Computers & Geosciences 53 (2013) 141–153

Contents lists available at SciVerse ScienceDirect

Computers & Geosciences

0098-30

doi:10.1

n Corr

E-m

brendon

meiburg

journal homepage: www.elsevier.com/locate/cageo

Polydisperse turbidity currents propagating over complex topography:Comparison of experimental and depth-resolved simulation results

M.M. Nasr-Azadani a, B. Hall a,b, E. Meiburg a,n

a Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USAb ExxonMobil Upstream Research Company, P.O. Box 2189, Houston, TX 77007, USA

a r t i c l e i n f o

Article history:

Received 17 March 2011

Received in revised form

11 July 2011

Accepted 27 August 2011Available online 14 September 2011

Keywords:

Turbidity currents

Lock-exchange flow

Polydisperse suspension

Complex topography

Numerical simulation

04/$ - see front matter & 2011 Elsevier Ltd. A

016/j.cageo.2011.08.030

esponding author. Tel.: þ1 805 893 5278.

ail addresses: mmnasr@engineering.ucsb.edu

.hall@exxonmobil.com (B. Hall),

@engineering.ucsb.edu (E. Meiburg).

a b s t r a c t

A computational investigation is presented of mono-, bi-, and polydisperse lock-exchange turbidity

currents interacting with complex bottom topography. Simulation results obtained with the software

TURBINS are compared with laboratory experiments of other authors. Several features of the flow, such

as deposit profiles, front location, suspended mass, and runout length, are discussed. For a mono-

disperse lock-exchange current propagating over a flat surface, we investigate the influence of the

boundary conditions at the streamwise and top boundaries, and we generally find good agreement with

corresponding laboratory experiments. However, we note some differences with a second set of

experimental data for polydisperse turbidity currents over flat surfaces. A comparison with experi-

mental data for bidisperse currents with varying mass fractions of coarse and fine particles yields good

agreement for all cases except those where the current consists almost exclusively of fine particles. For

polydisperse currents over a two-dimensional bottom topography, significant discrepancies are

observed. Possible reasons are discussed, including erosion and bed load transport. Finally, we

investigate the influence of a three-dimensional Gaussian bump on the deposit pattern of a bidisperse

current.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Turbidity currents represent an important mechanism bywhich sediment is transported from the continental shelves intothe deep oceans (Meiburg and Kneller, 2010). They play a crucialrole within the global sediment cycle and, over geological timescales, in the formation of hydrocarbon reservoirs (Syvitski et al.,1996). Turbidity currents can reach front velocities Oð10Þm=s,travel up to Oð1;000Þ km, and transport Oð100Þ km3 of sediment.

The formation of topographical features such as channels,gullies, sediment waves, and levees can occur as a result of thedepositional and/or erosional nature of turbidity currents inter-acting with the seafloor (Wynn et al., 2000a; Migeon et al., 2001;Nakajima and Satoh, 2001; Wynn and Stow, 2002). Conversely,the seafloor topography can influence the dynamics of turbiditycurrents, and hence their deposits. Examples of such effectsinclude the interaction of turbidity currents with large barriers(Pickering and Hiscott, 1985; Kneller and McCaffrey, 1999),differential deposition due to slope gradients (Garcia and Parker,

ll rights reserved.

(M.M. Nasr-Azadani),

1989; Kubo, 2004), and flows in meandering channels (Imranet al., 1999; Straub, 2007).

Due to the unpredictable and often catastrophic nature ofturbidity currents, there has been an intensive effort to studytheir behavior by means of laboratory experiments (e.g., Luthi,1981a; Bonnecaze et al., 1993; Gladstone et al., 1998; de Rooijand Dalziel, 2001), theoretical approaches including box modelsand shallow water theory (Luthi, 1981b; Rottman and Simpson,1983; Bonnecaze et al., 1993; Baines, 1995; Dade and Huppert,1995; Hallworth et al., 1998), and more recently, via numericalsimulations (Necker et al., 2002, 2005; Kassem and Imran, 2004;Blanchette et al., 2005; Huang et al., 2008; Nasr-Azadani andMeiburg, 2011).

These investigations frequently address the so-called lock-exchange currents; cf. Fig. 1. In the current study, we employ thesimulation tool TURBINS to address such flows, which was recentlydeveloped in our group (Nasr-Azadani and Meiburg, 2011). TURBINSis a highly parallel code that employs the Navier–Stokes equationsin the Boussinesq approximation to describe the motion ofthe suspension, along with a transport equation for the particleconcentration field. We employ TURBINS to reproduce and comparewith experiments and numerical simulations by Gladstone et al.(1998), de Rooij and Dalziel (2001), Necker et al. (2002), and Kubo(2004). All of these studies focus on the depositional behavior oflock-exchange, mono-, and/or polydisperse currents flowing over

Nomenclature

r0 density of ambient fluidr1 density of suspensiondp particle diameterrp particle densityus particle settling velocityu fluid velocityn fluid kinematic viscosityRe Reynolds numberSc Schmidt numberk particle diffusion coefficientci concentration associated with the ith particle sizect total concentrationp pressureLx computational domain size in x-directionLy computational domain size in y-directionLz computational domain size in z-directionH lock heightW lock widthLs lock lengthg gravitational accelerationh Gaussian bump heighteg unit vector in the direction of gravityCr initial volume fraction of suspension in the lockCi initial volume fraction associated with the ith particle

size in the lockub buoyancy velocityN number of different particle sizesLr characteristic lengthDt time stepS solid node

I immersed nodeO mirrored nodeF fluid noden unit normal vector on the solid surfaceX control point on the solid surfaceq fluid quantityD deposit height (mass)D1 final deposit height (mass)s packing fraction of settled sedimentms suspended mass of particle(s)xf front location (from the lock-gate)xg distance from the lock-gateU outflow convective velocityLt runout length of the currentxc Gaussian bump center x-coordinateyc Gaussian bump center y-coordinatezc Gaussian bump center z-coordinatee factor controlling the width of the Gaussian bumphr ramp heightlr ramp lengths hump heightd hump lengthmp0 added particles’ mass for producing the suspension in

the lock^ superscript: refers to any dimensional quantitycw concentration at the solid surfacei subscript and superscript: refers to the ith particle

concentration fieldRen particle Reynolds numberycr critical wall shear stressut friction velocitytw wall shear stress

