Numerical modeling of hyperpycnal plume

Marine Geology 222–223 (2005) 193 – 211 www.elsevier.com/locate/margeo

Numerical modeling of hyperpycnal plume Sadia M. Khan a,*, Jasim Imran a, Scott Bradford b, James Syvitski c a

Department of Civil and Environmental Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208, USA b Naval Research Laboratory, 4055 Overlook Ave. SW., Washington DC 20375, USA c Institute of Arctic & Alpine Research, University of Colorado at Boulder, 1560 30th Street, Campus Box 450, Boulder CO, 80309-0450, USA Accepted 15 June 2005

Abstract When the density of sediment laden river water exceeds that of the ambient ocean water, the river plunges to the ocean floor and generates a hyperpycnal plume. Hyperpycnal plumes can travel significant distances beyond the continental shelf and may be sustained for hours to weeks. There are several Apennine Rivers in Italy that are likely to develop hyperpycnal discharges on the Western Adriatic shelf. Among them, River Tronto is a moderately ddirtyT river capable of producing 64 hyperpycnal flow events (lasting z6 h) during a 100 year period. Numerical simulations of hyperpycnal events have been conducted for the Adriatic shelf near the mouth of River Tronto using a two-dimensional depthintegrated finite volume model to study the spreading of the plume and its interaction with the alongshore current. Simulation results indicate that the alongshore current has great impact on the spreading and deposition pattern of the hyperpycnal flow. Sedimentary deposits generated from a series of simulated hyperpycnal flow events have developed undulating bed forms. D 2005 Elsevier B.V. All rights reserved. Keywords: hyperpycnal flow; alongshore current; undulation; Adriatic shelf; Apennine rivers

1. Introduction When a river contains an elevated suspended sediment concentration, to the extent that the river density is greater than that of the receiving water body, the river can plunge and create a hyperpycnal plume or turbidity current. After a river plunges into the ocean, * Corresponding author. Tel.: +1 803 777 1210; fax: +1 803 777 0670. E-mail address: [email protected] (S.M. Khan). 0025-3227/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.margeo.2005.06.025

the resulting hyperpycnal plume can travel significant distances and may be sustained for hours to weeks until it loses its identity by entraining surrounding ambient water and dropping its sediment load. The driving force of a hyperpycnal flow is obtained from its bulk density difference with the ambient water. River water entering the marine basins are required to have suspended sediment concentration at least 35 to 45 kg/m3 (depending on the salinity and temperature of the coastal waters) to be able to plunge (Mulder and Syvitski, 1995). Many small to medium

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size rivers that discharge into the sea, produce hyperpycnal flows during large flood events (Mulder and Syvitski, 1995). Fig. 1 shows a schematic diagram of the formation of hyperpycnal flow. Hyperpycnal flows, though infrequent, can have a profound impact on the morphology of ocean basins. It is commonly accepted that hyperpycnal plumes are one of the potential processes through which sediment can be transferred to the deep sea environments. On their way toward the down slope direction, these bottom currents can influence the seabed morphology by depositing, eroding, and dispersing large quantities of sediment particles. Deposits (known as turbidites) from these types of flows often form porous layer of rocks which are potential sources of hydrocarbon. Oceanic sedimentary deposits have also strong relevance to acoustic and optical applications of the Navy. Therefore, it is important to have a clear and effective knowledge of the dynamics and depositional characteristics of hyperpycnal flow. Large-scale hyperpycnal flow or turbidity currents in the natural environment are difficult to monitor because of the unpredictable nature of the events. As a result, most of our knowledge about these flows is derived from small-scale laboratory experiments, numerical simulations or deduction made from the ancient sedimentary records. Numerous authors have reported the occurrence of hyperpycnal flow based on sedimentological evidence (e.g. Foster and Carter, 1997; Mulder et al., 1998; Normark et al., 1998). Most laboratory experiments (Middleton, 1967; Fietz and Wood, 1967; Garcı´a and Parker,

1993; Alexander and Morris, 1994) have been conducted at small scale to understand the physics of the flow. Recent proliferation in numerical modeling of hyperpycnal flow or turbidity currents arises from the fact that a numerical model can make predictions of the flow dynamics and deposition pattern over large scale. Numerical modeling can also provide a visualization of the various stages of flow and deposition. There are two approaches to numerically simulate turbidity currents. One approach is to use simple Newtonian force equilibrium approach based on the Che´zy equation (Skene et al., 1997). Another approach is the use of the depth-averaged Navier– Stokes equations (Fukushima et al., 1985; Chikita, 1991; Zeng and Lowe, 1992; Imran et al., 1998; Bradford and Katopodes 1999a,b; Salaheldin et al., 2000). In the present study, a numerical model of hyperpycnal flow generated by the plunging of a river has been developed. The model incorporates the interaction between a developing hyperpycnal flow and the alongshore current of specified magnitude and direction. In this model, the depth-averaged governing equations of dilute suspension and the Exner equation of the bed sediment continuity have been solved using a finite volume technique. The main focus of this paper is on investigating the influence of alongshore current on the development of a potential hyperpycnal flow generated in the Adriatic Sea. Numerical simulations have also been conducted to observe the change in bed elevation due to different initial and boundary conditions.

