Marine Geology 326–328 (2012) 55–66
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3-D numerical simulation of turbidity currents in submarine canyons off the Niger Delta S.M. Abd El-Gawad a, c,⁎, C. Pirmez b, A. Cantelli a, D. Minisini a, Z. Sylvester a, J. Imran c a b c
Shell International Exploration and Production, Houston, TX, USA Shell Nigeria Exploration and Production Company Ltd, Lagos, Nigeria Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC, USA
a r t i c l e
i n f o
Article history: Received 4 November 2011 Received in revised form 2 June 2012 Accepted 5 June 2012 Available online 1 July 2012 Communicated by D.J.W. Piper Keywords: turbidity currents deposition pattern submarine canyons numerical modeling Niger Delta
a b s t r a c t A three-dimensional unsteady numerical model is applied to simulate turbidity currents in deep submarine canyons located on the continental slope of the Niger Delta. In one of the few attempts to compare field core data to numerical simulations, we conduct several high resolution flow simulations with various boundary conditions to predict the grain size and deposition rates and compare the results to grain size and bed thickness from 22 piston cores collected at different elevations above the canyon thalweg. The model solves the Reynolds-averaged Navier–Stokes equations (RANS), the Mellor–Yamada turbulence closure equations, and the sediment conservation equations for different grain size classes. The bed evolution is modeled using the Exner equation of sediment conservation allowing adjustment of the numerical grid due to bed level changes caused by sediment entrainment/deposition during each time step. The simulated flow fields suggest that turbidity current dynamics is strongly controlled by the seafloor topography. Simulated mean bed thickness and grain size show trends where values of bed thickness and grain size are fining upwards with the elevation above the channel thalweg. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Sedimentation and erosion processes associated with turbidity currents are able to modify the bathymetry of the sea bottom, creating dramatic deep-sea landscapes (e.g. Deptuck et al., 2007; Kolla et al., 2012; Sylvester et al., 2012). Turbidite systems resulting from these currents are volumetrically the most significant clastic accumulations in the deep sea, and include some of the world's largest sedimentary bodies e.g., the Bengal and the Amazon Fan (Bouma et al., 1985; Pirmez, 1994). Turbidity currents are also associated with environmental hazards such as submarine cable breaks, reservoir sedimentation, and pollutant dispersal. Most of what is known about large natural turbidity currents is inferred from indirect sources, such as submarine cable breaks and heights of deposits above submarine valley floors. One notable exception is the observation of a large turbidity current triggered by the 2003 Tokachi-oki earthquake (Mikada et al., 2006). In 1929, the Grand Banks earthquake triggered turbidity currents that traveled down the slope with a speed of 27 m/s resulting in a breakage of twelve transatlantic telephone cables in 28 places hundreds of meters below sea level (Heezen & Ewing, 1952). Recently, the 2006 Pingtung earthquake triggered turbidity currents that caused eleven submarine cables to break across the Kaoping ⁎ Corresponding author at: Shell International Exploration and Production, Houston, TX, USA. Tel.: +1 8034762029. E-mail address:
[email protected] (S.M. Abd El-Gawad). 0025-3227/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.margeo.2012.06.003
submarine canyon and Manila trench in sequence at depths from 1500 to 4000 m (Hsu et al., 2008). Field observations and measurements of turbidity currents are scarce because of their rarity and the difficult underwater operating conditions, as well as the destructive nature of these currents (Inman et al., 1976). Notable exceptions include the work of Hay (1987), Khripounoff et al. (2003), and Xu (2004). Xu (2011) provides a summary of field measurements of turbidity currents. Experimental modeling is limited to small-scale flows impacted by Reynoldsmediated scale effects. A numerical model of turbidity currents can be a useful tool to overcome some of the difficulties associated with field and experimental measurements and may provide a better understanding of the flow properties and depositional patterns. The numerical models reported in the literature vary in complexity from simple one-equation to highly detailed 3-D models. These models can generally classified as Chezy-type balace equation, depth-averaged or shallow water, 2-D vertical structure resolving, and full 3-D models. Depth-averaged models integrate the governing equations over the flow height. Choi (1998) developed a 2-D depth-averaged model using the finite element scheme and showed that the model results are in good agreement with the laboratory experiment of Luthi (1981). Imran et al. (1998) simulated the formation of a submarine fan by unconfined turbidity current using a 2-D depth-averaged model. Felix (2001) developed a 2-D vertical structure model to simulate turbidity currents and their deposits on a natural scale implementing the Mellor–Yamada 2 12 level closure model (Mellor & Yamada, 1982).
