. Directional distribution of near-bottom wave orbital velocity variance from t = 66 h.

NEAR-BOTTOM WAVE ORBITAL VELOCITIES The burst-averaged velocity vector, i.e. the current velocity vector, is removed from each current m e t e r record, and the remaining time series is regarded as representing wave orbital velocities. MADS~N et al. (1988) and MADSEN (1992) showed from theoretical considerations of spectral wave boundary layer flows that the appropriate n e a r - b o t t o m orbital velocity amplitude of a periodic wave, which is equivalent to the spectral wave motion, is the rms amplitude of the near-bottom orbital velocity spectrum. For this reason, the total variance, o2~, is determined for each wave orbital velocity record and the n e a r - b o t t o m orbital velocity amplitude of the equivalent periodic wave is taken as Ub =

g~

o u

(1)

To estimate a wave direction u 2 + v 2 and direction ~ were calculated for each u,v pair of wave velocities. Using 1° bins in ~ the sum of u 2 + v2 was obtained for each directional bin and the resulting directional distribution of wave velocity variance was obtained as the running average using an 11 ° window. A typical directional distribution of wave orbital velocity variance (from t = 66 h) is shown in Fig. 4. The m e a n of the centroids of the two peaks, representing the forward and backward wave orbital velocity and differing by 180 ° , is taken as our estimate of wave direction. In our shore-parallel coordinate system the wave angle, Cw, indicates the direction from which waves are arriving, i.e. ¢,, = 90 ° is a normally incident wave. Finally, the wave orbital velocity time series is projected onto the wave direction, Cw, and the frequency spectrum, S,(f), of the projected wave orbital velocity record is obtained. A typical projected n e a r - b o t t o m orbital velocity spectrum (from t = 66 h) is shown in Fig. 5. Following MADSEN (1992) the period of the equivalent periodic wave, T, is taken as

T-

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(2)

1310

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S p e c t r u m of n e a r - b o t t o m w a v e orbital v e l o c i t y p r o j e c t i o n o n m e a n w a v e d i r e c t i o n f r o m t = 66h.

Figure 6(a)-(c) presents the variation of near-bottom equivalent periodic wave characteristics obtained from the current meter at elevation z = 124 cm starting from t = 0 at 0:00 h on 27 October. Since the current meters were located within the lower 1.25 m of the 13 m depth, linear wave theory suggests a negligible variation of wave orbital velocity characteristics with current meter location for the wave periods encountered here, e.g. a less than 10% difference in orbital velocity from lowest to highest current meter is expected for periods exceeding 3.4 s. This features is evident from our data which show near-bottom orbital velocities obtained from the current meters generally to differ by less than 10% percent. In addition, the wave-direction estimates obtained from different current meters exhibit maximum differences generally below 6 ° and yield wave period estimates that are identical within a fraction of 1 s. We interpret this internal consistency of our computed equivalent wave characteristics as evidence of our current meter records' ability to provide reliable estimates of the equivalent wave characteristics and as justification for our assumption that the time-varying portion of current meter records can be regarded as predominantly wave-associated, i.e. not significantly contaminated by turbulence. The variation of wave characteristics shown in Fig. 6 mimics the variation of surface wave characteristics shown in Fig. 3. In fact, the significant wave heights (Hmo) obtained by transformation of our near-bottom orbital velocity spectra agree, within a factor of 0.87, with those obtained by the F R F (puv)-gauge. The use of projected velocities and difference in water depths (13 vs 8 m) explains our lower significant wave heights whereas our different period-definition is responsible for the less pronounced decrease in period associated with locally generated wind waves around t - 36 h. Thus, with the exceptions of the erratic behavior of period and direction determined from the very last burst (signaling destruction of our tripod) and the spurious orbital velocity at t = 30 h, we have confidence in the reliability of the near-bottom equivalent periodic wave characteristics presented in Fig. 6. To interpret the wave characteristics in terms of the intensity of fluid-sediment interaction, we use the equivalent periodic wave conditions shown in Fig. 6 to calculate the skin friction Shields parameter (MADSEN and GRANT, 1976).

1311

Wind stress, bed roughness and sediment suspension

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Fig. 6. Time series of equivalent near-bottom periodic wave characteristics starting from t = 0 at 0:00 h on 27 October 1991. (a) Ub = rms near-bottom orbital velocity amplitude; (b) tpw = wave direction; (c) T = wave period.

O.s. MADSENet al.

1312

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Fig. 7.

Time series of mean current speed and direction measured 29 cm above bottom starting from t = 0 at 0:00 h on 27 October 1991.

lpw m --

1 ¢t 2 2JwUb

(s-1)gd

--

(Ul*wm)2

(3)

(s-1)gd

in which s = Ps/P is the relative density of the sediment (taken as 2.6 corresponding to quartz in seawater), g is gravity, fw is the wave friction factor obtained for a bottom roughness k" = ds0 = 0.10 mm, and U'wm is the skin friction shear velocity. Thus, based on the wave motion alone we obtain estimates of ~/)~vm ranging from 0.3 (at t = 0) through 0.8 (at t = 42 h) to as high as 1.1 (at t = 86 h). Since these estimates, even though they were obtained using rms rather than significant wave orbital velocities, exceed considerably the critical Shields parameter for initiation of motion 0Pcr = 0.09 for d = 0.10 mm, MADSEN and GRANT, 1976), we have no doubt that sediment transport took place during the storm. Based on empirical evidence for disappearance of wave-generated ripples (e.g. NIELSEN, 1981; SAa'O and HORIKAWA, 1988), we are furthermore confident that our storm data correspond to the condition of a flat movable bed. This is certainly true for t > 36 hrs and possibly also for most of the preceding period. NEAR-BOTTOM CURRENTS Burst-averaged current meter time series provide a time series of current speed and direction for the portion of the storm captured by our instruments. Figure 7 shows the variation of current speed and direction obtained from the lowest current meter, at elevation z = 29 cm, starting at 0:00 h on 27 October. The current direction is defined in our shore-parallel coordinate system as the direction in which the current is flowing. A strong correlation between the current record in Fig. 7 and the winds in Fig. 2 is apparent, e.g. the coincident rapid increase in current and wind speeds at t = 36 h and the maintenance of strong southerly slightly offshore-deflected currents during the ensuing period when winds from the northerly direction remained fairly constant. We shall explore this correlation after examination of our current velocity profiles. From the current speeds at the three elevations, z = 29, 88 and 124 cm, we may obtain estimates of u,c, the current shear velocity, and z0a, the apparent bottom roughness scale