Plunge point

Inflow from river mouth

Ambient water Entrainment of ambient water

Continental shelf

Hyperpycnal flow

Exchange of sediment particles

Fig. 1. Schematic of hyperpycnal flow generating by plunging of river water showing different mechanisms involved in the process.

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2. Model descriptions The numerical model Hyper (abbreviation for hyperpycnal flow) is a two-dimensional depth-averaged model. This finite volume model solves the depth-averaged equation of mass, momentum and sediment conservation of density driven flow along with the Exner Equation of bed sediment continuity. The model is based on earlier works of Bradford and Katopodes (1999a,b), and Imran and Syvitski (2000). To incorporate the effect of alongshore current on the development of hyperpycnal flow, the governing equations used in the earlier work of Bradford and Katopodes (1999a,b) have been slightly modified through coordinate transformation. The resulting governing equations for conservation of fluid mass, momentum and sediment concentration are as follows: Continuity pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Bh BðhuÞ B½hðv þ wÞ þ þ ¼ E w u2 þ v 2 ð1Þ Bt Bx By X-momentum   1 B hu2 þ gh2 RCT BðhuÞ B½huðv þ wÞ 2 þ þ Bt By Bx 2 ¼  ghRCT sx  u4 ð2Þ Y-momentum   1 2 B hvðv þ wÞ þ gh RCT BðhvÞ BðhuvÞ 2 þ þ Bt Bx By ¼  ghRCT sy  v42 ð3Þ Conservation of suspended sediment BðhCi Þ BðhuCi Þ Bðv þ wÞCi þ þ ¼ vsi ðpi Esi  Cbi Þ Bt Bx By ð4Þ The bed sediment conservation equation has the form ð 1  cÞ

Bz ¼ vsi ðcbi  pi Esi Þ Bt

ð5Þ

In the above equations, h represents current thickness, u and v are depth-averaged velocity in x- and ydirection, w is the alongshore current of constant

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magnitude. Though alongshore current may vary with the depth of water column, we consider constant magnitude of alongshore current for the entire water column due to the use of depth-averaged equations in the present model. C i represents vertically averaged volume concentration of ith sediment and C T is the summation of all sediment fractions. The parameter R i = (q si  q) / q, where q si is the density of ith sediment and q is the density of ambient water. The shear velocities are defined as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð6Þ u42 ¼ CD u u2 þ v2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v42 ¼ CD v u2 þ v2 ð7Þ Here, C D is the bed drag coefficient which ranges from 0.002 to 0.05 depending on the flow type (Garcia, 1990). The bed slopes in x- and y-directions are represented by s x and s y, respectively. In order to close the problem, it is necessary to use some internal relationships. Fluid entrainment coefficient E w is specified by using the relation of Parker et al. (1986). 0:00153 0:0204 þ Ri

EW ¼

ð8Þ

where, Ri is the bulk Richardson number and is defined as Ri ¼

RCT gh ð u2 þ v 2 Þ

ð9Þ

The expression developed by Garcia and Parker (1993) for sediment entrainment coefficient E si of ith sediment is used for model closure, i. e. Esi ¼

1:3  107 Zm5 i 1:0 þ 4:3  107 Zm5 i

ð10Þ

where, Zmi ¼ a1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u42 þ v42 vs

Rap2

ð11Þ

pffiffiffiffiffiffiffiffiffi and ð RgDÞD Rp ¼ is the particle Reynolds number, D is v characteristic grain size, m denotes the kinematic viscosity of water. The parameters (a 1, a 2) take respective values (1, 0.6) for R p N 2.36 and (0.586, 1.23) for Rp V 2.36. The fall velocity v s is calculated using the empirical relationship developed by Dietrich (1982).

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The near bed concentration of ith sediment c bi is calculated using the expression developed by Garcia (1994),   cbi Di 1:64 ¼ 0:4 þ 1:64 ð12Þ Ci Dsg where D sg denotes the geometric mean size of the suspended sediment mixture. The governing equations of the present model are solved using a finite volume method. In order to get a second order accuracy in time, a predictor–corrector time stepping approach is adopted to solve the governing equations for conservation of fluid mass, momentum and sediment concentration. For computing the interfacial fluxes, Roe’s approximate Riemann solver has been used in the present model. The bed continuity equation has been solved after solving the equations governing the flow field. In order to maintain the second order accuracy, Heun’s predictor and corrector method has been used to integrate the equation. More details on the numerical scheme can be found in Bradford and Katopodes (1999a). Due to the presence of source term in the continuity equation, some oscillations are observed near the front of the turbidity current head. These oscillations become higher when the current spreads out into the large scale domain. To dampen these oscillations, a constant coefficient artificial viscosity model given by Jameson et al. (1981) has been used. This procedure works to smooth large gradients while leaving the smooth areas relatively undisturbed. For the present model, we apply this smoothing procedure for current thickness (h) only.