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Choi and García (2002) used the k− model for the turbulence closure to determine the velocity and concentration profiles of a small-scale saline flow on an inclined surface. Huang et al. (2005, 2007) developed a 3-D numerical model that solves the RANS and employs k − model for turbulence closure. The model was verified using the experimental data of García and Parker (1993). Perez (2010) applied an open-source CFD model known as SSIIM (Olsen, 2006) to experiments performed by Baas et al. (2004) which involved a sloping channel flowing into a large tank. Salles et al. (2008) simulated a storm-generated turbidity current that occurred in the Capbreton Canyon in December 1999, using a cellular automata model. Field-scale applications of numerical models require guesswork of the initial conditions, as the magnitude and unpredictability of the events make it extremely difficult to gather the required input data (Perez, 2010). Heimsund (2007) applied the CFD software Flow-3-DTM to simulate turbidity currents in the Monterey Canyon system on the basis of high-resolution bathymetric and flow data. They concluded that the flow characteristics are highly sensitive to the topographic complexity and the large parts of the flows were ponded when they arrived into the dead-end arms of the canyon system. The simulated velocity profiles are comparable with the station-bound profiles. Several researchers (e.g., Hartel et al., 2000; Cantero et al., 2007; Meiburg & Kneller, 2010) studied the dynamics of the density currents using highly resolved numerical models known as Direct Numerical Simulation (DNS). Blanchette et al. (2005) studied the entrainment of sediment particles from the bed and the associated self-sustaining conditions. Depth-averaged models are computationally inexpensive but not capable of capturing the vertical structures of the flow. DNS simulations can solve all the length scales of motion and reveal rich turbulence features such as lobe–cleft structures and Kelvin–Helmholtz instability in lock-exchange flows, but they are computationally expensive and cannot be applied to large-scale problems with relatively high Reynolds numbers and complex topography. 3-D numerical models with RANS turbulence closure provide a reasonable middle ground. These models can predict the mean or Reynolds-averaged velocities and density structures on complex geometry using a reasonably fine mesh and can be applied to a wide range of scales. While still computationally expensive for large-scale (tens of km) and long term (hours) simulations, the computational time may be reduced by using high performance computing clusters. Advent of seismic and sonar technology has been revealing the seabed morphology with increasing details. In order to properly interpret these data and advance stratigraphic modeling of the seafloor, the flow field responsible for creating this morphology needs to be properly understood. A well-validated 3-D physics-based numerical model of flow and morphodynamics can be a useful tool for this purpose. Recently, Abd El-Gawad et al. (2012) applied a 3-D numerical model (Huang et al., 2005, 2007) to study flow and sedimentation of a low-relief sinuous channel on the sea-floor of the Niger Delta slope. In this paper, we take a similar approach to study two segments of a canyon characterized by complex topography and steep gradient located within the same geologic setting. We compare numerical model results to the available data obtained from the sampled beds in the collected cores within the canyon. Along with the work of Abd El-Gawad et al. (2012), this study represents a systematic approach towards modeling the three-dimensional flow field by utilizing bathymetric and core data for initial and boundary conditions. Due to long computational time involved, we considered a limited number of scenarios. To the authors' knowledge, a fully 3-D model that accounts for vertical structure of the flow field and changes in the bed level as the flow evolves has not been applied by others at such a large scale study area with complex topography.
