Chapter 7 Sediment Transport Model - Museum Of Natural .
Chapter 7Sediment transport model7.1IntroductionThis chapter describes the sediment transport model implemented in COHERENS. There are six sections. In the first one, a discussion is given of physical parameters and processes (bed shear stress, molecular viscosity, waves)which are of importance for the sediment and the influence of sedimentson the physics through density gradients. In the next section a descriptionis given of the basic sediment parameters (Shield parameter, fall velocity,critical shear stress), related to sediment transport. This is followed by anoverview of the bed and total load equations available in COHERENS. Then,the suspended sediment transport module is presented. Finally, numericaltechniques, specific for the sediment module, are described.7.2Physical aspects7.2.1Bed shear stressesThe bed shear stress is considered as the physical parameter which has thelargest impact on sediment transport, since it controls how much of the sediment in the bed layer becomes suspended in the water column. In thephysical part of COHERENS, bottom stresses are calculated using either alinear or a quadratic friction law (see Section 4.9). In the sediment transportmodule, however, a quadratic friction law is always taken, as given by equation (4.340) in 3-D or (4.341) in 2-D mode. The magnitude of the bottomstress can then be written asτb ρu2 b ρCdb u2bor τb ρu2 b ρCdb ū 2311(7.1)
312CHAPTER 7. SEDIMENT TRANSPORT MODELfor the 3-D, respectively 2-D case. In the equations, u b is the wall shear(friction) velocity1 , ub the bottom current, ū the magnitude of the depthmean current and Cdb the bottom drag coefficient given byhi2i2hκκ Cdb or Cdb (7.2)ln zb /z0ln H/z0 ) 1for the 3-D, respectively 2-D case. Here, κ is the Von Karman constant, zbheight of the first velocity node above the sea bed, z0 the roughness heightand H the total water depth.In the discussions of the load formulae, given in the sections below, otherformulations, obtained from engineering practice, are mentioned and givenhere for completeness:gC2gM 2Cdb 1/3HgCdb [18 log (2H/5z0 )]2Chezy(7.3)Manning(7.4)White-Colebrook(7.5)Cdb The coefficients C and M are denoted as the Chezy, respectively Manningcoefficients.In case of a rough bed, the roughness length z0 can be calculated usingthe following relation:z0 0.11kbνkb u 3030(7.6)Here, kb is the roughness height from Nikuradse, ν the kinematic viscosityand u the friction velocity.Different kinds of roughness height are considered: Physical or “form” roughness kb representing the heights of the elementscomposing the bottom roughness. The corresponding physical bottomstress is used as boundary condition for the momentum flux at thebottom. “Skin” roughness ks usually related to the median particle size. Skinstress is used in the sediment module to calculate the amount of sediment material resuspended from the sea bed, once the stress exceeds acritical value (see below).1Since the friction velocity always refers to the bottom in this chapter, the subscriptwill be omitted in the following.b
7.2. PHYSICAL ASPECTS313 The main effect of surface waves on the bottom stress is a significantincrease of both the form and skin roughness heights. The new roughness height, denoted as ka , is obtained from formulae for current-waveinteraction theories. The formulations are currently not implementedin COHERENS, but foreseen in a future version of the code.COHERENS provides different options for the selection of the skin bottomroughness. Either the form roughness, as used by the hydrodynamics, istaken as the skin roughess, or a constant user-defined value is supplied orspatially non-uniform values are provided by the user. A further advantage isthat the user can calibrate the sediment transport rates in this way withoutchanging the hydrodynamics. Note that, in the current version of the code,no formulation has been implemented for the skin roughness as function ofmedian size, although ks can always be externally supplied by the user.7.2.2Wave effectsAlthough surface waves effects have not been implemented in the physicalpart of the code, the bottom stresses used in the load formulae, discussedbelow, take account of both currents and waves. A summary of the appliedmethods is given in this subsection.The wave field is supplied externally by a significant wave height Hs ,a wave period Tw and a wave direction φw . The wave amplitude Aw andfrequency are defined byAw Hs /2 , ωw 2π/Tw(7.7)The near-bottom wave orbital velocity determined from linear wave theoryis given byAw ωw(7.8)Uw sinh kw Hwith the wavenumber kw obtained from the dispersion relationωw2 gkw tanh kw H(7.9)The latter equation is solved for kw using the approximate formula of Hunt(1979)sf (α)kw ωw(7.10)gHwithf (α) α 1.0 0.652α 0.466422α2 0.0864α4 0.0675α5 1(7.11)