3. Model verification Bradford and Katopodes (1999a) verified extensively the original finite volume model representing two-dimensional turbidity currents with analytical solutions and experimental data obtained from laboratory flumes. Here, we conducted an additional verification by simulating the experimental work of Kubo and Nakajima (2002) on the formation of sediment waves due to initial bed perturbation. The one-dimensional depositing turbidity currents described by Kubo and Nakajima (2002) can be easily adapted in the present model by changing the solution algorithm and boundary conditions to one-dimensional configuration. The laboratory experiment was carried out in a flume 10 m long, 0.2 m wide and 0.5 m deep. A surge-type turbidity current was created by using a gate box of 0.5 m length at the upstream end of the flume. The bottom of the flume consisted of initial slope of 0.1 for the first 1 m followed by four ridges of 0.036 m height and 1 m length. Suspended sediment material used in the experiment consisted of a mixture of fine sand (88 micron, 40%), coarse silt (62.5 micron, 50%) and medium silt (31.2 micron, 10%). We applied the model Hyper to simulate the bed evolution using the same initial condition used in the experiment. A total of 400 control volumes in the downstream direction has been used in the simulation. Same initial area of flow has been considered here by taking the control volume width same as the tank. The friction factor was set equal to 0.005. The amount of deposited or eroded sediment is calculated from the sediment flux at the bed and is converted to bed 0.6 Experimental Numerical Bed Topography

0.25

0.5

0.2

0.4

0.15

0.3

0.1

0.2

0.05

0.1

0

Bed elevation (m)

Deposit density (gm/cm2)

0.3

0 0

1

2

3

4

5

Distance from the gate (m) Fig. 2. The bed deposity density profiles with bottom topography. Experimental data are form the work of Kubo and Nakajima (2002).

S.M. Khan et al. / Marine Geology 222–223 (2005) 193–211

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thickness by assuming sediment porosity of 0.5. The results of the bed deposit density (which can be defined as deposited sediment mass per unit area) are compared with the experimental data. Model results (Fig. 2) show good agreement with the experimental data. The model captures the peak in the deposit density in the upstream flanks of the ridge as observed in the laboratory.

Table 2 Sediment concentration (kg/m3) predicted by HydroTrend model for post-dam river mouth conditions

4. Model application to Apennine rivers

tic shelf during five large rainstorm events within a simulation time of 100 yr. As an example, the Tronto River only experiences hyperpycnal conditions for 0.2% of the 100 yr period. Importantly, this small time interval was capable of transporting 38% of the total sediment load (7% of the total bedload, and 50% of the total suspended load for this period). The most important anthropogenic impact on the physical characteristics of sediment sources and their temporal variability on continentalmargin are building the dams on the river. Construction of the reservoir dams in the Apennine Rivers strongly affects the water and sediment discharges in the Adriatic (Syvitski, 2003). From the HydroTrend model results, it is observed that the total sediment concentration discharged by these rivers has been reduced considerably (30% to 40%). After the dam construction, the Apennine rivers are still capable of producing hyperpycnal flow albeit on a much less frequent basis and for a shorter duration (Table 2). Dam operators in the Apennine region control flow for irrigation, drinking supply and to maintain minimum flow levels, and not for floodwater mitigation. Among the several Apennine Rivers, Tronto is a moderately dirty river which carries large amount of suspended sediment during flood events. According to HydroTrend results, Tronto is likely to generate hyperpycnal flow events at 25 years return flood

Apennine Rivers, draining the watersheds (100 to 3100 km2) of the Apennine Mountains of Italy into the Western Adriatic Sea, are small to medium in size. Discharges from these rivers are highly episodic and carry large amount of sediment during flood events. Among them, Chienti, Potenza, Pescara, Tronto and Metauro Rivers are examples of rivers with the ability to generate hyperpycnal discharges on the Western Adriatic shelf during large flood events. Hyperpycnal flow generated at the mouth of these rivers carrying large concentration of silt and clay can have major impact on the continental strata formation (Mulder and Syvitski, 1995). For the simulation of hyperpycnal events, hydrologic data at the mouths of these rivers were generated by application of the model HydroTrend. This model is able to simulate daily sediment loads and water discharges for pre- and post-emplacement of reservoir dams (Syvitski, 2003). Simulation under the conditions prevailing prior to dam emplacement show that the Apennine rivers were likely to generate hyperpycnal discharges; between 2 and 4 events (i. e. 25 to 50 years return interval floods) would last for greater than 24 h, but many more events are likely to occur for shorter duration (z6 h). Table 1 shows the Sediment concentration of five Apennine Rivers discharging on the Western Adria-