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153142

flat or complex geometries. Specifically, we will focus on suchquantities as front location, runout length, and deposit profiles offine and coarse particles. Of particular interest are the couplingmechanisms between particles of different sizes, and their effects onthe transient and final deposit profiles. In addition, we investigatethe deposition of a bidisperse suspension interacting with a three-dimensional Gaussian bump, cf. Fig. 1. This will shed light on theinfluence of complex bottom topography with regard to generatingnonuniformities in the final deposit profiles. The emphasis of thecurrent investigation is not so much on the highly complextopographies that might be encountered on a real world sea floor.Rather, we focus on geometrically simple shapes such as the onesthat have been employed in various laboratory experiments. The

Fig. 1. Schematic representation of the initial setup of a lock-exchange flow

interacting with a nonerodible bed in the form of a Gaussian bump. The lock has

dimensions Ls � H � W and contains a suspension of density r1. It is initially

separated by a membrane from the ambient, clear fluid of density of r0. When the

membrane is removed, a turbidity current forms and propagates along the bottom

boundary.

hope is that the insight we gain from studying the interaction ofturbidity currents with such relatively simple geometries will allowus to gain an understanding of the fundamental mechanisms thatmay dominate the interaction between currents and realistic seafloor topographies. Hence we aim to address such important issuesas the relationship between nonuniformities in the deposit profilesand the shape of the obstacle, the effect of the geometry on thetransport and deposition of fine and coarse particles, and the runoutlength of these currents.

Section 2 formulates the governing equations. A brief discus-sion of the numerical methodology is presented in Section 3.Section 4 presents the numerical results obtained via TURBINS fora monodisperse lock-exchange flow, and validates them againstexperiments conducted by de Rooij and Dalziel (2001). Subse-quently, we proceed towards a comparison with experimentalresults for bidisperse turbidity currents (Gladstone et al., 1998).We analyze bottom shear stress data to evaluate the potential forbed load transport and erosion on the final deposit profiles.Finally, we investigate the influence of the bottom topographyon nonuniformities in the deposits of polydisperse suspensions.

2. Governing equations

We employ the incompressible Navier–Stokes equations forthe motion of the suspension, along with a convective–diffusivetransport equation for the Eulerian description of the particleconcentration field. A detailed discussion of the governing equa-tions is provided by Necker et al. (2002) and Nasr-Azadani and

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153 143

Meiburg (2011), so it suffices to present a brief summaryhere.

We focus on modeling incompressible flows of dilute suspen-sions, with typical particle volume fractions of Oð1Þ% or less. Thesuspension flow is governed by the incompressible Navier–Stokesequations in the Boussinesq approximation:

r � u¼ 0, ð1Þ

@u

@tþu � ru¼�rpþ

1

Rer

2uþcteg , ð2Þ

where the nondimensional quantities u, p, Re, and ct represent thefluid velocity, pressure, Reynolds number, and total particleconcentration (volume fraction), respectively. eg indicates theunit vector in the direction of gravity, eg ¼ ð0,�1;0Þ. By assuminga dilute suspension of small particles, we can neglect particleinertia and any particle–particle interaction. Consequently, theparticles are assumed to follow the fluid, with a constant settlingspeed us superimposed that acts in the direction of gravity. Weallow the suspension to contain N different particle sizes, all ofthe same density rp. For the ith particle size, we define acontinuum concentration field ciðx,tÞ, which is governed by

@ci

@tþ uþui

seg� �

� rci ¼1

Re Scir2ci, i¼ 1, . . . ,N: ð3Þ

Here, usi and Sci denote the ith particle settling speed and

Schmidt number

Sci ¼nk i

, i¼ 1, . . . ,N, ð4Þ

respectively. In Eq. (4), n and k i represent the kinematic viscosityof the fluid and the diffusion coefficient associated with the ithconcentration field. We remark that in Eq. (3), diffusion isincluded to account for the smearing of the sharp interfaces ofparticles (Ham and Homsy, 1988; Davis and Hassen, 1988) due tohydrodynamic diffusion of particles. Hartel et al. (2000b) demon-strate that this diffusion does not significantly affect the dynamicsof the flow, as long as the Schmidt number is equal to or greaterthan one. In the present investigation, we set all Sci’s to unity.Unless stated otherwise, for the given particle size, the settlingvelocity is taken to be identical to the Stokes settling velocity. Forsmall, spherical particles with low particle Reynolds number, theStokes settling velocity agrees closely with that of the empiricalcorrelations (Gibbs et al., 1971; Dietrich, 1982). On the otherhand, for irregularly shaped particles, considerable deviation fromthe Stokes value may occur in the settling velocity, cf. Gladstoneet al. (1998). All concentration fields Ci are scaled with the totalinitial volume fraction of the particles in the lock Cr; i.e.,

ci ¼Ci

Cr, i¼ 1, . . . ,N: ð5Þ

The total concentration ct introduced in the momentumequation (see Eq. (2)) is obtained as

ct ¼XN

i ¼ 1

ci: ð6Þ

Here, ct varies between 0 in the clear fluid, and 1 in the lock(see Fig. 1). In the remainder, we choose half the lock heightas the characteristic length scale, i.e. Lr ¼ H=2. The buoyancyvelocity

ub ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiH

2

ðrp�r0ÞCr

r0

g

sð7Þ

serves as the characteristic velocity to nondimensionalizethe flow quantities. Consequently, the Reynolds number (see

Eqs. (2) and (3)) is defined as

Re¼ubH=2

n : ð8Þ

Note that the ^ symbol refers to dimensional quantities.