spacing of 25 × 25 m for each trace. Depth was estimated by assuming an average sound velocity for the water column. Absolute depth thus calculated is not very precise (within about 1%), but depth change from trace to trace and local gradients should be quite accurate since average water column velocity varies slowly in the lateral direction. An estimate of the acoustic amplitude also is obtained by analysis of the seafloor interface reflection, which offers an indication of variations of lithology within the first several meters below the seabed. High amplitudes are generally an indication of sand/gravel near the seabed, but can also be an indication of cemented hard grounds (Figs. 1 and 4). Sediment cores were acquired with a 20 m long Jumbo Piston Corer (JPC), equipped with an acoustic transponder mounted on the 3-ton core head. The location of the transponder was measured with respect to the vessel by using a ship-mounted Ultra-Short Base Line (USBL) acoustic transducer integrated with a differential GPS system to locate the vessel. Prior to start of coring, the USBL transducer alignment with respect to the vessel was calibrated in shallower water (∼500 m) near the coring area by turning the vessel around a stationary transponder on the seabed and calculating the optimum alignment parameters. After calibration, the measured transponder positions fell within ±2.9 m in the E–W direction and 3.7 m in the N–S direction (1 std. dev.). Sound velocity in the water column was obtained by measuring the salinity and temperature profile of the water column with CTD casts. The standard deviation of transponder depth calibration measurements was 0.06 m. Twenty-two piston cores were collected in two areas along the Y channel of Fig. 1. At each specified core target selected on the 3-D survey the coring device was lowered to about 20 m above the seabed, and with the help of the USBL system steered to the target (within a tolerance of 8 m radius) before lowering it to the seabed. After the core penetration and before pull out, USBL data was acquired for about 2 min and the resulting statistics show one std. dev. of position of less than 3 m in both N and E coordinates for all cores (most within 1 m). Core recovery ranged from 3 to 20 m with most cores. Low core recovery at some sites particularly along the channel thalweg occurred because of the presence of coarse sand and gravel just below the seabed, which in some cases caused bent pipes. Core recovery on the flanks and terraces of the channel was generally good. The cores were described visually on a bed-by-bed basis, and using a hand-lens and grain size comparator for estimating the grain size. Detailed grain size analyses were conducted with a laser particle size analyzer and the D50 results are reported here.
2. Data description
The study area is a complex tectono-sedimentary system, with a number of structures and submarine channels active during the latest Pleistocene (Fig. 1 — (Pirmez et al., 2000)). The image of the seafloor shows three main channels: X, Y, and Y′. The X channel has sinuous
This study uses bathymetric data obtained from a compilation of 3-D seismic reflection surveys in the area. The seismic surveys had a
3. Numerical model A numerical model developed by Huang et al. (2007) is used to simulate the evolution of turbidity currents in time and space in Canyon 1 and Canyon 2 described above. The model solves the Reynolds averaged Navier–Stokes equations (RANS), turbulence closure equations, and mass conservation equation for each grain size class considered using the finite volume method. Turbulence closure is achieved using the Mellor–Yamada model by Mellor and Yamada (1974, 1982) and the bed evolution is modeled by solving the Exner equation for individual size classes. The numerical grid is adjusted according to the bed level changes due to sediment entrainment/ deposition during every time step. The governing equations and the solution algorithm are explained in more detail in Abd El-Gawad et al. (2012) and Huang et al. (2005, 2007). 4. Study area: Niger Delta slope
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1 2
Fig. 1. Seafloor mosaic based on 3-D seismic surveys offshore Nigeria (Pirmez et al., 2000). Red is high amplitude and blue is low amplitude. The study areas considered here are marked by the blue rectangles (see Fig. 7).
The top of all the cores acquired in the channel is characterized by a 5 to 6 m thick homogeneous greenish-gray mud, that has a draping geometry on high-resolution seismic profiles (Fig. 6). The mud is bioturbated, displays a complete absence of sand and silt layers and has a grain size ranging from 5 to 30 μm. The coarse component is
a 150
Elevation (m)
segments with high amplitudes at channel banks where overbank spilling occurred. The amplitude map shows that channel Y seems to have been inactive except at the junction with the channel Y′ which has zones of sand deposition. The channel downdip the junction is incised into the past fill of channel Y and displays complex geometry with multiple terraces along the submarine valley as shown in Fig. 1 (also refer to Fig. 3a, and b). The geometry of the canyons is quite complex with significant variations in the local slope. The longitudinal slope along the channel thalweg is around 0.86 ∘ for both canyon segments studied (Fig. 1); the profile of Canyon 1 shows less irregularity than Canyon 2, which has low sinuosity but significant variations along the channel thalweg as shown in Fig. 2. Typical cross sections of both canyons are presented in Fig. 3, showing a central incised channel with multiple terraces on both banks with steep slopes of 18–33% which are equivalent to 10 ∘ − 19 ∘ (Fig. 5).
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Distance (Km) Fig. 2. Longitudinal section along the thalweg of Canyons 1 and 2. The thalweg slope is around 1.5% for both. The bed slope changes more significantly in Canyon 2 compared to Canyon 1. The vertical exaggeration is 20×.