Wind stress, bed roughness and sediment suspension

1313

experienced by the current in presence of waves, by the log-profile method. Such an analysis could be p e r f o r m e d by determining the best-fit log-profile to the three current speed estimates obtained for each burst and use an R2-based criterion for the acceptance of the resulting values of u,c and Zoa ( G R o s s and NOW~LL, 1983). However, since three data points exceed the minimum required by only one, an R2-based acceptance criterion does not m a k e much sense here. To evaluate the acceptability of u,c and Zoa values obtained from our current profiles we therefore chose to obtain, for each burst, two estimates of u,~ and z0a from the lowest current at z = 29 cm combined with either of the two highest currents at z = 88 and 124 cm, respectively; and base our assessment of acceptability on the internal consistency among the two estimates. (A third estimate, obtainable from the two highest current m e t e r elevations, is discarded on the grounds that it is overly sensitive to m e a s u r e m e n t errors in current velocity measurements). F r o m the two estimates of u , c (U,cl and U,~e) and z0~ (z0~l and z0a2) for each burst we express the internal consistency in terms of parameters e, = lU,cl - U , c 2 l / ( U , c 1 '}- U , c 2 ) and e0~ = (ZoamaX/Zoa,min). In addition to these consistency p a r a m e t e r s it should, of course, be realized that the direction of currents at the three elevations must be comparable for our analysis to m a k e sense. A third consistency parameter, Aq~c, the difference in current direction obtained from the current meters, is therefore also considered. F r o m analysis of all 22 current profiles, t = 2 h through t = 90 h, in the m a n n e r outlined above a definite grouping of our data emerges. The first group, consisting of all bursts prior to t = 38 h, i.e. when current speeds were below 20 cm s-1 at z = 29 cm (Fig. 7), and the very last burst t = 90 h, which has already been discarded based on its erratic wave prediction, give values of e, greater than 0.5 (with several u,~ estimates being negative), eOa exceeding 103, and directional inconsistencies, Aq~C, above 30 ° with one exception (Aq~c = 20°). Clearly, the results obtained from analysis of these bursts, characterized by their low current speeds, are not acceptable. The second group, consisting of the bursts from t = 38 h to t = 54 h and the next to last burst at t = 86 h (announcing tripod failure), have values of e , in the range of 0.15-0.4 with an average of ~-, = 0.23, an average value of eOa ~ 102 with only one value below 8, and directional consistency better than 15 °. The last group, the seven bursts from t = 58 h through 82 h, give values of e, less than 0.08, i.e. about half the lowest variability exhibited by the second group, typical of values of eOa = 1.2 and all below 2, i.e. significantly better than the second group, and a directional consistency which, with two exceptions, is comparable to that of the second group, i.e. Aq~C< 15 °. These two exceptions, t = 70 and 74 h, have values of Aq~c = 34 and 18 °, respectively, and are seen from Fig. 7 to correspond to current speeds at z = 29 cm less than 20 cm s -1. Since the low current speed was the c o m m o n feature of the burst that definitely yielded unacceptable results, there is good reason to regard the bursts at t = 70 and 74 h as being of inferior quality. Based on the preceding assessment of the internal consistency of our current velocity profiles only the five directionally consistent bursts, i.e. from t = 58 h to 82 h excepting the bursts at t = 70 and 74 h, are accepted for further analysis. These acceptable data sets are listed in Table 1 along with the estimates of U,c and Zoa obtained from a best-fit log-profile analysis using all three data points for each burst and the associated R e values. Since our acceptance criteria were based on the consistency of results obtained from each burst it is encouraging to note that the consistency of the results presented in Table 1 is comparable with the consistency of individual bursts, e.g. e, = (u,c - U , c , m i n ) / ( t l , c + U,c,min ) ' ( 0.17 with an average of g , = 0.10 and e0~ = Zoa/ZOa,min < 13 with an average of g0a = 7. More importantly, the two bursts (t = 70 and 74 h) that were rejected on the grounds of low

1314

O . S . MaDSEN et al.

Table 1.

Current profile data and estimates of shear velocity and apparent bottom roughness scale

uc t (h)

29 cm

58 62 66 78 82

21.1 35.4 35.5 31.1 36.1

~

88 cm 124 cm 29 cm Aq~ U,c (crn s -1) (deg) (deg) (cm s -1) 27.2 42.2 43.8 41.6 44.7

30.3 44.0 45.0 42.8 47.5

0.4 17.6 8.5 5.3 13.9

4.9 3.8 5.3 5.4 4.9

2.44 2.37 2.71 3.35 3.14

z0a (cm)

R2

0.938 0.073 0.151 0.689 0.295

0.9880 0.9995 0.9880 0.9800 0.9999

current velocity and poor directional consistency would have given values of Zoa -~ 6 and 5 cm, i.e. e0a -~ 75, clearly placing them in the same category as data sets that were rejected. We may now examine the hypothesis that the currents shown in Fig. 7 were predominantly wind-driven. To this end we adopt the linearized depth-averaged momentum equation in the alongshore (our x) direction. Neglecting the Coriolis force associated with a weak shore-normal flow, this reads OUc