River

Event–1

Event–2

Event–3

Event–4

Event-5

Chienti Potenza Metauro Pescara Tronto

16.79 18.93 12.69 15.77 18.94

17.74 20.11 13.79 15.54 19.24

23.77 30.46 17.95 18.38 25.8

36.41 41.95 28.42 29.17 39.78

16.92 20.58 13.55 9.8 16.09

Table 1 Sediment concentration (kg/m3) predicted by HydroTrend model for pre-dam river mouth conditions

Table 3 Hydrologic data of River Tronto for the flood event–4

River

Event–1

Event–2

Event–3

Event–4

Event-5

Data

Chienti Potenza Metauro Pescara Tronto

32.15 35.34 23.51 33.11 47.26

33.37 36.91 25.13 32.05 46.55

66.79 83.78 49.22 51.36 93.53

53.42 58.98 41.53 46.76 71.11

30.64 35.81 23.65 24.59 36.8

River River River River River

mouth mouth mouth mouth mouth

discharge width depth sediment conc. velocity

Pre-dam

Data source

331.6 m3/s 54.1 m 4.1 m 71.1 kg/m3 1.8 m/s

HydroTrend HydroTrend HydroTrend HydroTrend HydroTrend

Model Model Model Model Model

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interval (lasting longer than 24 h) under the pre-dam condition and hyperpycnal events every second year (on average) that last longer than 6 h. Though the placement of dam on this river reduces its sediment

carrying capacity to a considerable amount, it is still capable of generating hyperpycnal flow every few years but most of these do not last longer than 6 h. We have considered the flood discharges from River

(a) 5 Depth (m)

Ambient water 0

-5 0

250

500

750

1000

Distance across the shore (m)

(b) 5 Depth (m)

Ambient water 0

-5 0

250

500

750

1000

Distance across the shore (m)

(c) 5 Depth (m)

Ambient water 0

-5 0

250

500

750

1000

Distance across the shore (m)

(d)

Depth (m)

5

Ambient water 0

-5 0

250

500

750

1000

Distance across the shore (m) Fig. 3. Simulation results obtained from FLUENT to capture the transformation process of open channel flow into hyperpycnal flow from River Tronto. Formulation process of a stable plunge are shown at different time level, (a) time = 20 s; (b) time = 80 s; (c) time = 160 s and (d) time = 480 s.

S.M. Khan et al. / Marine Geology 222–223 (2005) 193–211

Tronto for the simulation of hyperpycnal events and their impact on the sea floor morphology as a case study. 4.1. Capturing the plunging process using FLUENT When a river discharges sediment laden water into the ocean, it will travel some distance depending on the bottom slope before plunging. A depth-averaged model cannot simulate the plunge process itself and the flood discharge data needs to be converted into input conditions for a depth-averaged turbidity current model. The hydraulic parameters involving a plunge flow can be obtained either from semi-empirical models (e.g., Akiyama and Stefan, 1984) or from the solution of Navier–Stokes equations (e.g., Kassem and Imran, 2001). Here, hydrologic data generated from HydroTrend model runs have been converted into inflow conditions for Hyper by using a commercially available three-dimensional hydrodynamic model FLUENT. In FLUENT, solution of the Reynolds-averaged Navier–Stokes equations along with the conservation equation of suspended sediment simulates the transformation of a river flow into a hyperpycnal plume through the plunge process. Kassem and Imran (2001, 2004); Imran et al.

199

(2004); Kassem et al. (2003) have extensively used FLUENT to study density currents. From HydroTrend model runs, a typical flood event that generates large flow and sediment concentration under pre-dam scenario has been selected for inflow boundary conditions in FLUENT (Table. 3). Flow characteristics downstream of the plunge point obtained from FLUENT simulation provides the necessary input conditions for running the depth-averaged model Hyper. Fig. 3 shows the plunge process and the subsequent formation of turbidity current due to a typical flood discharge from River Tronto under the pre-dam condition. 4.2. Input parameters and boundary conditions for model hyper A computational domain of 10 km  10 km in size has been selected for the numerical simulation and navigational charts have been used to construct the bottom boundary. Across the shore, the bed consists of a relatively steep slope followed by a mild gradient. Variation of the sea bed in the alongshore direction has not been considered. We took simplified bathymetry for the computational domain as the main focus of this study is to observe the effect of alongshore current. Test

Solid wall River Tronto

Solid wall Outflow

0 Bed elevation (m)

-5

10000

-10 0

8000 Outflow 2000 Dis tan 4000 ce a cro ss t 6000 he sho re

Outflow

4000 8000 (m)

2000 10000 0

ce

g lon

the

r ho

s

a

an

st Di

m)

e(

6000

Fig. 4. A three dimensional view of ocean floor of the computational domain.