Fig. 3. Typical cross sections of the canyons showing steep side slopes and terraces. The vertical exaggeration is 20×.
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represented by foraminifera and shell fragments of benthic organisms. The mud drape is interpreted to represent hemipelagic sedimentation from river plumes, and is associated with the general reduction of sediment input into the channel as the coastline retreated landward during the late Pleistocene–Holocene sea level rise. Below the mud drape the cores show beds of sand and silt with thickness ranging from less than 0.01 m to 0.5 m or more (Fig. 6). The beds are massive or normally graded, with sedimentary structures typical of turbidite deposits, including parallel laminated and ripple cross-laminated sands (e.g., photo in Fig. 6). Some massive sand beds have floating mud clasts, probably transported as bedload, and occasional granule-grade coarse grains were observed in some beds. Cores were acquired in transects across the channel, and the results suggest a strong correlation between the grain size and bed thickness with elevation above the thalweg at any given cross-section. Measurements of sand–silt bed thickness and of the grain size at the base of each bed were tabulated for each core for comparison with the synthetic deposits derived from the numerical simulations. A detailed description of the coring results is presented elsewhere, here we focus on the comparison of key measurements and observations to the numerical simulation results.
a) slope map of Canyon 1
Slope High : 19.61 1,000
0
2,000 Meters
Low : 0.02
b) slope map of Canyon 2
4.1. Inflow parameters The inflow boundary condition is not known and reasonable values for velocity, concentration, and current thickness must be assumed. However, the inflow sediment grain size can be estimated based on the range of grain size observed in different beds in the cores.
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2 km
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X (m)
x 105
Fig. 4. Bathymetry of Canyons 1 and 2 showing core locations. The contour interval is 10 m. Canyon 1 has several bends along its course while Canyon 2 has a single bend.
High : 19.405 0
1,000
2,000 Meters
Low : 0.001
Fig. 5. Bed slope map of Canyons 1 and 2 in degrees. The side slopes are around 15–20 ∘.
We searched for a relationship between the inlet flow condition and channel slope that leads to minimal erosion or deposition by running a set of 2-D simulations. Such conditions would represent near-equilibrium conditions, which are thought to be representative of turbidity currents that have traveled long distances along the channel. A recent study by Sequeiros (2012) shows strong dependence between channel slope and densimetric Froude number. The 2-D simulations consisted of a wide range of parameters: 10 different bed slopes ranging from 0.25 to 5s, three different diameters: 64, 125, and 250 μm, three different inlet velocities: 1.2, 2.5, and 4 m/s, and two different inflow current thicknesses: 25 and 50 m. Cases that showed bypass or near-bypass condition lead to the following relationship between the initial bed slope, S and the equilibrium densimetric Frd: 0:13
Fr d ¼ 1:78S
:
ð1Þ
The densimetric Froude number is a dimensionless parameter calculated as: Frd = U/Rcgh, where U is the depth-averaged velocity; R is the submerged specific gravity of natural sediment (1.65); c is the volumetric concentration; and h is the current height. Using Eq. (1), the equilibrium Froude number Frd is found to be around 1.0 for slopes of 1.5%. This provided us with a reasonable basis for selecting the input parameters. Based on the literature (e.g., Kuenen, 1966; Middleton & Hampton, 1973), a value of 2.5% is assumed for basal concentration. Two inflow heights are assumed based on the channel cross section geometry
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mud sand planar lamination
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forams
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bioturbation core gap
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Fig. 6. Cores 16, 17, and 18 measured sections with photos showing the parallel laminated and ripple cross-laminated (see Fig. 7-1 for core location).
(low and high) and the velocities of 4–5 m/s are obtained using the relationship between the densimetric Froude number and slope. The sediment mixture considered in the simulations is composed of four grain size classes; 20 μm (silt), 50, 100, and 200 μm (fine-medium sand) as shown in Fig. 8. We use higher fractions of silt in the flow that can remain suspended easily by turbulence and sustain the flow over long distances. The simulation matrix is a combination of two grain size distributions to test uncertainty in the proportion of the various fractions in the field (Fig. 8) and either a low or high flow in terms of
inlet current thickness. A total of eight simulations were performed. Since each run takes 10 to 15 days of computation in a high performance computing cluster, additional runs for sensitivity analysis were not practical. 4.2. Computational grid and boundary conditions The computational grid is constructed using a grid size of approximately 27 m which is close to the bathymetric data resolution. The
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5
1 2 3
7,8 9
11
19 20 10 21
6 4
22
14
12
16
15 14
17 18
Fig. 7. Study areas (1) and (2) represent low and high sinuosity channels. Cores are concentrated at one of the bends in area (1) while area (2) has cores distributed at 4 different transects.