Of? + tax - Rb Uc

(4)

o-7 = - g ox

with Uc denoting the depth-averaged shore-parallel current, 0 the burst-averaged free surface elevation, tax the alongshore wind stress, h (= 13 m here) the water depth and Rb is the linearized bottom resistance parameter which is related to the depth-averaged bottom drag coefficient, Cb, by Rb = Cb[ Uc]/h. Since the wave boundary layer thickness, as shown later, is less than the elevation of the lowest current meter at z = 29 cm the best-fit values of u,c and Zoa listed in Table 1 define the best-fit logarithmic profile. Uc = u,¢ In ~ K

(5)

ZOa

for the neat-bottom current in the presence of waves. Since the alongshore current is treated as a wind-driven turbulent Couette flow, reasonable estimates of U c and Cb = (u,c/U~) 2 are obtained from equation (5) by taking z = h/2 (= 6.5 m here) and the values for U,c and z0a listed in Table 1. In this manner the five bursts in Table 1 produce values of Uc and Co ranging from 0.4 to 0.6 m s -1 and 1.9 to 3.7 x 10 -3, respectively. Based on the average values, Uc = 0.54 m s - 1 and Cb = 2.8 X 10 -3, a representative value for the linearized bottom resistance parameter in equation (4), Rb ~-- 1.2 X 10 -4 s -1, is obtained for the period covered by the results presented in Table 1. It is now seen from equation (4) that the characteristic response time to alongshore forcing, Ro -1 = 2.3 h, is significantly shorter than the typical time scale for variation in wind condition shown in Fig. 2, with the exception of the aforementioned period of rapid on-offshore variation around t -~ 78 h. It is therefore reasonable to conclude that wind-driven currents along the 13-m isobath for the period of interest are essentially in steady-state equilibrium with local 2-h (or so) averaged winds, i.e. Tax = PaCa U2 c o s (~/~a -- 180°) = /9/'/* 2 COSq~c

(6)

Wind stress, bed roughness and sediment suspension Table 2. t (h)

58 62 66 78 82

Calculated wind drag coefficient

U, c ~)c Ua ~)a (cms -1) (deg) (ms -1) (deg)

2.44 2.37 2.71 3.35 3.14

1315

0.4 17.6 8.5 5.3 13.9

12.6 13.0 12.5 13.5 14.3

123 133 132 162 168

Ca (×103)

5.6 3.8 4.7 5.3 3.9

in which Pa denotes air density (1.25 kg m-3), Ua and ~a 136 min-averaged wind speed and direction (from Fig. 2), p water density (1025 kg m-3), and u,c and q~care the current shear velocity and direction, respectively. Formally, equation (6) is valid only for purely winddriven flows, in which case Ca is the wind drag coefficient. If we, however, adopt equation (6) with the values of u,¢ and ~clisted in Table 1, the resulting Ca-values would in addition to wind drag reflect the influence of unsteadiness and alongshore pressure gradients. As seen from the Ca-values listed in Table 2 the five estimates are remarkably similar with only a 20% variation around an average value of Ca = 4.7 × 10 -3. Since the Ca variability reflects the relative importance of alongshore pressure gradients, the near-constancy of the Ca-values listed in Table 2 supports the assumption that the flow is predominantly wind-driven. It is of interest to note that the wind drag coefficient, Ca = 4.7 × 10 -3, obtained here is considerably larger than estimates resulting from the application of deep water formulas, e.g. Wv (1982) gives a value of C a - ~ 1.64 × 10 -3 for Ua ~ 13 m s -1. In fact, the difference between our Ca-value and that obtained from Wu's formula is increased from a factor of three, suggested above, to a factor of nearly four when it is recognized that our Ca-value is referred to the 19.5-m wind speed whereas Wu's formula is based on the 10-m wind speed. Since wave breaking is known to have a pronounced effect on wind drag, e.g. MELVILLE (1977), we attribute our large wind drag coefficient to the frequent occurrence of wave breaking for the extreme wave condition in the depth-limited inner-shelf environment where our data were obtained. The alternative explanation of our large Ca-value is that a constant alongshore pressure gradient existed corresponding to a mean sea level slope of Ofl/Ox = 3.8 × 10 -6. This possibility is discarded based on examination of water depth variations recorded at the Duck pier and by the tidal gauge station at Chesapeake Bay Bridge. We therefore conclude that Ca -~ 4.7 × 10 -3 is a representative value for the wind drag coefficient corresponding to the storm wave and wind conditions present at the site for the period of our measurements. BOTTOM ROUGHNESS

AND WAVE-CURRENT

INTERACTION

The equivalent near-bottom periodic wave characteristics may be used in conjunction with a model of wave-current interaction and the current characteristics listed in Table 1 to extract much-needed information on movable bed roughness corresponding to severe, sheet flow, storm conditions. As our wave-current model we choose the Grant-Madsen model as presented by GRANTand MADSEN (1986). This model is chosen for its simplicity and because it is fairly widely used. The model has only one free parameter, the parameter

1316

O . S . MADSEN et al.

Table 3.