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Sediment concentration Discharge

80

500

75

400 65 60 55

300

50

Discharge (m3/s)

Sediment concentration (kg/m3)

Peak

70

45 200 40 35

Critical concentration level for the formation of under current

30 19884

100 19886

19885

No. of days in 100 years Fig. 5. Sediment concentration history and discharge hydrograph during a typical flood event for River Tronto (predicted by HydroTrend model).

runs have shown that the Coriolis parameter has nominal effect for the cases considered and it is therefore, neglected in the simulations. The upstream boundary (Fig. 4) is considered as solid wall except for a distance equal to the width of the river mouth in the middle which is treated as the inflow boundary. The other three sides of the domain are treated as outflow boundaries which allow the flow to leave the domain when it reaches one of these boundaries. For a supercritical flow (i.e. Ri b 1.0), the present model requires information on current thickness, velocity, sediment concentration and grain size at the inflow boundary. Erodible bed type is considered as bottom boundary condition provided that maximum bed erosion will occur up to certain depth. In nature, it has been observed that turbidity currents can be sufficiently erosive on relatively steep slopes (e.g. Inman et al., 1976; Parker et al., 1986; Normark and Piper, 1991). If the initial current is strong and erosive, it may become even stronger by efficient conversion of turbulent kinetic energy to potential energy through the entrainment of sediment from the ocean bed (Imran and Syvitski, 2000). If the conservation of turbulent kinetic energy is not considered in a numerical model, it sometimes predicts ignition of the

flow to an energy violating catastrophic state. As a result unrealistic bed erosion can be predicted. In the present model we did not consider the conservation of turbulent kinetic energy. Instead, we consider the bed to be consolidated below a certain depth, to prevent the flow from igniting to an energy violating state. 4.3. Effect of alongshore current on hyperpycnal plume An alongshore current usually develops due to wind velocity and can transport considerable amount of sediment in the direction parallel to the shore. It is Table 4 Inflow data for Case I and Case II used in Model dHyperT Flow parameters

Case-I

Case-II

Simulation time Current thickness Inflow velocity Sediment conc. Grain size, D 50 Along shore current (Southward dir.)

8h 2.0 m 1.2 m/s 0.0163 m3/m3 30 Am 0.0 m/s

8h 2.0 m 1.2 m/s 0.0163 m3/m3 30 Am 0.4 m/s

S.M. Khan et al. / Marine Geology 222–223 (2005) 193–211

(a)

201

10000

Reference velocity 1.0 m/s

Distance along the shore (m)

North 7500

5000

2500

0 0

2500

5000

7500

10000

Distance across the shore (m)

(b)

10000

7500

0. 0 7

-0.8907 -0.3 43 0 0.09 51

1

5000

0.2046

95

0. 09 51 -0 .1 240 0 .4 23

Distance along the shore (m)

North

2500

0 0

2500

5000

7500

10000

Distance across the shore (m) Fig. 6. Plot of (a) velocity vector and (b) contour of net change in bed elevation of River Tronto for Case I. Erodible bed condition has been considered. Contour values are given in meters.

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(a)

Distance along the shore (m)

10000

North

7500

Reference velocity 1.0 m/s 5000

2500

0

0

2500

5000

7500

10000

Distance across the shore (m)

(b)

Distance along the shore (m)

10000

North

7500

5000 -0. 0 -0.174 582 1

-0.58

2500

72

-0.8234

0.9273 0. 6 52 0

-0 .

-0 .

17

42

82 -0

41

.1

74

1

0

0

2500

5000

7500

10000

Distance across the shore (m) Fig. 7. Plot of (a) velocity vector and (b) contour of net change in bed elevation of River Tronto for Case II. Erodible bed condition has been considered. contour values are given in meters.

S.M. Khan et al. / Marine Geology 222–223 (2005) 193–211

likely that alongshore current may have significant influence on the shape and direction of turbid underflows generated at the shelf. To investigate this effect, the numerical model Hyper has been applied with and without the presence of alongshore current. We considered a typical flood event (Fig. 5) of pre-dam condition in which River Tronto has been predicted to generate hyperpycnal flow by discharge of a large amount of suspended sediment to the Western Adriatic shelf. Geyer et al. (2003) measured strong southward alongshore current near the Chienti river mouth on the Western Adriatic Sea. The measured data shows that this current can reach a velocity of 1.0 m/s during a flood event. We have considered 0.4 m/s to be a typical value for the Western Adriatic Sea. For both cases, the model has been run for an 8-h flow period with constant inflow conditions. Erodible bed condition without any consolidation effect is used in both cases. Though the model is capable of handling non-uniform grain size, we considered uniform grain size for this case. Tables 3 and 4 summarize the hydrologic data of River Tronto predicted by HydroTrend and the converted inflow parameters for model Hyper obtained using FLUENT. Velocity vector plotted in Fig. 6a indicates that in the absence of alongshore current, hyperpycnal plume simply moves towards the downstream direction following the natural gradient. The model predicts significant erosion of the bed material (up to 0.9 m) at the steeper part of the shelf near the river mouth (Fig. 6b). Low height levees have formed near the river mouth which are weakly flared outward from the inlet, creating a channel between them but could not elongate in the mild slope region because of rapid sediment deposition near the slope break. In the second case, a southward alongshore current with a constant magni-

203

tude of 0.4 m/s has been applied. From Fig. 7a, it is clearly evident that an alongshore current can significantly change the spreading pattern of the hyperpycnal plume. The southwardly directed alongshore current can turn the head of the plume towards the southeast direction instead of allowing the plume to flow in the downslope direction. After 8 h of simulation, the plume hits the downstream boundary whereas without the alongshore current, it only travels half of the distance. Sediment dispersion pattern has also been changed due to the presence of alongshore current (Fig. 7b). Erosion becomes more significant and extends to the end of the domain. As the hyperpycnal flow near the river mouth becomes concentrated within a narrow region, the current velocity increase in the downstream direction and a substantial amount of erosion occurs along the path of the current.