grid is non-uniform with fine cells near the bed and expanding logarithmically above the bed and away from the channel across the overbank area in the vertical and lateral directions, respectively. Canyon 1 has 170 nodes in the downstream direction, 190 nodes in the lateral direction, and 90 nodes in the vertical direction, totaling approximately 3 million nodes. Similarly for Canyon 2, approximately 3 million nodes are used with 160 × 220 × 90 nodes in the stream-wise, span-wise and vertical directions, respectively (Fig. 7). Huang et al. (2007) observed that a flow originating with an imposed inlet condition goes through an initial adjustment period before it becomes fully developed. In the present case, the upstream or inlet boundary is not a physical boundary. To avoid the artifact of
Fraction of Total Concentration (%)
100
GSD1 GSD2
imposed inflow boundary conditions, an additional entry grid block with 70–80 nodes in the stream-wise direction is used. This allows the flow to develop as it enters the domain of our interest. An example of developed inflow velocity and concentration in the added block upstream of Canyon 1 is presented in Fig. 9. Table 1 summarizes the inflow condition at the inlet of the main domain developed from the entry block. 5. Results The simulated sediment deposition pattern is used to calculate the fraction of each grain size class and the mean grain size diameter as well as the bed thickness at the core locations. Table 1 shows a list of 8 simulations performed for the two canyons. Simulation results for the case of the high flow thickness and fine grain size distribution are presented as the results from this run show similar trend
90 Table 1 Depth-averaged flow parameters at the main domain inlet.
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Scenario
70
Run
Avg. concentration
Canyon 1 boundary condition Coarse low flow 1 1.5 Coarse high 2 1.5 flow Fine low flow 3 1.5 Fine high flow 4 1.5
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Avg. velocity (m/s)
Current height (m)
3.00 3.50
25 45
3.00 3.50
25 40
3.00 3.50
30 55
3.00 3.50
30 55
40 30 10
20
40
60 80 100
200
300 400
Diameter (µm) Fig. 8. Fraction of the total concentration for each grain size class at the inlet boundary.
Canyon 2 boundary condition Coarse low flow 1 1.6 Coarse high 2 1.6 flow Fine low flow 3 1.5 Fine high flow 4 1.5
100 80 60 40 20 0
5 4 3 2 1
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Velocity (m/s)
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a) Developed flow velocity contours
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0.03 0.02 0.01
1.5
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Concentration
Elevation (m)
b) Developed flow concentration contours
0
Transversal Distance (km) Fig. 9. Typical velocity and concentration field in the upstream extra numerical block. The vertical exaggeration is 2×.
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when compared to observed bed thickness and upward fining of grain size. 5.1. Canyon 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The magnitude of the velocity vector u2 þ v2 þ w2 at different elevations is presented in Fig. 10. The flow remains confined in the straight part following the channel entrance for about 2–3 km and the velocity magnitude is maximum near the channel thalweg. Further downstream, the flow starts to spill over the terraces as the sinuosity of the channel planform begins to affect the current. Fig. 10a shows the velocity magnitude close to the channel bed where the flow pattern is controlled by the local topography of the channel. The canyon cross section geometry shows high value of slope up to
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15–20%, which basically changes the flow momentum in the lateral direction as well as the streamwise direction due to the significant effect of gravity. At channel bends, the local transversal slope is higher towards the outer bends compared to the inner banks. At higher elevations above the bed (Fig. 10b and c), the velocity magnitude increases in the straight part with lower velocities observed over the banks outside the channel. The velocity decreases as the current flows in the downstream direction in the canyon due to water entrainment, with lateral spilling as well as sediment deposition within the channel and in the overbank areas. Sediment concentration decreases with elevation above the bed; some higher concentration values are observed near the outer banks (see Fig. 11). The average concentration within the
a) Volumetric concentration at 2.5 m from the bed x 105
a) Velocity magnitude at 2.5 m from the bed x
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c) Velocity magnitude at 20.0 m from the bed 5.28
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x 105
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fig. 10. Velocity magnitude ( u2 þ v2 þ w2 ) at different elevations above the bed in Canyon 1.