Calculated movable bed roughness

t (h)

u,c (cms - l )

Ucl0O (cms -l)

ub (cms -1)

T (s)

q~wc°

58 62 66 78 82

2.44 2.37 2.71 3.35 3.14

28.5 42.8 44.0 41.7 45.7

73.4 78.8 82.9 90.9 96.2

10.1 11.1 11.1 11.8 11.8

88 69 81 86 79

U~wra U*m (cms -1) (cms - l ) 3.95 4.20 4.31 4.54 4.84

6.69 4.80 5.57 7.73 6.84

6wc

kn

(cm)

(cm)

8.6 6.8 7.8 11.6 10.2

0.591 0.021 0.070 0.516 0.136

defining the level at which the eddy viscosity switches from wave-current interaction scaling to current scaling. The choice of this parameter was discussed extensively by GRANT and MADSEN(1986) and to make our results compatible with those obtained if the GRANTMAt)SEN (1979) model were used we choose the definition of the wave boundary layer thickness. 6 ~ = 2 Ku,m o)

(7)

where K = 0.4 is von Karman's constant,/'/*m is the shear velocity based on maximum combined wave-current bottom shear stress, and ~o is the radian wave frequency (2 at/T). Wave-current interaction models are usually used to predict u.¢ and Zoa values defining the current profile above the wave boundary layer, i.e. equation (5), from knowledge of current (at a point), near-bottom wave orbital velocity, and physical bottom roughness characteristics (expressed as the equivalent Nikuradse sand grain roughness, kn). In the application here we obtain the usual current specification at, say, 100 cm above the bottom from equation (5) and knowledge of u.c and z0a (Table 1), and use the wave-current model iteratively until a value of k n is obtained that reproduces the observed value of u.c. The input values, including the acute angle, ~ wc, between waves and currents, necessary to perform these calculations are listed in Table 3 along with the resulting estimates of U.m, the maximum combined wave-current shear velocity, wave boundary layer thickness, 6wc from equation (7), and equivalent Nikuradse movable bed roughness, kn. Also listed in Table 3 is the value of U~wm, the maximum skin friction shear velocity, previously discussed in conjunction with fluid wave sediment interaction, equation (3). It is seen from the results presented in Table 3 that the wave boundary layer thickness, 6wc, as anticipated earlier, is less than the lowest current meter elevation (29 cm), although it attains surprisingly large values towards the end of our measurements. The equivalent movable bed roughness estimates reflect, of course, the variability of experimental z0, estimates from Table 1. Since kn enters wave-current interaction calculations as a factor in the argument of the logarithmic function, the value of In (kn) and not k, by itself is of primary importance in the present context. We therefore obtain a representative value of the physical movable bed roughness as the geometric (rather than the arithmetric) mean of the five values listed in Table 3, i.e. k, = {II(k~)} °2 = 0.144 cm. It is of some interest to note that this value of the physical bottom roughness is about 60 times smaller than the apparent bottom roughness, k,, a = 30Z0a, obtained from Table 1. The variation of k~-values listed in Table 3 hardly justifies a more elaborate analysis (e.g. seeking a dependence of k, on flow intensity) than the extraction of the single, representative, value given by the geometric

Windstress, bed roughnessand sedimentsuspension

1317

mean. Since the mean grain size, ds0, was 0.10 mm our results suggest a general movable bed roughness of the order k,~ ~ 15 ds0 within a factor of four corresponding to sheet flow conditions. It should be mentioned here that the movable bed roughness predicted by GRANT and MADSEN (1982) for these flow conditions falls in the range of 240-300 d, far exceeding the values obtained here. The results reported here are, however, in qualitative agreement with those of CACCI-IIONEand DRAKE(1990) and others who conclude that the GRANT--MADSEN (1982) bedload correction overpredicts movable bed roughness. As mentioned earlier, the choice of 6we defined by equation (7) was predicated by the relatively wide-spread use of the GRANT--MADSEN(1979) model. If a definition of ~w¢ = KU.m/W had been adopted, values of ~,,¢ would have, not surprisingly, decreased by a factor of about two and the movable bottom roughness estimates would have increased by a factor of about 1.5 resulting in an estimate of k, = 22 ds0. SUSPENDED SEDIMENT CONCENTRATIONS Recently, the size-dependent response of optical backscatter sensors (OBS) has received some attention in the literature. Assuming OBS response to be linear this means that the output voltage, V, for a total concentration of a sediment mixture, c, may be assumed to be given by V = £1.1, = Eb,,cn = ~,(bnfn)C

(8)

where V , is the partial voltage contributed by the nth size class whose fraction in the mixture is fn =Cn/C and has a size-dependent calibration constant b,,. Thus, in order to interpret the OBS signal, V, in terms of concentration, c, equation (8) suggests that the size distribution, fn, in the sampled volume must be known if the OBS response, i.e. bn, is strongly size dependent. Evidence of strongly size-dependent OBS response has been presented by LUDWIGand HANES (1990) who concluded that the strong response of OBSs to the fine fractions prevented them from producing reliable results when suspended sediment could be expected to contain an appreciable amount of fines. GREEN and BOON (1993) demonstrated the applicability of equation (8) and suggested to overcome the problem associated with the unknown fns by using two sensors with different size-dependent responses. From theoretical considerations of the mechanics of suspended sediment mixtures, based on the reference concentration formulation of SMITH (1977), we derive in an appendix a methodology for the estimate of grain size distributions as a function of hydrodynamic conditions (waves and current) and sediment composition in the bed. Treating our sediments as composed of two size classes (n = 1 for fines with d < 0.09 mm (3,55), a median diameter of d l = 0.04 mm, and a fractionfbx = 0.36 in the bottom sediments; n = 2 for the coarse fraction of median diameter d2 = 0.12 ram) separate calibrations showed bl/b 2 = 5, i.e. a pronounced size-dependency as suggested by previous investigators. Introducing these results in equation (8) gives V = b1

(yl %1 + bl

]c

(9)

which shows that a reasonable estimate (accurate to within 10%) of total concentration of suspended sediment, c, may be obtained from our OBS voltage output by using the

1318

o.S. MADSENet 61

° I

I

I

I

I

al.