3. Numerical method

A detailed description of the numerical method is presented inNasr-Azadani and Meiburg (2011). We solve the momentumequations using a projection method (Chorin, 1968) in conjunc-tion with the fractional step method (Kim and Moin, 1985), on aMAC-staggered grid. In this approach, the velocity componentsare stored at the cell faces, while scalar quantities includingpressure and concentration(s) are stored at the cell centers.Viscous and diffusion terms in the momentum and transportequations are discretized via a fully implicit central differencingmethod, while the convective terms are discretized via an explicitthird-order essentially nonoscillatory (ENO) scheme (Hartenet al., 1987). The time integration for the transport and momen-tum equations is performed via a third-order total variationdiminishing Runge–Kutta method (TVD-RK3; cf. Harten, 1997).This method ensures a solution without any spurious oscillations,as long as no oscillations are generated by the Euler methodduring each substep integration. We briefly present one Runge–Kutta substep (not the entire step) of the time integrationprocedure in the following. First, the concentration fields of allparticle sizes are updated from time level tn to tnþ1 as

cnþ1i �cn

i

Dtþ unþui

seg� �

� rcni ¼

1

Sci Rer

2cnþ1i þ f nþ1

c ,

i¼ 1, . . . ,N: ð9Þ

Here, fc is the forcing term employed to apply the boundaryconditions on the solid boundaries (Nasr-Azadani and Meiburg,2011). Next, the velocity field is updated to an intermediatevelocity field un

un�un

Dtþun � run ¼�rpnþ

1

Rer2unþcnþ1

t þfn, ð10Þ

with fn accounting for the forcing term for boundary conditionimposition on the solid boundaries. The divergence-free velocityfield unþ1 at the new time level tnþ1 is obtained via

unþ1�un

Dt¼�rcnþ1, ð11Þ

where the scalar variable c is computed from the solution of aPoisson equation of the form

r2cnþ1

¼1

Dtr � un: ð12Þ

Again, we remark that Eqs. (9)–(12) represent only one out ofthe three Runge–Kutta substeps associated with the TVD-RK3methodology. We refer the reader to Nasr-Azadani and Meiburg(2011) for a detailed description of the solution procedure.

We have adopted an immersed boundary method with directforcing (Mittal et al., 2008) to enforce the boundary conditionsaccurately on the solid surface. This method benefits from ease ofimplementation, no additional constraints on the time step, andaccurate calculation of shear stress profiles on the solid surface.The last is of great importance when erosion of particles from thesediment bed into the flow plays a significant role.

Fig. 2 shows the sketch of the Cartesian grid, along withdifferent nodes tagged in accordance with the location of thesolid surface G. We employ a bilinear (trilinear) in two (three)dimensions interpolation scheme to obtain the value of any fluidquantity q at the mirrored node O, based on the surrounding fluid

Fig. 2. Sketch of the solid surface G and the tagged nodes. ~: immersed nodes,

S: solid nodes, �: fluid nodes, ’: control point X at the boundary, and m: mirrored

node O. n is the unit normal vector at the control point X pointing toward the fluid

region. A bilinear interpolation is performed to obtain the value at the mirrored

node O from the Fl’s located at the four vertices of the shaded box.

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153144

nodes Fl:

qO ¼XMl ¼ 1

wlql: ð13Þ

Here, the wl’s are the interpolation coefficients, which solelydepend on the locations of the Fl’s and point O. M is the totalnumber of Fl’s used for interpolation. Then, qO is employed todetermine the value at the immersed node I, so that the correctboundary condition at control point X is enforced. For instance, ano-slip Dirichlet boundary condition can be applied via

qX ¼ 0-qI ¼�qO ¼�XMl ¼ 1

wlql: ð14Þ

We remark that Neumann and Robin type boundary condi-tions can be implemented in corresponding fashion.

Fig. 3. Sketch of the computational setup employed in the present two-dimen-

sional simulation of a particulate lock-exchange current. The suspension of

density r1 has an initial particle volume fraction equal to Cr. To initiate the flow,

the membrane separating the two fluids (at x¼ Ls) is removed.

Table 1Velocity boundary conditions for three different particle-driven lock-exchange

simulations discussed in the text (see Fig. 3).

Case Left wall boundary

condition

Top wall boundary

condition

a Free-slip No-slip

b No-slip Free-slip

c No-slip No-slip

4. Results

4.1. Validation

Nasr-Azadani and Meiburg (2011) presented a detailed valida-tion study of the numerical methodology implemented inTURBINS. Specifically, they were able to demonstrate theexpected performance in terms of accuracy and convergence forconstant density and gravity-driven flows over complex geome-tries. In this section, we will extend their investigation byfocusing on particle-driven flows, in order to demonstrate theability of TURBINS to accurately reproduce experimental andcomputational results provided by de Rooij and Dalziel (2001)and Necker et al. (2002). Specifically, we will focus on suchquantities as front velocity, runout length, and deposit profiles.

The experiments carried out by de Rooij and Dalziel (2001) arebased on a lock-exchange configuration in which the suspension isinitially in a reservoir of Ls � H � W ¼ 10� 26� 26:5 cm filledwith tap water. The suspension includes 50 g of silicon carbideparticles with diameter dp ¼ 37 mm and density rp ¼ 3:217 g=cm3.The initial volume fraction of the particles is Cr¼0.0023, whichallows us to assume that the suspension is dilute. The Stokes andDietrich (1982) relationships result in identical particle settlingvelocities of us ¼ 0:16 cm=s. The reference length Lr ¼ 13 cm yieldsa buoyancy velocity (see Eq. (7)) of ub ¼ 8 cm=s. The

nondimensional settling velocity and the Reynolds number (seeEq. (8)) hence take the values us¼0.02 and Re� 10;400,respectively.

Fig. 3 shows the computational setup employed for ournumerical simulation. The domain has a size of Lx � Ly ¼ 20� 2.Hartel et al. (2000b) observe that for sufficiently large values ofReynolds number, such flow quantities as the front velocitydepend only very weakly on Re. Hence, we employ a value ofRe¼5000 in our simulations, in order to limit the computationaleffort. We employ a uniform grid in both x- and y-directions, withgrid spacings of Dx¼ 0:02 and Dy¼ 0:01, respectively. The lock, inwhich the fluid initially is at rest, has a dimensionless height ofH¼2 and length of Ls¼0.75, respectively.

The appropriate set of boundary conditions for the solution ofthe concentration field includes no-flux boundary conditions atthe left, right, and top walls, respectively:

@c

@x¼ 0 x¼ 0,Lx, ð15Þ

cus�1

Sc Re�@c

@y¼ 0 y¼ Ly: ð16Þ

At the bottom wall, the particles should leave the computa-tional domain freely with a settling velocity us. This means thatthe effect of the evolving thin deposit layer on the subsequentflow is neglected. To this end, Necker et al. (2002) employed aconvective outflow boundary condition for the concentrationfield. For the current MAC-staggered grid, we accomplish this inthe following way. At the first concentration node above thebottom boundary, which is located half a grid cell above thebottom wall, we solve the usual transport equation (see Eq. (3))for the concentration field. In doing so, we assume @c=@y¼ 0 aty¼0. We remark that this approach is applicable only to situa-tions where resuspension of particles from the bottom bed intothe flow is negligible, which is the case for the experiments of deRooij and Dalziel (2001). This was analyzed in detail by Neckeret al. (2002), based on the approach of Shields (1936), Mantz(1973) and Yalin and Karahan (1979). Necker et al. (2002)demonstrated that, based on the maximum bottom shear stressobserved in their simulations, resuspension of particles wasunlikely to have occurred in the experiments of de Rooij andDalziel (2001).