Concentration
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Fig. 11. Total volumetric concentration of all grain size classes at different elevations from the bed showing how the concentration decreases along the vertical direction and how the flow follows the channel topography.
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3
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Transversal Distance (km) Fig. 12. Streamwise and lateral velocity and the total sediment concentration at Bend 1 (Fig. 4). + ve value of the lateral velocity (Vlat) refers to flow from right to left. The vertical exaggeration is 2×.
a) Deposition rate of 20 µm
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5.23
1 0.5
5.22 6.67 6.68 6.69 6.7 6.71 6.72 6.73 6.74 6.75 6.76
X (m)
Fig. 13. Deposition rate (m/s) for grain size classes 20, 50, 100, and 200 μm.
x 105
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x 105
d) Deposition rate of 200 µm
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105
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2 km
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b) Deposition rate of 50 µm
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channel is higher than that in the overbank areas and generally decreases as the current travels downstream. The streamwise and lateral velocities as well as the total concentration at Bend 1 located in the vicinity of the cores are presented in Fig. 12. The figure shows that the streamwise velocity has high values on the inner bank and separates from the outer bank with a core of high velocity occurring in the shallower part of the channel. Near the bed, the lateral velocity is oriented towards the outer bank but is stopped by a return flow coming towards the thalweg from the outer bank due to the steep lateral slope. In the upper part of the cross section, the lateral flow is oriented towards the inner bank. High sediment concentration is observed to be consistent with the locations of high streamwise velocity. Part of the flow spills over the outer bank but only with low concentration as seen in Fig. 12c. The sediment deposition rate for each grain size class at a given location is calculated based on the bed level changes within a time window where the rate approaches a constant value, for example, between time step 1000 and 1200 and 1200 and 1400. The spatial distribution of the deposition rate for each grain size class is shown in Fig. 13. The deposition rate is high in the first few kilometers and starts to decrease in the downstream direction with higher rates inside the channel. Finegrained sediment material is widely more spread over the banks as fine material can remain suspended easily at higher elevations (Fig. 13a and b). At each core location, fractions of different grain size classes are calculated based on the deposition rate. The coarser material tends to deposit more inside the channel, with higher rates and patchy distributions. This patchiness results from the fact that coarser grains (100 and 200 μm) are initially placed on the floor before the flow enters the channel and experience localized reworking/erosion. The core data used here presents median grain size diameter and bed thickness observed in approximately 1000 beds in the cores for Canyons 1 and 2. The fraction of each grain size class from the simulation is used to estimate the mean grain size diameter at the core locations. The total deposition is adjusted by an appropriate time scale that would give best overall match with the observed bed thicknesses. This adjustment or calibration of flow duration is necessary since we do not know the actual duration of the events that deposited these beds. The adjustment was made by multiplying the deposition rate by a scalar to compute thickness. The scalar value was selected for an approximate match at one of the cores and the same scalar is applied to all cores. In this way, the relative thickness derived from the numerical model at the various locations is preserved and can be tested against the core measurements. Predicted grain-sizes at cores 17, 18 and 22 match the median grain size from the core data (Fig. 14). However, the model predicts finer 45
Simulation Core Data
30
Elev.=-39.29ln(D)+212.77 R²= 0.43 Core13 Core18
Elev.=-48.32ln(D)+240.87 R²= 0.78
15 Core12
10
Core15
5 0 10
The same analysis is applied to the second canyon. The velocity magnitude decreases within the channel due to lateral downward flow from both channel walls moving towards the thalweg, which creates a zone of low velocity. The flow is confined within the channel in Canyon 2 compared to Canyon 1 because the channel relief is much higher and the side slopes are steeper, which hinders the spreading of the flow outside the channel. Streamwise and lateral velocities and the concentration field at Bend 2 are presented in Fig. 16. The core of the streamwise velocity is located in the deeper part of the channel away from the outer over bank and the current is also thicker here compared to the overbank areas. The steep lateral slope of the channel completely dominates the curvature effect as the lateral flow moves towards the channel thalweg from both sidewalls. Fig. 16c shows that there is no significant overspilling and most of the current remains confined within the channel. The comparison of the predicted median grain size and bed thickness from simulation run fine high flow (cf Table 1) with core data in Canyon 2 is presented in Figs. 17 and 18, respectively. In general, bed grain size variation shows coarser material located at lower elevations and fining upward trend. The grain size predicted by the model is in general finer from what is observed in the cores. However, values at cores 10, 21, 20, and 4 fall within the grain size range of different beds at those cores. Cores 2, 3, 5, 6, 7, and 8 are located at elevations 0–3 m above the thalweg where the model predicts a grain size range of 170–190 μm. The simulated bed thickness values fall within the range observed in different beds at cores 10, 21, 20, 1, 19, and 4 (Fig. 18). 45