I

I

I

I

I

5"4" o--o27 cm I - - - , 5 4 cm ,--v120cm 4./T o--o87cm . - - . 1 , 7 cm

i

/" /" J", ~ ~ " . / F ~ / ~ /

3/

/

/"

1 0/0

o)

/ 4"1" / /

OI ~

o

i

10

- I 20

I 30

I 40

I 50

I 60

Time

from O:00 on Oct, 27 (hours)

0--027 cm " - - " 54. cm - - - . a 7 cm ----120cm

1'o

2"0 Time

:

3o

I 70

I 80

I gO

1

~ ' f

:

4o

',

so

:

6o

1

7o

/-

'

so

I

go

loo

from 0:00 on Oct. 27 (hours)

Fig. 8. Time series of burst-averaged concentration of suspended sediments at elevation z~ = 27, 54, 87, 120 and 147 cm above the bottom using sensor calibration obtained from fine fraction (d < 0.09 ram) of bottom sediments. (a) Uncorrected (raw) data; (b) drift-corrected data.

calibration, bl, obtained from the fine fraction if the fraction of coarse sediment, f2, is less than 0.1. As we shall see, the methodology derived in the appendix results in f2 < 0.1 for all our sensors, so we can obtain reasonable estimates of burst-averaged suspended sediment concentration as recorded at the five OBS elevations by simply using the sensor calibration obtained for the fines. The time series of burst-averaged suspended sediment concentration obtained in the manner described above from the five OBS elevations are shown in Fig. 8(a) starting at 0:00 h on 27 October. The series presented in Fig. 8(a) makes little sense in that maximum concentrations are indicated at OBS elevations 54 and 87 cm with concentrations above and below being lower. To ascertain whether or not meaningful information could be extracted from the data, we examined the entire OBS record more closely. Inspection of the OBS records during the period preceding the Halloween Storm on 27 October, 10 days after deployment, reveal that the burst-averaged sediment concentration profiles behaved as expected during passage of a typical autumn storm on 20-21 October.

Wind stress, bed roughness and sediment suspension

1319

Table 4. Resuspension parameter, 70, for reference concentration specified at z = 7 dso

Burst (h) zS(cm) c~= V/b1 (g 1-1) cs(gl -l) fsJ

fs2 Yo×

104

58 27 1.44 1.53 0.93 0.07 3.6

54 2.29 2.36 0.96 0.04 6.3

87 1.80 1.84 0.97 0.03 5.3

66 120 1.10 1.12 0.98 0.02 3.4

147 0.57 0.58 0.98 0.02 1.8

27 1.86 1.95 0.94 0.06 4.0

54 2.76 2.83 0.97 0.03 6.5

87 2.19 2.23 0.98 0.02 5.5

82 120 1.35 1.37 0.98 0.02 3.5

147 0.72 0.73 0.98 0.02 1.9

120 2.08 2.15 0.96 0.04 3.7

147 1.19 1.22 0.97 0.03 2.2

Prior to this storm all OBS measurements showed zero concentration in the water column for hydrodynamic conditions of Ub = 15 cm s -1 and u c - 5-10 cm s -1. Following this moderate disturbance hydrodynamic conditions prevailed at the pre-storm levels for a period of 3 days. However, during these 3 calm days the OBS data showed a steady increase in burst-averaged suspended sediment concentrations. This behavior is probably the result of an electronic drift problem; a c o m m o n ground for the OBS sensors was found to be defective upon recovery of the data logging canisters and therefore lends some credibility to this explanation of the drift exhibited by the OBS data. Assuming a linear drift in time during the quiescent period we fitted straight lines to the data and corrected subsequent OBS concentrations by removing the linear drift. In this manner the time series starting at 0:00 h on 27 October of drift-corrected burst-averaged concentration, shown in Fig. 8(b), were obtained. With the exception of the lowest OBS sensor at z = 27 cm the drift-corrected burst-averaged concentrations now make physical sense in that they indicate a decreasing concentration with elevation above the bottom for the intense storm period, t > 36 h. Given the caveat of the uncertainty of the drift-correction applied to the raw data, a point we shall return to, we can now analyze the resulting drift-corrected concentration measurements shown in Fig. 8(b) using the procedure derived in the appendix. The hydrodynamic conditions necessary to carry out this analysis (u,c, U,m, 6wc and U,wm) are given in Table 3, i.e. we limit our analysis to the bursts, t = 58, 66 and 82 h, for which we have reliable experimental information. Additional parameters needed are the fall velocities, w~ = 0.13 cm s -1 for the fine fraction ( d 1 = 0.04 mm) and wf2 = 1.00 cm s -1 for the coarse (d2 = 0.12 mm), and the critical shear velocities for initiation of motion, u,cr. For the coarse fraction, d2 -- 0.12 mm, we obtain U,~r.2 = 1.24 cm s -1 from the modified Shields diagram of MADSEN and GRANT(1976). This diagram can, however, not be used for the fine fraction since da -- 0.04 mm is beyond the range of diameters covered. Instead, use is made of limited experimental results for initiation of fine natural shaped grains presented by RAUDKM (1976, Fig. 3.13, p. 41) to obtain an estimate of l~l,cr.1 0.98 cm s 1. With fbl = 0.36, fb2 = 0.64, and b l / b 2 = 5 as given previously the results of these computations are presented in Table 4. From the predicted fraction of fine and coarse sediments, fsl and fs2 in Table 4, it is seen that fs2 < 0.1 (even at the lowest sensor) as previously assumed when interpreting our OBS output in terms of suspended sediment concentration using the sensor calibration obtained for the fines, i.e. Cs = V/b1. Nevertheless, we used the theoretically correct transformation (A5) from voltage to total concentration, c~ in Table 4, for our calculations. Also, it is noted in Table 4 that only the data from OBS sensors at zs = 120 and 147 cm were analyzed for the burst at t = 82 h. The =