314CHAPTER 7. SEDIMENT TRANSPORT MODELandα ωw2 Hg(7.12)With this option, it is assumed that the near bed wave period is equal to themean wave period, such that the near bed wave excursion amplitude can bewritten asUw(7.13)Ab ωwThe combined effect of currents and waves on the bed shear stress is calculated using the method described in Soulsby (1997). Two types of bottomstress are defined The mean value over the wave cycle which should be used for currents" 3.2 #τwτm τc 1 1.2(7.14)τc τwwhere τc is the bottom stress for currents alone as given by (7.1)–(7.2). The maximum value during the wave cycle used in the criterion forresuspensionp2 τ 2 2τ τ cos φ(7.15)τmax τmm wwwwhere the wave bottom stress is defined by1τw fw Uw22(7.16)Two formulations are used for the wave friction Swart (1974)fw 0.3 for Ab /kb 1.57 0.19fw 0.00251 exp 5.21(Ab /kb )for Ab /kb 1.57(7.17) Soulsby et al. (1993)fw 0.237(Ab /kb ) 0.52(7.18)
7.2. PHYSICAL ASPECTS7.2.3Density effects7.2.3.1Equation of state315The fluid density is an important parameter for calculating settling velocitiesand entrainment rates in sediment transport. The equation of state that isused to calculate the fluid density as function of the water temperature andsalinity is discussed in Section 4.2.3. When sediment is present, an additionaleffect is present in the equation of stateρ (1 NXcn )ρw n 1NXcn ρs,n(7.19)n 1Here ρ is the density of the mixture, ρw the density of the fluid (including theeffects of temperature, pressure and salinity), cn the volume concentrationof fraction n, N the number of sediment fractions and ρs,n the particle density for sediment fraction n. A stable vertical sediment stratification leads todamping of turbulence and affects the settling velocity of the sediment. However, care must be taken when applying this in combination with hinderedsettling (Section 7.3.3.2), because hindered settling models already accountfor the increased buoyancy of the mixture. Thus using a changed equationof state in combination with hindered settling will result in too low settlingvelocities.7.2.3.2Density stratificationTo a large extent, the two-way coupling effects between flow and sedimenttransport are due to density stratification effects. Villaret & Trowbridge(1991) showed that the effects of the stratification from suspended sedimentare very similar (even with the same coefficients) to the ones produced bytemperature and salinity gradients. This means that the effects of sedimentturbulence interaction in COHERENS can be implemented within the existingturbulence models in the same way as T and S.The (squared) buoyancy frequency in the presence of vertical sedimentstratification becomes:2N Nw2 gNXn 1βc,n cn z(7.20)where Nw2 is the value in the absence of sediment stratification, as given by(4.130) and βc,n , the expansion coefficient for sediment fraction n, which is
316CHAPTER 7. SEDIMENT TRANSPORT MODELcalculated from the density of each sediment fraction ρs,n using:βc,n ρs,n ρw1 ρ ρ cnρ(7.21)The baroclinic component of the horizontal pressure gradient contains anadditional term due to horizontal sediment stratification. Equation (5.223)now becomesZ ζ N T q S X c 0βT 'g βS βc,ndz(7.22) xi xi xi n 1 xizIn transformed coordinates the following term is added to right hand side of(5.224) for each fraction n: Z ζ cn z 0 cnc,n 0Fi gβc,ndz 0(7.23) x z xssiizThe numerical methods, described in Section 5.3.13 for discretising the baroclinic gradient are easily extended to include sediment stratification.7.2.4Kinematic viscosityThe kinematic viscosity ν is an important parameter that has a significantinfluence on the settling velocity and the critical bed stress. Its value can beselected in COHERENS either as a user-defined constant or as a temperaturedependent value using the ITTC (1978) equation for sea water ν 10 6 1.7688 0.659.10 3 (T 1) 0.05076 (T 1)(7.24)Here T is the water temperature in 0 C and ν is given in m2 /s.ImplementationThe following switches are available:iopt sed tau Selects type of roughness height zs used for sediment transport1: set equal to the form roughness used in the hydrodynamics2: user-defined uniform value3: spatially non-uniform value supplied by the useriopt waves Disables/enables wave effects and selects type of input data wavedata, for use in the sediment transport models.