Core Data (several beds)
Core16
20
5.2. Canyon 2
Simulation Core22
35
25
material in the deposit than what exists in the core, especially at cores 12 and 15. The model results show a decrease in the mean deposit diameter with elevation above the thalweg following a logarithmic fit with R2 of 0.78. The core data shows a similar trend but with a relatively poor correlation of 0.43. The simulated deposit thickness over a period of 20 min during which the deposition rate is relatively constant is compared to the core bed thickness in Fig. 15. The model predicts bed thicknesses within the range of the median bed thickness observed at different beds at each core. The modeled bed thickness variation with elevation shows a good correlation of R2=0.92 while the data shows a correlation of 0.78. The mismatch in grain size vs elevation probably results from the inability of the flow to lift a specific grain size to higher elevation in the channel because of insufficient turbulent energy that is needed to keep sediment particles in suspension.
Core17 Cores11 and14
100
Bed Base Grain Size (µm)
Elevation above thalweg (m)
Elevation above thalweg (m)
40
63
40 35 30 25 20 15 10 5 0
0.1
1
10
100
Bed Thickness (cm) Fig. 14. Median grain size variation with elevation above the channel thalweg. The bed base grain size is obtained by analyzing around 1000 beds from the collected cores in both Canyons 1 and 2. The simulated median grain size is obtained using the rates for the different classes deposited at each core location.
Fig. 15. Bed thickness (BT) variation with elevation above the channel thalweg. The simulated bed thickness is obtained by scaling the deposition rate with a time scale that would give the best overall match with the data.
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−1200
6
Outer Bend
−1250
4
−1300
2
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2
3
U s (m/s)
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0
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b) Lateral velocity at Bend 2 −1250
1
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0.03 0.3%
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2
Concentration
Elevation (m)
c) Total concentration at Bend 2
3
Transversal Distance (km) Fig. 16. Streamwise and lateral velocity and the total sediment concentration at Bend 2 located in Canyon 2. The +ve value of lateral velocity means that the flow is towards the left. The vertical exaggeration is 2×.
The model predicts higher rates of deposition at cores 10 and 21 that are located 57 m above the thalweg. In general, the simulation results show good agreement with the data good correlations (R2 values of 0.81 and 0.80) of grain size and bed thickness with elevation. The core data show slightly better correlations. 6. Discussion Along with the work of Abd El-Gawad et al. (2012), the present paper represents one of the first detailed field-scale simulation of turbidity currents with deposition and erosion in 3-D, with simulation results compared to sediment samples from the field. We did not attempt to determine every input parameter and boundary condition; instead we have developed a means to estimate the input 60
Simulation
55
Elevation above thalweg (m)
flow conditions from the field data itself. For instance, the Froude number of the flow is estimated from the local slope and an approximate estimate of the flow thickness is obtained from the height of the channel so that the initial flow velocity and density can be estimated given the Froude number and flow height. The selected inlet concentration is somewhat arbitrary. However, our experience with numerical modeling of turbidity current has shown that the development of the flow is less sensitive to inflow concentration, and more sensitive to inlet flow discharge and channel slope. For this reason, model sensitivity to inlet concentration is not studied in the present case which requires long computational time. The initial grain size distribution of the flow and the distribution of grain sizes present in the bed are more difficult to estimate without direct information. In this study we used the range of grain sizes most commonly observed in the cores as the initial value, and tested the effect of
Core Data (several beds) Simulation
50
Core Data
45 40 35 30 25 20 15 10 5 0 10
100
Bed Base Grain Size (µ µm) Fig. 17. Variation of median grain size with elevation above the channel thalweg in Canyon 2.
Fig. 18. Variation of bed thickness (BT) with elevation above the channel thalweg.