1320

O.S. MADSENet

al.

reason for this is that only at these elevations did the raw records of voltage output during the burst remain below a preset maximum level corresponding to a concentration of 5 g 1-1"

The 12)'0 values listed in Table 4 are remarkably consistent with a mean value 7o = 4.0 × 10 -4 and a standard deviation of 1.6 × 10 -4. The y0-values obtained here (Table 4) were based on drift-corrected OBS sensor records. Inspection of Fig. 8(a) and (b) shows that the ratios of mean concentrations before and after drift-correction for the period of t = 58-82 h are approximately 1.2, 1.4, 2.2, 1.2 and 1.3 for the zs = 27, 54, 87, 120 and 147 cm sensors, with an average for all sensors of 1.5. Thus, had the raw data been used in our computation of Y0, we would have obtained an average 70 which would have been higher than that obtained from the drift-corrected data by approximately 50%. Another factor affecting our predicted values of y0is the choice of grain size, dl, representing the fine fraction. Here we chose d l = 0.04 mm as the median diameter of the fine fraction. Had we chosen a value of dl corresponding to a dLweighted (fall velocity proportional to d 2) mean for the fine fraction we would have obtained a value of d 1 -~ 0.05 mm. This choice of d I (= 0.05 mm) would have resulted in an increase of y0 estimates over those listed in Table 4 by a factor of approximately 1.5. Hence, the influence of our drift-correction is comparable to the internal variability of our yo-estimates and places the uncertainty of our drift-correction in perspective.

SUMMARY AND CONCLUSIONS

Data on near-bottom velocities and suspended sediment concentration were recovered from 13 m depth off Duck, NC, during the severe Halloween Storm of late October 1991. The current meter data were used to establish the characteristics of the equivalent periodic wave, which had near-bottom rms orbital velocity amplitudes and periods ranging from 0.6 to 1.0 m s -1 and from 10 to 12 s, respectively, during the most severe conditions captured by our instrumentation prior to its demise. Based on the wave conditions alone it is concluded that the fluid-sediment interaction during our experiment was sufficiently intense with ~p',~ > 0.8, to ensure that ripples were washed out. Hence, our data were obtained from movable flat bed conditions. The mean current profiles were analyzed using the log-profile method to obtain shear velocity and apparent bottom roughness characteristics. Only the internally most consistent mean current profiles were accepted for analysis. The acceptable current profiles produced five estimates of the shore-parallel bottom shear stress. A balance of this bottom shear stress and the alongshore wind shear stress was justified and used to obtain a value for the air drag coefficient C a = 4.7 × 10 - 3

(10)

representative of the environmental conditions that prevailed during our experiment. The equivalent periodic wave characteristics and the acceptable current profiles were analyzed using the GRANT--MADSEN (1986) wave-current interaction model, to obtain estimates of the equivalent Nikuradse sand grain roughness, kn, for a movable flat bed. Five acceptable estimates of k,, were obtained and their geometric average, expressed in terms of the median grain size dso (=0.10 mm), k,, -~ 15 d

(11)

Wind stress, bed roughness and sediment suspension

1321

is s u g g e s t e d to be r e p r e s e n t a t i v e for flat m o v a b l e b e d c o n d i t i o n s e x p e c t e d d u r i n g s e v e r e storms. A m e t h o d o l o g y f o r t h e analysis o f O B S m e a s u r e m e n t s o f s e d i m e n t m i x t u r e s was d e r i v e d f r o m t h e o r e t i c a l c o n s i d e r a t i o n s . This m e t h o d o l o g y was e m p l o y e d to an al y ze t h e m e a n s u s p e n d e d s e d i m e n t c o n c e n t r a t i o n profiles c o r r e c t e d for an a p p a r e n t e l e c t r o n i c drift, using t h e h y d r o d y n a m i c v a r i a b l e s d e t e r m i n e d f r o m the a c c e p t a b l e c u r r e n t m e t e r bursts. F o r a r e f e r e n c e c o n c e n t r a t i o n d e f in e d at z = Zr = 7 ds0 a b o v e t h e b o t t o m 12 v a l u e s o f the r e s u s p e n s i o n p a r a m e t e r , Y0, w e r e o b t a i n e d . T h e m e a n v a l u e 90 ~ 4.0 x 10 -4

(12)

is c o n s i d e r e d a p p r o p r i a t e f o r m o v a b l e flat b e d conditions. In a f o r t h c o m i n g p a p e r t h e Ca, k-n, a n d Y0 v a l u e s p r e s e n t e d h e r e will b e used to i n t e r p r e t o u r o b s e r v a t i o n s f u r t h e r a n d to discuss th e i m p l i c a t i o n s o f o u r results for s e d i m e n t t r a n s p o r t p r o c e s s e s in i n n e r shelf w a t e r s d u r i n g e x t r e m e s t o r m ev en t s.

Acknowledgements--This study has been supported by the National Science Foundation, Marine Geology and Geophysics Grant OCE-9017828. The expert seamanship and cooperation aboard the R.V. Cape Hatteras by the captain and crew of that vessel were essential to the study. Field assistance was also provided by Bob Gammisch, Durand Ward, Danny Gouge and Jerome Maa. Dan Hepworth and Jingping Xu assisted in the data analysis and Frank Farmer was instrumental in recovering the data from the OBS data logging canister. Bill Birkemeier, Kent Hathaway, Chuck Long, and their colleagues at the U.S. Army Corps of Engineers Field Research Facility (FRF) at Duck, NC, are thanked for retrieving the remains of our tripod following the storm, for providing the wave and wind data recorded by the FRF, and for their ongoing cooperation. Also acknowledged are comments received from anonymous reviewers, one of which prompted a re-evaluation of our 70 estimates and the theoretical development presented in the appendix. The manuscript was typed by Beth Marshall and by Read Schusky in its final version.