For the velocity field, we employ no-slip conditions at thebottom and right walls. Since the experiments were conducted in

Fig. 4. Comparison of the experimental final deposit profile by de Rooij and

Dalziel (2001) with corresponding computational results for different velocity

boundary conditions imposed at the left and top walls. ’: Experimental results

obtained by de Rooij and Dalziel (2001). Two-dimensional simulations in the

present study include dashed line (a), solid line (b), and dotted line (c) (see Table 1

for the boundary conditions in each case).

Fig. 5. Front location xf (measured from the lock gate), and temporal evolution of

the mass of suspended particles ms (t) normalized by the initial mass msð0Þ, as

functions of time for different boundary conditions imposed on the top and left

walls. Dashed line(a), solid line (b), and dotted line (c) (see Table 1 for the

boundary conditions in each case). Good overall agreement is observed between

the present study and the results of Necker et al. (2002) (�).

Fig. 6. Temporal evolution of the concentration field (black c¼1 and white c¼0) for

conditions are imposed at the left and top walls. (a) Free-slip at the left wall, no-slip at

both left and top walls. Nondimensional settling velocity is us¼0.02 (conditions are the

the detached packet of particles for the case of no-slip conditions at the left wall.

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153 145

a tank with a free surface, it would seem reasonable to apply afree-slip boundary condition at the top boundary of the computa-tional domain. However, as discussed by Britter and Simpson(1978), a no-slip boundary condition may be more appropriate, asimpurities in the water may cause the free surface to behavesimilarly to a solid wall. To investigate the effect of the conditionsapplied at both the top and left boundaries, we present resultsfrom three sets of simulations as described in Table 1.

The deposited particle layer thickness can be obtained byintegrating the particle flux through the bottom boundary intime:

Dðx,tÞ ¼Cr

s

Z t

0uscwðx,tÞ dt: ð17Þ

Here, cw denotes the concentration at the lower boundary. Theconstant s is introduced as the packing fraction of the settledsediment. It typically takes an approximate value of s¼ 0:63(Torquato et al., 2000). However, since the experiments referredto above report deposit profiles only in terms of particle mass, notlayer thickness, we are not concerned with the porosity of thesediment layers in the present study, so that we simply set s¼ 1.

Fig. 4 shows the final deposit profile along the bottomboundary for the experiment (de Rooij and Dalziel, 2001), alongwith corresponding two-dimensional simulation results for thethree cases presented in Table 1. The overall agreement is good,with differences being primarily evident in the lock region. Asdiscussed by Necker et al. (2002), possible reasons for thediscrepancy can be found in the initial turbulence added to thesuspension due to stirring (Gladstone et al., 1998), the initialsuspension not being perfectly homogeneous, and perturbationsintroduced by the mechanical removal of the lock-gate. Finally,we cannot exclude the possibility that, in spite of the stirringapplied, some particles may nevertheless have already settled outwithin the lock by the time the gate is opened, which may explainthe relatively large amount of deposit within the lock region. Therelatively strong oscillations observed in our results are notunexpected, as two-dimensional simulations at fairly low

turbidity currents produced by lock-exchange configurations. Different boundary

the top wall, (b) No-slip at the left wall, free-slip at the top wall, and (c) No-slip at

same as in the experiment of de Rooij and Dalziel, 2001). The symbol ‘‘k’’ indicates

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153146

Reynolds numbers show more coherent vortical structures thancomparable three-dimensional simulations (Necker et al., 2002).

Fig. 5 displays the front location and the total suspended massin the domain, as functions of time. Case (a) with free-slipboundary condition at the left wall shows good agreement withthe results of Necker et al. (2002), who also employed a free-slipboundary condition at the left wall, due to the constraints on theirnumerical method.

A comparison of the results in Figs. 4 and 5 suggests that thecondition at the top boundary does not have a significantinfluence on the front location and the final deposit profile. Incontrast, the difference between implementing a no-slip or free-slip boundary condition at the left wall is more significant, whichis a somewhat surprising result. We observe that in case (a), thecurrent travels faster and maintains more particles over longertimes. Also, the oscillatory behavior of the deposit profile near thelock-gate is less pronounced for this case, Fig. 4. In order tounderstand the reason behind the significant influence of the left

Fig. 7. Final deposit profiles for bidisperse lock-exchange turbidity currents, for differen

gate). Solid line: present study, ’: experiments conducted by Gladstone et al. (1998).

and 0.004, respectively.

wall boundary condition, we show instantaneous contours of theconcentration field at different times in Fig. 6.

For the no-slip condition at the left wall, a packet of particles(indicated by the symbol ‘‘k’’ in Fig. 6) detaches early on from thebulk of the current, due to the drag exerted by the left wall. Theseparticles settle out fairly quickly, and hence are no longeravailable to drive the current but contribute to the increaseddeposited mass within the lock region for the no-slip case. Wefurthermore note that, regardless of the boundary conditionimposed at the top wall, the vortical structure of the flow fieldis similar at corresponding times (see Fig. 6).

4.2. Bidisperse particle-driven current

Gladstone et al. (1998) investigated the effects of having abidisperse mixture of particle sizes on the sedimentation behaviorand runout length of turbidity currents. Toward this end, theyvaried the initial mass fractions of fine and coarse particles, while

t initial mass fractions of coarse and fine particles (xg is the distance from the lock

The nondimensional settling velocities for the coarse and fine particles are 0.0314

Fig. 8. Temporal evolution of the maximum friction velocity ut computed over the

bottom wall. Results are from a two-dimensional simulation of the case (C: 0%–F:

100%) for a bidisperse turbidity current produced by a lock-exchange configura-

tion (same as the setup used in experiments by Gladstone et al., 1998).

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153 147

keeping the total volume fraction of particles in the lock at aconstant value of Cr¼0.00349. Here, we duplicate their experi-ments by conducting two-dimensional simulations.