5. Evolution of complex bed feature by successive hyperpycnal events The shore parallel undulating bed features observed on the western Adriatic shelf (Correggiari et al., 2001) are complex in nature and the interpretation of their origin puts the researchers at odds. Correggiari et al. (2001) described the observed undulation as sediment wave field. They considered sediment failure as the possible mechanism for the formation of these crenulations. However, Lee et al. (2002) analyzed the sedimentary deposits on the Adriatic shelf based on nine diagnostic characters and suggested that the bed formation is due to a series of turbidity current events rather than submarine land slide. Later on, Cattaneo et al. (2004) suggested that flood related hyperpycnal flows proposed by Lee et

Table 5 Data used for the sediment wave formation on the Adriatic shelf Parameters

Event-1

Event-2

Event-3

Event-4

Inflow velocity Inflow current thickness Inflow sediment conc. Along shore current Grain size, D 50

1.3 m/s 4.0 m 0.012 m3/m3 0.0 m/s 30 Am

1.3 m/s 4.0 m 0.012 m3/m3 0.4 m/s (northward direction) 30 Am

1.3 m/s 4.0 m 0.012 m3/m3 0.0 m/s 30 Am

1.3 m/s 4.0 m 0.012 m3/m3 0.4 m/s (southward direction) 30 Am

Same data has been used for Case I *, Case II ** and Case III ***. * Non-erodible bed condition. ** Erodible bed condition – 0.5 m depth of maximum erosion considered. *** Erodible bed condition – 1.0 m depth of maximum erosion considered.

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the possible impact of hyperpynal flow on the deposition pattern on the Adriatic shelf. Here, numerical simulations have been conducted considering several successive hyperpycnal flow events and their interaction with the alongshore current. Different types of bed condition (erodible / non-erodible) have also been considered to study the effect of bed consolidation. We have assumed that the bed is sufficiently consolidated beyond 1.0 m of depth. Numerical simulations have been conducted for three different cases, (a) Case I (non-erodible bed): erosion is not allowed below initial bed elevation; (b) Case II (erodible bed): initial bed is consolidated beyond 0.5 meter of depth and (c) Case III (erodible bed): initial bed is consolidated

al. (2002) are less likely to have caused these undulations because of the lack of preserved event beds (deposition from river-flood) observed on the western Adriatic shelf. According to Cattaneo et al. (2004), steady alongshore bottom currents observed on the western Adriatic shelf (e.g., Gacic et al., 1999; Poulain, 2001) are probable cause for the formation of these undulations. There is no observed record of hyperpycnal flow generation at the mouths of Apennine rivers. However, based on the characteristics of these rivers and the prediction made by HydroTrend model (Syvitski, 2003), these rivers are likely to go hyperpycnal in frequent intervals. It is, therefore, important to explore Z

Z

(a)

X

(b)

Y

X

Y

0

-10 0

0 2000

-10 0

0

20 00

tan

ce

400 0

alo

ng

4000

the

6000

sho

re

600 0 80 00

(m

8000

) 10 000 100 00

nce

he ss t

sho

20 00

Dis

m)

200 0

tan

re (

ce

400 0

alo

ng

o

acr

the

6000

sho

re

ta Dis

600 0

(m

)

800 0

80 00 10 00 0 10 00 0

Z

(c)

m)

4000

nce

e s th

re ( sho

os

acr

ta Dis

(d)

X

Z

Y X

Y

0

-10 0

0 2000

Dis

20 00 400 0

tan

ce

alo

ng

4000 6000

the

sho

600 0

re

80 00

(m

)

8000 1000 0 100 00

tan

Dis

ce

he

t oss acr

sho

re (

m)

Bed elevation (m)

-5

0

-5

-10 0

0 200 0

Dis

tan

200 0

ce

400 0

alo

ng

re (

40 00

the

60 00

sho

re

60 00 800 0

(m

)

800 0

tan

Dis

ce

m)

he

t oss acr

sho

100 00 10 00 0

Fig. 8. Bed evolution for (a) event-1; (b) event-2; (c) event-3 and (d) event-4. Initial bed is considered non-erodible.