REFERENCES BIRKEMEIERW. A., A. W. DEWALL,C. S. GORaICSand H. C. MILLER(1981) A user's guide to C.E.R.C. 's Field Research Facility. U.S. Army Corps of Engineers, C.E.R.C., MR 81-7. CACCHIONED. A. and D. E. DRAKE(1990) Shelf sediment transport: An overview with applications to the northern California continental shelf. In: The sea, Vol. 9: Ocean engineeringscience, Part B, B. LEMEHAUTE and D. M. HANES,editors, Wiley, New York, pp. 729-773. DOLANR. and R. E. DAVIS(1992) Rating northeasters. Mariners Weather Log, 36, 4-16. DOLANR., H. LINSand B. HAYDEN(1988) Mid-Atlantic coastal storms. Journal of CoastalResearch, 4,417-433. DOWNINGand Associates (1985) Model OBS-2 optical backscatterance suspended solids monitor. Operations manual, version 2/85. GLENNS. M. and W. D. GRANT(1987) A suspended sediment stratification correction for combined wave and current flows. Journal of Geophysical Research, 92, 8244-8264. GRANTW. D. and O. S. MADSEN(1979) Combined wave and current interaction with a rough bottom. Journal of Geophysical Research, 84, 1797-1808. GRANTW. D. and O. S. MADSEN(1982) Movable bed roughness in oscillatory flow. Journal of Geophysical Research, 87,469-481. GRANTW. D. and O. S. MADSEN(1986) The continental shelf bottom boundary layer. Annual Review of Fluid Mechanics, 18, 265-305. GREEN M. O. and J. D. Boon (1993) The measurement of constituent concentrations in nonhomogeneous sediment suspensions using optical backscatter sensors. Marine Geology, 110, 73-81. GROSST. F. and A. R. M. NOWELL(1983) Mean flow and turbulence scaling in a tidal boundary layer. Continental Shelf Research, 2, 109-126. HILL P. S., A. R. M. NOWELLand P. JUMARS(1988) Flume evaluation of the relationship between suspended

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sediment concentration and excess boundary shear stress. Journal of Geophysical Research, 93(Cl0), 12499-12509. LUDWIG K. A. and D. M. HANES (1990) A laboratory evaluation of optical backscatterance suspended solids sensors exposed to sand-mud mixtures. Marine Geology, 94, 173-179. MAA J. P.-Y. (1993) VIMS Sea Carousel: Its hydrodynamic characteristics. In: Proceedings, Workshop for Nearshore and Estuarine Cohesive Sediment Transport, A. J. MEHTA, editor, American Geophysical Union, Washington DC, pp. 265-280.. MADSEN O. S. (1991) Mechanics of cohesionless sediment transport in coastal waters. Proceedings, Coastal Sediments '91, ASCE, 1, 15-27. MADSEN O. S. (1992) Spectral wave-current bottom boundary layer flows. 23rd International Conference on Coastal Engineering (Abstracts), ASCE, 197-198. MADSEN O. S. and W. D. GRANT(1976) Quantitative description of sediment transport by waves. Proceedings, 15th International Conference on Coastal Engineering, ASCE, 2, 1093-1112. MADSEN O. S., Y.-K. POON and H. C. GRABER (1988) Spectral wave attenuation by bottom friction: Theory. Proceedings, 21st International Conference on Coastal Engineering, ASCE, 1,492-504. MELVILLE W. K. (1977) Wind stress and roughness length over breaking waves. Journal of Physical Oceanography, 7,702-710. NIELSEN P. (1981) Dynamics and geometry of wave generated ripples. Journal of Geophysical Research, 86, 6467-6472. RAUDraVI A. J (1976) Loose boundary hydraulics, 2nd Edition, Pergamon Press, Oxford, 397 pp. SATO S. and K. HOmKAWA(1988) Sand ripple geometry and sand transport mechanism due to irregular oscillatory flows. Proceedings, 21st International Conference on Coastal Engineering, ASCE, 2, 1748-1762. SMITHJ. D. (1977) Modeling of sediment transport on continental shelves. In: The sea, Vol. 6, E. D. GOLDBERGet al., editors, Wiley, New York, pp. 53%577. SMITHJ. D. and T. S. HOPKINS (1972) Sediment transport on the continental shelf off of Washington and Oregon in light of recent current measurements. In: Shelf sediment transport: Process and pattern, D. J. P. SWXFT,D. B. DUANE and O. H. PILKEY, editors, Dowden, Hutchinson and Ross, pp. 143-180. STERNBERGR. W. (1986) Transport and accumulation of river-derived sediment on the Washington continental shelf, U.S.A. Journal of the Geological Society, 143, 945-956. STERNBER~ R. W., D. H. CACCmONE, D. E. DRAKE and K. KRANCK(1986) Suspended sediment transport in an estuarine tidal channel within San Francisco Bay, California. Marine Geology, 71,237-258. VINCEm" C. E., R. A. YOUNG and D. J. P. SWIFT (1981) Bedload transport under waves and currents. Marine Geology, 39, M71-M80. WRIGHT L. D. (1987) Shelf-surfzone coupling: Diabathic shoreface transport. Proceedings, Coastal Sediments '87, ASCE, 25-40. WRIGHTL. D., J. D. Boor~, M. O. GREEN and J. H. LIST (1986a) Response of the mid shoreface of the southern mid-Atlantic Bight to a "northeaster". Geo-Marine Letters, 6, 153-160. WgmnT L. D., A. D. SNORTand M. O. GREEN (1986b) Short-term changes in the morphologic states of beaches and surf zones: An empirical model. Marine Geology, 62,339-364. WRIGHT L. D., J. D. BOON, S. C. KIM and J. H. LIST (1991) Modes of cross-shore sediment transport on the shoreface of the Middle Atlantic Bight. Marine Geology, 96, 19-51. Wu J. (1982) Wind-stress coefficients over sea surface from breeze to hurricane. Journal of Geophysical Research, 87, 9704--9706.