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two distributions. The low-coarse flows tend to have lower depositional rates at all elevations due to weak turbulent kinetic energy, however, these flows deposit coarser material at higher elevations. On the other hand, the high-fine flows have high momentum maintained by the presence of fine particles and also high turbulent kinetic energy which allows better mixing of the flow and keeps a smooth distribution of rates as well as grain size in the vertical direction. The modeled turbidity currents are affected by the bathymetry they flow on and the flow tends to adjust to the topography of the channel/canyon. Rather than trying to impose velocity and concentration profiles as well as turbulent kinetic energy across the inlet, we used an entry block to allow developed flow conditions in the actual domain of interest so as to avoid any artifact due to artificial inflow conditions. The simulated bed thickness variation with elevation shows trend similar to the one seen in the data. The scalar time scale factor is used to match one core and then scale all the other rates with the same factor. Therefore, this adjustment does not ensure global match at the cross section level. The fact that the match is good at all levels in the vertical direction suggests that the model accurately predicts the average sedimentation rate profile for the flow (which is the combination of average concentration times average settling velocity). The match in absolute grain size is not as good as the bed thickness, although we observe similar trends of grain size change with elevation between simulation and field data. The grain size range observed in the core is practically the same as in the simulation although the field deposits tend to have a small proportion of coarser material (>250 μm). Abd El-Gawad et al. (2012) simulated four grain sizes in the flow and compared them to grain size ranges for 7 piston cores located at a channel bend. The study concluded that the predicted D50 value falls within the core data range while the D90 values fall towards the finer limit of the range observed in the recovered beds which also indicates that deposits tend to have small portions of the coarser material. Increasing the coarser fraction in the input flow grain size did not improve the match, in fact it tended to cause the flow to deposit more and decelerate. The fractions coarser than 200 μm were not included in the simulation because most of it does not show up in the deposits recovered a few meters of elevation above the thalweg, and is probably incipiently suspended or in the bedload fraction. The mismatch in absolute grain size can be explained in terms of the ability of the flow to suspend each size class. The downward flux of each grain size class (dominated by the settling velocity) is counteracted by a vertical flux, determined by the level of turbulence in the flow. If there is not enough turbulence, the grains will settle and the flow will eventually cease. In our numerical model, turbulence is calculated using the Mellor–Yamada 2 12 level. To date, it is not known whether this model, adapted from oceanographic models, is appropriate for turbidity currents. Nor there is any field data with which to calculate the actual turbulence profile of a turbidity current. The results shown here indicate that the turbulence model used does not produce sufficient turbulence to explain the observed deposition of fine sand on the flanks of the channel as high as 35–45 m above the thalweg. 7. Conclusion In this paper, we present numerical simulations of turbidity currents flowing in deep submarine canyons located offshore West Niger Delta. The study area has complex topography with a sinuous channel thalweg and multiple terrace levels. We were able to simulate turbidity current flows through this channel, and show that the resulting synthetic deposits match reasonably well the bed thickness and grain size of sediment recovered from the seafloor. The model solves the Navier– Stokes equations with the Mellor–Yamada turbulence closure model. Four grain size classes are considered in the simulation and the deposition rates of each size class are used to calculate the mean grain size and
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the bed thickness by scaling the total deposition rate by a calibrated time that would give the best overall match with the observed bed thicknesses in the cores. The key observations are the following: 1. The flow pattern is affected by the channel geometry and the local slope, especially in the spanwise direction. In both Canyons 1 and 2, the slope maps (Fig. 5) show that at the bends, the channel wall is steeper towards the outer bank than in the inner bank. Therefore, the flow high-velocity core follows the inner bank. 2. Complex flow patterns including flow separation are observed at the channel bends. Helical flow is not observed at either of the bends due to the dominance of the lateral bed slope over the curvature effect. The flow spreading outside of the channel is minimal. In both cases, a lateral flow attached to the bed moving down the side slope towards the channel thalweg can be observed. High sediment concentration is observed in the channel thalweg and the overbank parts of the flow are dilute (Figs. 12c and 16c). 3. Four grain size classes are included in the simulation and the deposition rate maps for each class are presented. For the introduced inflow, the model predicts slightly finer grain sizes than those observed in the data at some core locations and the variation of grain size with elevation above thalweg shows an upward fining trend with reasonably good correlation. 4. The simulated bed thicknesses at core locations are calibrated by scaling the total deposition rate by a reasonable time to match the range of bed thicknesses observed in the cores. Both data and simulation results show a decrease in deposit thicknesses with increasing elevation above the channel thalweg.
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