Bed elevation (m)

Dis

-5

Bed elevation (m)

-5

Bed elevation (m)

0

S.M. Khan et al. / Marine Geology 222–223 (2005) 193–211

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5.1. Three-dimensional bed features

beyond 1.0 meter of depth. In each case, a series of hyperpycnal flow events with same flood intensity but with different magnitude and direction of alongshore current has been used. The initial bathymetry at the beginning of this series of events consists of steep slope followed by mild gradient. No perturbation in the original bed elevation has been considered. In each subsequent event, the bathymetry obtained from the previous event has been used as the initial bed. Although in nature, hemipelagic sedimentation (i.e., surface plume rainout, nepheloid deposition) will occur between turbidity current events which will affect the bedform (Lee et al., 2002); these processes are not considered in our numerical simulations for the sake of simplicity. Table 5 summarizes the input conditions used in different numerical experiments.

Figs. 8–10 show the evolution of the bed after each flow event for the three cases. Complex undulating bed has evolved in all cases. In Case I, an incipient channel with levees have formed after the first event. The levees continue to grow towards the downstream direction and move further apart after 8 h of flow period. The flow decelerates as it reaches the milder part of the basin and forms fanlike depositional feature (Fig. 8a). In Cases II and III, similar deposits are also observed after the first event. The levees in these cases, unlike Case I, are low in height and flare weakly outward from the river mouth creating gullies in between (Figs. 9a and 10a). Near the slope break, rapid deposition of sediment is observed in Case III.

Z

Z

(b)

(a) Y

X

Y

-5

-10 0

0

Bed elevation (m)

0

0 20 00

tan ce

-10 0

2000 4000

alo ng the 60 00 sho re ( m)

40 00 6000 8000

8000 1000 0 10 00 0

D is

ce tan

o acr

s he ss t

e hor

0 20 00

D is

) (m

2000

tan ce

40 00

40 00

alo ng the 600 0 sho re ( m)

60 00 8000

80 00 10 00 0 10 00 0

D is

ce tan

o acr

s he ss t

e hor

) (m

Z

Z

(c)

(d) X

X

Y

Y

0

-5

-10 0

0 200 0

D is

tan ce

20 00 40 00

alo ng the 6000 sho re ( m)

4000 60 00 80 00

80 00 1000 0 1000 0

D is

ce tan

o acr

s

es s th

e hor

) (m

Bed elevation (m)

0

-5

-10 0

Bed elevation (m)

D is

-5

Bed elevation (m)

X

0 2000

D is

tan ce

2000 4000

alo ng the 60 00 sho re ( m)

4000 600 0 8000

800 0 10000 10000

D is

ce tan

o acr

s

es s th

e hor

) (m

Fig. 9. Bed Evolution for (a) event-1; (b) event-2; (c) event-3 and (d) event-4. Initial bed is considered consolidated beyond 0.5 m of depth.

206

S.M. Khan et al. / Marine Geology 222–223 (2005) 193–211 Z

(a)

(b)

X

Z

Y X

Y

-10 0

0 2000

tan

ce

4000

alo

ng

the

6000

sho

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re

(m

)

ce

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n ista

-10 0

) e (m

he ss t

sho

Dis

tan ce

o

acr

0 200 0

r

4000 6000

-5

20 00 40 00 60 00

the

60 00 800 0

sho

re

D

10000 10000

(c)

ore

40 00

alo ng

(m

)

80 00 10 000 10 00 0

ce tan

s

os acr

Dis

(d) Z

Z

X

Y

0

-5

-10 0

0 20 00

tan ce

alo ng

40 00 60 00

the

600 0 8000

sho

re

(m

)

80 00 10 00 0 10 000

c tan

ss cro ea

0

-5

-10 0

0 20 00

2000 400 0

Y

Bedelevation (m)

X

Dis

)

(m

sh the

)

e (m

or e sh

th

Dis

Bedelevation (m)

Dis

2000

Bedelevation (m)

-5

0

Bedelevation (m)

0

Dis ta

nce

2000 40 00

ore e sh

alo n

40 00 60 00

e sh

ore

8000

(m )

10 00 0 10 00 0

cro

a nce

80 00

h

ss t

6000

g th

) (m

ta Dis

Fig. 10. Bed evolution for (a) event-1; (b) event-2; (c) event-3 and (d) event-4. Initial bed is considered consolidated beyond 1.0 m of depth.

In the second flow event, a northward directed alongshore current of 0.4 m/s has been considered which helps to create another incipient channel near the river mouth extending into the milder region by depositing sediment particles in the northward direction (Figs. 8b, 9b, 10b). Event-3, in which the alongshore current has been set to zero magnitude contribute further deposition in the milder region in all three cases (Figs. 8c, 9c, 10c). In the last event (Event-4), a southward directed alongshore current of 0.4 m/s has been considered that leads to the formation of channel and levees in the southern region of the domain (Figs. 8d, 9d, 10d). In Case III, it is observed that the deposited sediment on the slope break from

previous events has been washed away in the downstream direction due to alongshore current. 5.2. Shore-parallel bed profiles Bed elevation profiles parallel to the shore have been plotted at two different sections (Figs. 11–13) for each of the three cases. One section has been considered on the steeper part and another one on the milder part. For the non-erodible bed condition (Case I), undulated surfaces have been found in the steeper part (Fig. 11a) while due to significant erosion of the bed material, only gullies form in Cases II and III (Figs. 12a and 13a). Wavy bed structure can be