APPENDIX:

ANALYSIS OF OBS-RECORDS

FOR SEDIMENT

MIXTURES

Given the sensitivity of optical backscatter sensors' response to grain size, we start our analysis by assuming the mean reference concentration for suspended sediment in combined wave-current flows to be given by

c,,,= yoc~bn ( ~ ) Tcr,n

(A1) t

for the nth sediment size class of diameter dn. This expression, or slight modifications thereof, for the reference concentration has been widely used since the pioneering work of SMITH(1977). In equation (A1), Jbn denotes the fraction of size class n in the bottom sediments, cb is the volumetric concentration of sediment in the bed (here taken as 0.65), rcr,n is the critical shear stress for initiation of motion of the nth size class, e.g. obtained from the

Wind stress, bed roughness and sediment suspension

1323

modified Shields diagram of MADSEN and GRANT (1976) using d = d~, and r' is the skin friction shear stress, i.e. the shear stress based on a bottom roughness equal to the median diameter ds0 of the bottom sediments and () denotes time averaging. For combined wave-current flows dominated by the wave motion we have ]v'[ = r" m tcos ~ot[ = pu',w,.21 cos ~ot[ and equation (A1) may be written c rn -- - ~' c¢ [2/u--~wm/21] YO b J b n 1 7 |

(A2)

yoCbfbnan

L2~\U,cr,n/

where u,cr, n = ~ is the critical shear velocity for initiation of motion of the nth size class. Equation (A2) specifies the magnitude of the reference concentration but not the elevation where this applies. Because of the rapid increase of suspended sediment concentration as the bottom is approached the choice of reference elevation, z = zr, where equation (A2) applies is a crucial choice with pronounced effect on the resulting value of Y0, the resuspension parameter. Indeed much of the variation of reported 70 values in the literature may be attributed to different choices of z~, e.g. STERNBERGet al.'s (1986) choice of zr = 20 cm, HILL et al.'s (1988) choice of Zr = 2 cm and GLENN and GRANT'S (1987) choice of z~ = Z0a = the apparent roughness scale. Based on the simple bedload transport model developed by MADSEN (1991) we choose zr = 7d50 since this height above the bottom roughly corresponds to the thickness of the bedload layer, i.e. with this choice the transport above z = z~ is regarded as suspended load whereas the transport below z = z~ is obtained separately from bedload calculations. Consistent with the GRANT--MADSEN(1986) wave-current interaction model an eddy diffusivity is chosen as the turbulent eddy viscosity, i.e. we neglect stratification effects and scale the eddy diffusivity by u , m , the maximum combined wave-current shear velocity, inside the wave boundary layer, z < 6we, and by u,c,the current shear velocity, outside the wave boundary layer. Treating each size class separately, see GLENN and GRANT (1987) for details, we obtain the concentration of suspended sediment of size class n at elevation z s > 6 wc as

/6 \-wr,/Ku*m/ z \ - w t , IKu*, Csn = Crn [~wc} [ ¢-~__s] = Crnfls n \ Zr / \Owc]

(A3)

in which dwc is given by equation (7), z~ = 7d50, and w f , is the fall velocity of the nth size class. From equation (A3) it follows that the fraction of suspended sediment of the mth size class at elevation zs is given by fsm-

Crmflsm

(A4)

-- fbmamflsm

X(Crg~,n) X(fb~a~,,) when equation (A2) is introduced. It is noted that the size distribution of suspended sediment obtained in this manner is independent of the value of the resuspension parameter, 70. Thus, equation (A4) may be used to obtain an estimate of size distribution from knowledge of bottom sediment characteristics and hydrodynamic conditions, i.e. equation (A4) provides the information necessary to transform size-sensitive OBS output voltages, V, to total suspended sediment concentrations, % for mixtures via the formula V c, - E(bff,,)

(A5)

where b~ is the size-dependent calibration factor of the OBS obtained from laboratory calibration of the sensor. Combining equations (A4) and (A5) the concentration of individual size classes may be obtained - f c. . . . . . .

(A6)

c = fbmamflsm V E(fb,,a,,fl,,,) E ( b f f ~ , )

and upon introduction of Csm as given by equation (A3) with Crm given by equation (A2) we obtain the following expression for the resuspension parameter 1

V

1 _

ro = X(£.a~s~) X(b~f~) c~

1

q

(A7)

X(fb~a~) c~

It is of some interest to contrast equation (A7) to the result obtained if a single grain size is used in the analysis of an OBS signal. Denoting the single grain size result by subscript r we would obtain

1324

O.S. MADSENet al.

1 V1 Yor - arfls,, br Cb

(AS)

or, taking the ratio of equations (A7) and (A8), Yo _

Yo,

arflsr b~ X(fb,,anflsn) X(b,Js,,)

brarfls, X(fb,,b,,a,,flsn)"

(A9)

This expression suggests a pronounced sensitivity of the estimate of the resuspension parameter to choice of a single representative grain size not only when OBS response is strongly size-dependent but also when the parameter fls,, is strongly size dependent--which it will be unless the exponents wf./(Ku.m) and wln/(ru.c ) in equation (A3) are very small for all size classes present.