The lock used in the experiment has dimensions of

Ls � H � W ¼ 20� 40� 20 cm. The fine and coarse particles con-

sist of silicon carbide with density rp ¼ 3:217 g=cm3, and they

have diameters d1

p ¼ 25 mm and d2

p ¼ 69 mm, respectively.

Gladstone et al. (1998) suggest that the particle settling velocityis approximately one-third smaller than the Stokes value, due tothe additional drag originating from the angular particle shapes;cf. Hallermeier (1981) and Sparks et al. (1991). In this way, weobtain settling velocities of fine and coarse particles as

u1s ¼ 0:05 cm=s and u

2s ¼ 0:387 cm=s, respectively. Clearly, there

is some uncertainty and possibly nonuniformity associated withthe settling velocity, due to variations in the shapes of individualparticles, and the mixture not being perfectly sorted.

With the reference length Lr ¼ H=2¼ 20 cm and a particlevolume fraction of Cr¼0.00349, the buoyancy velocity and corre-sponding Reynolds number are computed as ub ¼ 12:33 cm=s andRe� 24;700, respectively; cf. Eqs. (7) and (8).

The computational setup is as follows (see Fig. 3). The domainhas a size of Lx � Ly ¼ 32� 2, with uniform grid spacing(Dx¼ 0:032 and Dy¼ 0:01) in both directions. Again, we employa reduced value of Re¼4000 to limit the computational cost. Forthe velocity field, free-slip conditions are imposed at the left andtop boundaries, while no-slip is enforced at the bottom wall. Atthe right domain boundary a nonreflective convective outflowboundary condition of the form

@q

@tþU

@q

@x¼ 0 ð18Þ

is implemented, to allow any flow quantity q (i.e., u and ci) toleave the domain with minimal disturbance on the solution in theinterior of the domain. In Eq. (18), U is a constant velocity chosento be the maximum velocity in the domain at each time step. Atthe top, left, and bottom boundaries, we employ the conditions ofEqs. (15) and (16) on the concentration field, along with @c=@y¼ 0at y¼0. We study a total of six cases, in which the relative initialmass fractions of coarse (C) and fine (F) particles in the suspen-sion are given by (C: 100%–F: 0%), (C: 80%–F: 20%), (C: 60%–F:40%), (C: 50%–F: 50%), (C: 20%–F: 80%), and (C: 0%–F: 100%),respectively (see Table 1 in Gladstone et al. (1998)).

Fig. 7 compares the final computational deposit profiles againstthe experimental data of Gladstone et al. (1998). We observe verygood agreement for the first four cases, in which the suspensioncontains more coarse than fine particles. For the last two cases,where the fine particles outweigh the coarse ones, there are moresignificant differences regarding the location of the profile peaks,with the experimental profiles indicating that the particles aredeposited somewhat further downstream. Interestingly, Bonnecazeet al. (1996) observed a similar discrepancy when comparing theirresults obtained by an algebraic model with their experimental data.Those authors suggest that one possible reason for this differencemay be found in the potential bed load transport of the particlesalong the bottom wall. In the following, we will further investigatethis matter in more detail.

If the flow is sufficiently vigorous, the deposit layer canpotentially be altered due to resuspension of particles and/orbed load transport. We will now evaluate the potential for thesemechanisms to have an effect for the flow under consideration.Toward this end, we focus on the results obtained for the (C: 0%–F: 100%) case, which shows the largest discrepancy in the depositprofile between simulation and experiment (see Fig. 7). Weemploy the approach proposed by Shields (1936) and Mantz(1973) and use the computed wall shear stress data to check for

the possibility of incipient particle motion and/or resuspension.For this purpose, we have to analyze whether or not the ‘‘critical’’states are reached in which the particles commence their inci-pient motion along the bottom wall or are being resuspended.This critical state is defined by means of particle Reynoldsnumber Ren and nondimensional wall shear stress ycr:

Ren ¼utdp

n , ð19Þ

ycr ¼ru

2t

ðrp�rÞg dp

: ð20Þ

Here, ut is the so-called friction velocity related to wall shearstress tw by

ut ¼

ffiffiffiffiffiffitw

r

s, tw ¼ m

@u

@y

����y ¼ 0

: ð21Þ

We define the nondimensional friction velocity ut using thebuoyancy velocity (see Eq. (7)) which is related to the non-dimensional flow quantities by

ut ¼ut

ub¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

Re

@u

@y

����y ¼ 0

s: ð22Þ

For the given case (C: 0%–F: 100%), the time evolution of themaximum ut over the entire bottom wall is shown in Fig. 8. Themaximum ut observed in the simulation is recorded approxi-mately at time t¼4.6. This time corresponds to the point whenthe upper, light current has been reflected from the left wall(Fig. 9). Fig. 9 displays the spatial distribution of the frictionvelocity over the bottom wall and the corresponding concentra-tion field at t¼4.6. The maximum friction velocity occurs in theregion where the intense vortex in the wake of the currentimpinges on the bottom wall. The friction velocity has a second-ary maximum close to the nose region. To perform our investiga-tion, we employ the maximum value of ut ¼ 0:13 and obtainycr � 0:5 and Ren � 0:4 (see Eqs. (19), (20), and (22)). For any givenvalue of Ren, Mantz (1973) suggests two thresholds for ycr, whichare associated with (a) the incipient motion of the particles in the

Fig. 10. Effect of adding fine particles on a bidisperse lock-exchange turbidity

current. �: runout length of the coarse particles only, ~: runout length of the total

deposit. Nondimensional settling velocities of coarse and fine particles are 0.0314

and 0.004, respectively (Gladstone et al., 1998). Corresponding quadratic fits (solid

and dashed lines) are shown for each dataset.

Fig. 9. (Top) Spatial distribution of friction velocity ut on the bottom wall at time

t¼4.6. (Bottom) Snapshot of the concentration field (black c¼1, white c¼0) at the

same given time. Results are from a two-dimensional simulation of case (C: 0%–F:

100%) of a turbidity current produced by lock-exchange configuration (same as the

setup used in experiments by Gladstone et al., 1998).