7.3. SEDIMENT PROPERTIES3170: wave effects disabled1: waves enabled with input of wave height, period and direction2: waves enabled with input of wave height, period, velocity, excursionand directioniopt sed dens Disables (0) or enables (1) effects of sediments in the equationof state and density stratification.iopt kinvisc Selects type of kinematic viscosity.0: user-selected uniform value1: from the ITTC (1978) equation7.37.3.1Sediment propertiesIntroductionSediment concentrations can be represented either as a volumetric concentration c in units of m3 /m3 or as a mass concentration cmass in kg/m3 .Thetwo forms are related bycmass ρs c(7.25)The volumetric form is taken in COHERENS, which is considered as morephysically meanigfull, especially in processes as hindered settling.A dimensional analysis by Yalin (1977) shows that the sediment transportcan be expressed by a number of dimensionless parameters:Re u dνρu2 (ρs ρ)gdρss ρhg i1/3d d (s 1) 2νqΦ p(s 1)gd3θ (7.26)(7.27)(7.28)(7.29)(7.30)where d is the particle diameter, Re the particle Reynolds number, θ thedimensionless shear stress or Shields parameter (Shields, 1936), s the relativedensity, d the dimensionless particle diameter and q the sediment load perunit width (in m2 /s).
318CHAPTER 7. SEDIMENT TRANSPORT MODELThese non-dimensional diameters are often used to describe sedimentproperties, such as critical shear stresses or settling velocities, which arediscussed below.7.3.2Critical shear stressIn many transport relations, a critical shear stress is required, which is thevalue of the bed shear stress at which the sediment particles start to move(the threshold of motion). The value of the bed shear stress is in engineeringpractice obtained from the Shields curve, which relates the non-dimensionalcritical shear stress θcr to the particle Reynolds number Re .For numerical models, some fits to these curves are made, expressing θcras a function of d rather than Re , in order to avoid the iteration processnecessary for the determination of the threshold of motion in the originalcurve obtained by Shields (1936), as both θ and Re are a function of u .Brownlie (1981) obtained the following relation from a fit through the data: 0.9θcr 0.22d 0.9 0.06.10( 7.7d )(7.31)An alternative form, also obtained by fitting of the Shields curve, is proposed by Soulsby & Whitehouse (1997)θcr 0.3 0.055 1 e 0.02d 1 1.2d (7.32)Another equation, available in COHERENS from Wu et al. (2000), is toassume a constant critical Shields stressθcr 0.03(7.33)This equation should only be used in combination with the bed load andtotal load equations from Wu et al. (2000). In COHERENS, the critical shearstress is calculated for each fraction separately at each horizontal location,using the local values of the kinematic viscosity and the mixture density.The sediment transport model in COHERENS has an option available forthe user to manually set the critical shear stress. The user can either setthe critical shear stress to a uniform value throughout the whole domain,or to a spatially varying value. Be aware that the value given should bethe kinematic critical shear stress defined as the square of the critical shearvelocity u2 ,cr τcr /ρ.
7.3. SEDIMENT PROPERTIES7.3.2.1319Hiding and exposureA hiding and exposure factor can be implemented for the critical shear stressτcr or the critical Shields parameter θcr to account for the change in sedimenttransport when different fractions are present. In general, the correctionfactor will increase the critical value for the smaller, hidden fractions andwill reduce the critical threshold for motion for the coarser, exposed, fractions. Several formulations can be found in literature, usually as a functionξ(dn /d50 ).Two methods are available in COHERENS for hiding and exposure. Thefirst one uses the formulation of Wu et al. (2000) based upon a stochasticrelation between size and gradation of bed materials and the hidden andexposed probabilities. The probability of particles dm in front of particles dncan be assumed to be the fraction of particles dm in the bed material, pbm .The total hidden and exposed probabilities of particles dn can be describedby:phn pen NXm 1NXpbmdmdn dm(7.34)pbmdndn dm(7.35)m 1and phn pen 1. The hiding/exposure factor is then defined by: ξn penphn m 1 phnphn m(7.36)where m is an empirical parameter which Wu et al. (2000) determined asm 0.6 in their study.Alternatively, hiding and exposure can be calculated with the equationof Ashida & Michiue (1972), which is an adapted form of Egiazaroff (1965)(ξn 0.8429 dd50nhlog 19log 19 log(dn /d50 )ifi2ifd50dnd50dn 0.38889 0.38889(7.37)where d50 is the median grain size diameter, which, in case multiple sizefractions are present, means that particles with sizes less than d50 accountfor 50% of the total mass.