S.M. Khan et al. / Marine Geology 222–223 (2005) 193–211

(a)

0

Initial After Event1 After Event2 After Event3 After Event4

-1

Bed Elevation (m)

207

-2

-3

-4

-5

0

2500

5000

7500

10000

Distance along the shore (m)

(b) Initial After Event1 After Event2 After Event3 After Event4

-2

Bed Elevation (m)

-4

-6

-8

-10

0

2500

5000

7500

10000

Distance along the shore (m) Fig. 11. Bed elevation at distance (a) 1000 m and (b) 3000 m across the shore. Initial bed is considered non-erodible.

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(a) 0

Initial After Event 1 After Event 2 After Event 3 After Event 4

Bed Elevation (m)

-1

-2

-3

-4

-5 0

2500

5000 7500 Distance along the shore (m)

(b)

Initial After Event 1 After Event 2 After Event 3 After Event 4

-2

Bed Elevation (m)

10000

-4

-6

-8

-10 0

2500

5000 7500 Distance along the shore (m)

10000

Fig. 12. Bed elevation at a distance (a) 1000 m and (b) 3000 m across the shore. Initial bed is considered beyond 0.5 m of depth.

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(a) 0

Initial After Event 1 After Event 2 After Event 3 After Event 4

Bed Elevation (m)

-1

-2

-3

-4

-5 0

2500

5000

7500

10000

Distance along the shore (m)

(b) Initial After Event 1 After Event 2 After Event 3 After Event 4

-2

Bed Elevation (m)

-4

-6

-8

-10 0

2500

5000

7500

10000

Distance along the shore (m) Fig. 13. Bed elevation at a distance considered (a) 1000 m and (b) 3000 m across the shore. Initial bed is considered beyond 1.0 m of depth.

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observed in the milder part of the sea bed in all three cases where deposition is dominant (Figs. 11b, 12b, 13b). It should be noted that the orientation of the predicted sea bed undulation is different from the field observation. The observed crenulations on the western Adriatic shelf mapped by Correggiari et al. (2001, Fig. 9 there in) are parallel to the shore whereas the undulations predicted by the model are mostly perpendicular to the shelf. Here, the series of successive hyperpycnal flow events together with alongshore current have generated shifting channel-levee complexes by eroding and depositing the sediment. It is observed from the simulations that alongshore current tends to shift the path of hyperpycnal plume parallel to the shore instead of allowing the flow to travel in the downstream direction. It is, therefore, possible that stronger alongshore current may lead the bed features that are oriented parallel to the shore.

6. Summary and conclusions A two-dimensional depth-averaged turbidity current model is developed. The mathematical foundation of the model is based on the depth-averaged equation of mass, momentum and sediment conservation of density driven flow along with the Exner Equation of bed sediment continuity. The governing equations are solved using the finite volume method. The effect of alongshore current has been considered in the governing equations through coordinate transformation, while empirical relations have been used for model closure and treatment of sediment transport. The model is validated by simulating sediment wave formation in a laboratory flume. Model results are in good agreement with the experimental data. In addition, the model Hyper is utilized to simulate the hyperpycnal flow generated from simulated flood discharges from the River Tronto of Italy. A threedimensional hydrodynamic code FLUENT has been used to capture the plunge process and convert the hydrologic data at the river mouth into inflow conditions for the two-dimensional depth-averaged model. It is found that alongshore current can significantly change the direction and the spreading pattern of a hyperpycnal plume.

Numerical experiments on the evolution of bed features at the field scale have been conducted by considering a series of hyperpycnal flow events. Simulation results show that when occurring in conjunction with alongshore current, hyperpycnal flow can generate complex channel–levee systems which cause undulation perpendicular to the shore. It is observed that bed consolidation also affects the deposit pattern. Although a maximum 1.0 m/s southward alongshore current has been observed near the mouth of River Chienti, we have considered an average value of 0.4 m/s for our study area. A stronger alongshore current can turn a hyperpycnal flow in a direction parallel to the shore that is likely to create coast-parallel sea bed undulation. In nature, sea bed undulations are formed over long periods of time and contain deposits of many turbidite events (Syvitski et al., 1987). For the present simulations, we have considered only four events in each case. Consideration of numerous flow events may lead to a more complete picture of the seabed architecture. As documented by Lee et al. (2002) hemipelagic sedimentation between individual hyperpycnal events, and modifications by bottom boundary layer currents should also play a role in the final architecture of the bedforms observed on the continental shelf.

Acknowledgements This work was supported by the U.S. Office of Naval Research EuroSTRATAFORM Program (N00014-02-0031; N00014-02-1-0041). The authors would also like to acknowledge Dr. Albert Kettner of INSTAAR for providing the hydrologic data.

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