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153148

form of bed load transport and (b) incipient resuspension ofparticles, respectively. According to Mantz (1973), at the particleReynolds number Ren ¼ 0:4, the critical value for the onset ofresuspension is ycr � 0:4, which is below the computed value incurrent simulation. This suggests that particle resuspension mayhave some influence on the deposit profiles. However, we pointout that according to Fig. 8, the maximum friction velocity occursonly in a very short time interval during the early stages of thecurrent’s development. It rapidly drops to values significantlybelow the critical value of ycr � 0:4, which suggests the absence ofparticle resuspension. Second, the deposit layer potentially influ-enced by the resuspension of particles is limited only to a smallspatial region (see Fig. 9). Finally, by time t¼4.6, only 3% of theinitial suspended mass is deposited onto the bottom bed, whichindicates that only a very small number of particles can poten-tially be resuspended into the current. On the other hand, theobtained value of ycr � 0:5 is significantly above the secondthreshold (ycr � 0:1) suggested by Mantz (1973) at which theincipient motion of particles on the bottom wall may occur. Thisobservation suggest the possibility of bed load transport of fineparticles, which could possibly be responsible for the ‘‘shift’’observed in the deposit profiles of the last two experimentalcases of experiments by Gladstone et al. (1998) (see Fig. 7). In thisdiscussion, however, we have to keep in mind that our computa-tional Reynolds number was lower than the experimental one,which means that the experimental wall shear stress valuesprobably did not reach the computational values. Hence, adefinitive conclusion as to whether bed load transport and/orerosion may have occurred in the experiment is not possible.Finally, as we had noted above, there are considerable uncertain-ties regarding the precise value of the settling velocity, which mayalso account for some of the observed differences.

In summary, the present depth-resolved simulations confirmthe observations of earlier authors, in that they show that evenmoderate fractions of fine particles cause the current, and with itthe coarse particles, to travel significantly further downstream.Fig. 10 shows the runout length Lt both for the overall deposit,and for the coarse particles only, for different initial fractions offine particles. To obtain Lt, we search for the location at which thenormalized final deposit height D1 of the concentration fieldunder consideration (coarse or total) is equal to a prescribedtolerance, e.g., 0.005 in this particular example.

4.3. Polydisperse particle-driven current traveling over a complex

bottom surface

As a next step, we focus on a comparison of two-dimensionalTURBINS simulation results with two sets of experimentsconducted by Kubo (2004). This author conducted a series ofexperiments to investigate the degree to which turbidity currentsare affected by bottom topography, modeled by ramps withslopes similar to those found in deepwater regions. Kubo (2004)also employed the depth-averaged Navier–Stokes equations as asimplified model for such currents.

The first comparison addresses run A4 in Kubo (2004). Theexperimental suspension is made by mixing siliceous, noncohe-sive, sand- to silt-sized particles of density rp ¼ 2:65 g=cm2. Themixture in the lock is represented by six size fractions withrespective diameters of 125.0, 105.1, 88.4, 62.5, 44.20, and31:25 mm (see Fig. 1 in Kubo, 2004). The relative mass fractionsof these particle sizes in the lock are 0.1, 0.15, 0.25, 0.3, 0.15, and0.05, respectively. The mixture has an overall particle volumefraction of Cr¼0.02. Kubo (2004) employed the relationshipproposed by Gibbs et al. (1971) to relate the settling velocity tothe particle diameter. In this way, he obtained settling velocitiesof 1.136, 0.846, 0.623, 0.33, 0.17, and 0.0864 cm/s, respectively.The lock has dimensions Ls � H � W ¼ 50� 20� 17 cm. UsingEqs. (7) and (8), the corresponding buoyancy velocity andReynolds number are computed as ub ¼ 18cm=s and Re� 18;000,

Fig. 13. Final deposit profile for a polydisperse lock-exchange turbidity current

traveling over complex bottom topography. Solid line: present study (Re¼5000),

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153 149

respectively. Our simulations employ a reduced value of Re¼5,000.The nondimensional settling velocities are given by 0.0631, 0.047,0.0346, 0.0183, 0.0094, and 0.0048. The numerical setup is asfollows: the domain has a size of Lx � Ly ¼ 55� 2, with uniformgrid spacing (Dx¼ 0:039 and Dy¼ 0:0125) in the x- and y-direc-tions. The velocity and concentration boundary conditions are thesame as in the previous section, except that we impose a no-slipcondition on the velocity field at the left wall.

Fig. 11 compares the final computational deposit profileobtained with the experimental results for run A4 in Kubo(2004). While the overall trends of the profiles are similar innature, there exist significant quantitative differences. Specifi-cally, the experimental data show a much longer runout of thecurrent. This is puzzling, as our simulation results had shownmuch better agreement with the very similar experiments ofNecker et al. (2002). Among the potential experimental reasonsfor the discrepancy could be (a) smaller effective settling velo-cities than those obtained above from the relationship by Gibbset al. (1971), (b) the presence of bed load transport, and (c) thepresence of erosion. We also note that in Fig. 11 the total areasbelow the experimental and computational profiles are different.Specifically, the integral over the experimental profile is muchsmaller than that over the computational profile. Since the figureshows only the section of the flow field downstream of the gate,this indicates that in the experiments substantial depositionoccurred already within the lock, which may substantially affect

Fig. 12. Schematic of the experimental setup employed by Kubo (2004) in run C5,

for a particle-driven current traveling past a complex geometry.

dashed line: experiments conducted by Kubo (2004) (Re¼18,000, run C5). Both

curves are normalized by the total initial particle mass.

Fig. 11. Final deposit profiles for a polydisperse particle-laden current produced

by a lock-exchange configuration. Solid line: present simulation results

(Re¼5000), dashed line: experiments conducted by Kubo (2004) (Re¼18,000,

run A4). Both curves are normalized by the total initial particle mass.

the dynamics of the current downstream of the lock. We willfurther discuss these issues below.

The second set of experiments conducted by Kubo (2004)includes a nontrivial bottom topography. Fig. 12 shows theschematic of run C5. The geometry includes an initial ramp ofsize length lr¼10 and height hr¼1 (all dimensions are scaled withthe reference length Lr ¼ 10 cm). Three successive, identicalhumps are located downstream of the ramp, with heights¼0.36 and length d¼10, respectively. As pointed out by Kubo(2004), the resulting slope of 0.036 is of the same order as that ofsediment waves produced by turbidity currents in deep-searegions; cf. Wynn et al. (2000b).

The particle size distribution and settling velocities are iden-tical to those for run A4. In the absence of erosion, the conditionimposed at the bottom boundary now reads

n � rci ¼ 0, i¼ 1, . . . ,6: ð23Þ

The numerical setup and the lock dimensions are identical tothose for run A4, except for the length in the y-direction which isgiven by Ly¼3.

The final deposit profile obtained from a simulation of thiscase is compared against experimental run C5 by Kubo (2004) inFig. 13. Experiments and simulations alike indicate that deposi-tion seems to be stronger in those regions where the flowdecelerates due to an upward slope of the bottom topography.

Fig. 14 provides the deposit profiles for the individual particlesizes. We note that the finer particles are least influenced by thegiven geometry, and therefore can travel past three humps.

Similarly to run A4, this case shows significant discrepanciesbetween current simulation results and the experiments by Kubo(2004). As discussed above, factors such as erosion, bed loadtransport, the lower Reynolds number of the simulation, anduncertainty in the settling velocities may contribute to thesedifferences. Concerning the resuspension of particles, we remarkthat Kubo (2004) presents theoretical results for both with andwithout erosion which indicate that erosion does not have asignificant effect on the deposit profile (see Fig. 9 in Kubo, 2004).

Fig. 15. Front location xf as a function of time. Solid line: two-dimensional

simulation results (Re¼5000), �: experiments by Kubo (2004) (run C5). Dashed

lines represent the temporal evolution of the mass of suspended particles misðtÞ,

normalized by the initial mass misð0Þ, for the six different particle sizes (solid line:

total mass).

Fig. 16. Deposit profiles obtained by ‘‘dumping’’ the remaining suspended

particles once the current has reached a near stand still. The difference between

dumping at time 160 and at time 300 is seen to be small when compared to the

final deposit profile (DN) obtained at t¼1000. Results are from a two-dimensional

simulation to reproduce experiments (run C5) by Kubo (2004).

Fig. 14. Nondimensional final deposit profiles for a polydisperse particle-laden

current traveling pass a complex geometry. The different curves represent the

different particle sizes in the suspension.

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153150

We note that, given the initial volume fraction of particles(Cr¼0.02), the lock dimensions, and the particle density, the totalparticle mass initially added to the lock is mp0 � 900 g. On theother hand, if we integrate the area under the curves in Figs. 11and 13 to obtain the total deposited mass, we obtain for bothcases (A4 and C5) a value significantly lower than 900 g, andcloser to mp � 500 g. This indicates that a substantial fraction ofthe particles, close to 45%, settles out before it reaches thelock gate.

The front location as a function of time, shown in Fig. 15,indicates that initially the simulation results duplicate the experi-mental data very accurately. However, beyond t¼30 the compu-tational current slows down significantly as compared to itsexperimental counterpart. Possible reasons for this discrepancyinclude the lower Reynolds number in the simulation, thepotential presence of erosion, and/or a lower effective settlingvelocity in the experiment.

Fig. 15 also displays the temporal evolution of the suspendedmass for each particle size, normalized by each particle’s initial

suspended mass. We note that at the final simulation time oft¼160, there are still some particles in suspension, even thoughthe current has come to a nearly complete standstill. When themaximum horizontal particle flux (including advective and diffu-sive fluxes) in the entire flow field drops below a certain thresh-old value, we terminate the simulation and ‘‘dump’’ the remainingsuspended particles at their current streamwise location. Fig. 16provides information on the accuracy of this procedure, and on itspotential to reduce the computational cost associated with thetime integration of the flow field. In this figure, we compare thedumped deposit profiles obtained at two different times t¼160 andt¼300 with the ‘‘most accurate’’ deposit profile (D1) obtained att¼1000 where only 0.2% of the initial particle mass is still insuspension. At t¼160, t¼300, and t¼1000, the maximum recordedhorizontal particle fluxes in the entire domain are found to be0.0047, 0.00067, and 0.000014, respectively. We note that the errordue to the dumping of the particles is very small, while thisprocedure can substantially reduce the computational cost.

4.4. Three-dimensional topography

We now investigate a three-dimensional bidisperse turbiditycurrent flowing past a Gaussian bump in the bottom topography.Our interest focuses on the influence of the bottom topography onthe flow structure, and on any resulting nonuniformities of thedeposit profile.

Fig. 1 displays the configuration of this problem. The computa-tional domain is given by Lx � Ly � Lz ¼ 17� 2� 2, respectively.The center of the Gaussian bump is located at ðxc ,yc ,zcÞ ¼

ð0:32Lx,0,0:5LzÞ, while its surface height is given by

Gðx,zÞ ¼ h exp �ðx�xcÞ

2þðz�zcÞ

2

2e2

!: ð24Þ

Here, h¼ 0:125Ly denotes the bump height and e¼ 0:125Ly

controls the width of the bump. The lock has dimensions of

Fig. 17. Time evolution of the ct¼0.1 concentration isosurface for a lock-exchange

turbidity current interacting with a Gaussian bump for Re¼2000. The suspension

contains a mixture of two particle sizes, with nondimensional settling velocities

equal to ucs ¼ 0:035 and uf

s ¼ 0:0035, and initial mass fractions 90% and 10%,

respectively.

Fig. 18. Final deposit profiles for a bidisperse turbidity current flowing past a

Gaussian bump. The nondimensional settling velocities are ucs ¼ 0:035 and

ufs ¼ 0:0035, with relative initial mass fractions of 90% and 10%, respectively. The

nonuniformities are especially pronounced in the wake of the bump. The dashed

lines show the boundaries of the bump.

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153 151

Ls � H �W ¼ 1� 2� 2. The suspension includes two particlesizes with nondimensional settling velocities of uc

s ¼ 0:035 anduf

s ¼ 0:0035, and initial relative mass fractions of 90% and 10%,respectively. At the bottom, top, and left boundaries we enforceno-slip, while a free-slip boundary condition is imposed along thetwo lateral spanwise walls. At the outflow boundary (x¼ Lx), weemploy the convective condition discussed earlier (see Eq. (18))for all flow quantities. For the concentration fields, we enforce avanishing normal derivative everywhere on the boundariesexcept for the top wall (see Eq. (16)) and the end wall at x¼ Lx

(see Eq. (18)):

n � rci ¼ 0, i¼ 1;2: ð25Þ

We set Re¼2000 and employ uniform grid spacing in all threedirections, with Dx¼ 0:0157 and Dy¼Dz¼ 0:0148.

Fig. 17 shows the flow evolution at different times. Initially, itis dominated by the formation of two spanwise startup vortices,cf. the discussion by Hartel et al. (2000b) and Necker et al. (2002).Due to the absence of any initial three-dimensional perturbations,

the current maintains its two-dimensional structure until itencounters the bump, at which point the interaction betweenthe front and the bottom boundaries results in the developmentof strong three-dimensional effects. Once the current has passedthe bump, spanwise deformations along the front, known as lobe-and-cleft instabilities (Hartel et al., 2000a), are clearly visible.A strongly three-dimensional flow field, increased turbulent mixingand nonuniformities in sediment deposition (Necker et al., 2005) aredirect consequences of these instabilities on the flow.

Clearly, nonuniform effects including depletive/accumulativeflow regimes mostly arise where the current experiencesconstrictions and/or expansions. Kneller and Branney (1995)showed that such effects can have an influence on the spatialdistribution of turbidites. The topography of the Gaussian bumpcauses the current to be deflected laterally, thus resulting innonuniformities of the deposit profile (see Fig. 18). The figureshows that these nonuniformities are more pronounced for thecoarse than for the fine particles. In this context we remark that AlJa Aidi (2000) showed that if the obstacle height is more than 10%of the current’s height, the flow develops a dividing streamline.The flow sections below this dividing streamline are deflected tothe sides of the obstacle, while the upper portions of the flow passover the obstacle (see Fig. 17).

Fig. 19 compares the streamwise deposit profiles in twoplanes, the midplane (z¼ 0:5LzÞ and at the edge of the bump(z¼ 0:15Lz), with the case of a flat surface. While the deposition ofparticles near the bump decreases strongly in the midplane, itincreases closer to the lateral walls. This is consistent with thelateral motion of the current. Fig. 19b investigates the influenceseparately for fine and coarse particles. It indicates that theinfluence of the bottom topography is more pronounced for thelarger particles.

Fig. 20 displays the spanwise deposit profiles of the coarseparticles at different x-locations. It confirms the significantinfluence of the topography on the deposit profiles near thebump, in terms of reducing deposition in the midplane whileenhancing it near the spanwise boundaries. This effect progres-sively diminishes in the far wake.

5. Summary and conclusions

In an earlier publication (Nasr-Azadani and Meiburg, 2011) wehad demonstrated the accuracy of the software tool TURBINS forsimulating constant density and gravity-driven fluid flows incomplex geometries. Here, we have discussed the extension ofTURBINS for simulating particle-driven flows. Comparisons ofsuch quantities as deposit profiles, front location, and runout

Fig. 19. Influence of the Gaussian bump on the deposit profile of a bidisperse turbidity current. (a) Comparison of the total final deposit profiles against a similar current

flowing over a flat surface. (b) Influence of the bump on the deposition of coarse and fine particles, respectively. All deposit heights D1 are normalized by the

corresponding total initial mass multiplied by W. Note that solid lines represent the edge of the bump (z¼ 0:15Lz) and dashed lines correspond to the midplane (z¼ 0:5Lz),

respectively. The Gaussian bump causes significant spanwise nonuniformities in the deposition profile of the current propagating over the bump.

Fig. 20. Spatial variation of the final deposit profile for the coarse particles, for a

bidisperse turbidity current flowing past a Gaussian bump. For each streamwise

location, the deposit profile is plotted along the spanwise direction z. Curves (1–6)

correspond to x¼4.8, 5.5, 6.2, 6.9, 7.6, and 8.3, respectively. The dashed line

represents the cross section of the bump at xc¼5.5. Note that all D1 ’s are

normalized by total initial mass of coarse particles multiplied by Ls.

M.M. Nasr-Azadani et al. / Computers & Geosciences 53 (2013) 141–153152

length with the experimental and computational data of de Rooijand Dalziel (2001) and Necker et al. (2002) demonstrate theability of TURBINS to accurately reproduce corresponding experi-ments. We extended the investigation of Necker et al. (2002) byfocusing on the influence of the conditions imposed at the leftside wall and the top boundary.

We subsequently focused on bidisperse turbidity currents, bycomparing with the experiments of Gladstone et al. (1998).Varying the initial mass fractions of coarse and fine particles,we observe that the runout length and final deposit profiles of thecoarse particles are altered significantly by the influence ofthe fine particles. This clearly indicates the coupling between thedifferent particle sizes in polydisperse mixtures and their effect onthe deposit profiles. We also carried out a detailed analysis using themaximum friction velocity to assess the occurrence of resuspension

of particles and also bed load transport. We employed theapproached by Mantz (1973) and found that the discrepanciesappearing in the final deposit profiles are more likely due to bedload transport than to resuspension of particles.

In order to investigate the effect of complex bottom topogra-phy on turbidity currents, we compared with the experiments ofKubo (2004). While we find qualitative agreement, there arequantitative discrepancies. Among the reasons for these may bean overestimation of the experimental particle settling velocity(cf. also the comments in Gladstone et al., 1998), along with thepresence of bed load transport and/or erosion.

To demonstrate the three-dimensional capabilities ofTURBINS, we study the deposit profiles obtained for turbiditycurrents flowing over a Gaussian bump. As the current interactswith the bump, we observe the generation of so-called lobe-and-cleft instabilities. Furthermore, the flow is deflected laterally,which results in the development of nonuniformities in thedeposit profiles especially in the near wake region of the bump.Deposit profiles plotted in various spanwise and streamwiseplanes suggest that the fine particles are less influenced by theobstacle geometry than the coarse particles.

In summary, TURBINS has been demonstrated to be a versatilenumerical tool for investigating the interactions between turbid-ity currents and seafloor topography. The implementation of aturbulence model in TURBINS is currently underway.

Acknowledgments

We are grateful to Professor Ben Kneller for numerous helpfuldiscussions on the physics of turbidity currents. MN was fundedvia research support to Professor Kneller’s group from BG Group,BP, ConocoPhillips, DONG, GDF Suez, Hess, Petrobras, RWE Dea,Total, and Statoil. EM acknowledges financial assistance throughNSF Grants CBET-0854338, CBET-1067847, and OCE-1061300.The simulations were carried out at the Community SurfaceDynamics Modeling System (CSDMS) high-performance comput-ing facility at the University of Colorado in Boulder. We wouldlike to thank CSDMS director Professor James Syvitski and theresearch scientist at CSDMS, Dr. Eric Hutton.

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