320CHAPTER 7. SEDIMENT TRANSPORT MODEL7.3.2.2Bed level gradientThe threshold of motion is also influenced by the bed level gradient in thecurrent direction hθcr θcr,0 1 (7.38) cwhere θcr,0 is the critical Shields parameter in absence of bed slopes, h themean water depth and h/ c the bed slope along the current direction, defined below (equation (7.81). Since many of the bed boundary conditions forsuspended sediment concentrations depend on the critical Shields parameters, this correction will also affect the amount of sediment in suspension.7.3.3Settling velocity7.3.3.1Single particle settlingDifferent methods are available to calculate the settling velocity of sedimentparticles in COHERENS. A general formula for settling velocity was derivedby Camenen (2007), based on two formulations for the drag coefficient: sws ννRep dd 2/m 3 1/m 1/m m4 d 1 A1 A 4 B3B2 B(7.39)with d defined by (7.29) and Rep ws dp /ν the particle Reynolds number.The coefficients A, B and m have been given different values in literature.Camenen (2007) recalibrated these coefficients using results of Dietrich (1982)and data from 11 previous studies. He found for natural sand that A 24.6,B 0.96 and m 1.53, for flocs he found A 26.8, B 2.11 and m 1.19.Note that when using this equations for calculating the settling velocity formud flocs, the diameter that is used is the floc diameter, not the one of theprimary particles.For small Reynolds numbers (Rep 1), the settling velocity can becalculated from the Stokes equation (Stokes, 1847), valid for small sphericalparticlessgd2ws (7.40)18νwhere s is the relative density defined by (7.28), g the acceleration due togravity, d the particle diameter and ν the viscosity. This equation should onlybe used for very small particles, because it can give large overestimations forlarger ones.
7.3. SEDIMENT PROPERTIES321The following formulation is recommended by Soulsby (1997) for naturalsandsiν hp10.362 1.049d3 10.36(7.41)ws dAnother equation for the settling velocity, available in COHERENS is theone by Zhang & Xie (1993)r ν 2ν(7.42)ws 13.95 1.09 (s 1) gd 13.95dd7.3.3.2Hindered settlingIn case of high concentrations (mass concentrations larger than 3 g/l) thesettling of particles is not only influenced by the surrounding fluid and theweight and shape of the particles, but also by the other particles in suspension. The settling of the particles is reduced by a number of processes, e.g.return flow, particle collisions, changed mixture viscosity, buoyancy due toincreased mixture density and wake formation.For sand, hindered settling can be calculated with the equation of Richardson & Zaki (1954). They described the settling velocity in high sedimentconcentrations as a function of the sediment concentration, Rep and undisturbed settling velocity ws,0 (i.e. the one of a single particle without beingdisturbed):ws ws,0 (1 c)n(7.43)In this equation, n is a user-defined constant. Note that this formula isnot advisable for cohesive sediments because it does not take into accountthe maximum sediment concentration (i.e. the settling velocity should reduceto zero at the maximum packing concentration cmax ). This is not a severedisadvantage, because in most practical applications, the concentrations arenot so high, except close to the sea bed. Note that some hindered settlingeffects are already calculated when the fluid density depends on the sedimentconcentrations, and that this equations are only valid when a net depositionoccurs (Breugem, 2012). Therefore, it is recommended not to use hinderedsettling in that case.Winterwerp & van Kesteren (2004) introduced a different formula for mudws ws,0(1 cf )(1 c)1 2.5cf(7.44)Here ws,0 is the settling velocity of a single mud-floc, cf c/cgel , cgel is thegelling concentration (the mass concentration at which the mud flocs form a
322CHAPTER 7. SEDIMENT TRANSPORT MODELspace filling network), which can be calculated withcgel ρsdp 3 nfdf(7.45)The parameters needed to calculate the gelling concentration (nf and df )are difficult to determine. Therefore, the user must provide a value for cgel ,which should be obtained from measurements.7.3.3.3Influence of flocculationIn COHERENS, the influence of turbulence and sediment concentration onthe flocculation of mud flocs can be simulated. The effect of salinity is notconsidered. For simulating the influence of turbulence the empirical modelby Van Leussen (1994) is used for the fall velocity of settling flocs1 aGws ws,r1 bG2(7.46)pHere ws,r is a reference velocity, G the shear rate, defined as G ε/νand a, b empirical constants. In order to estimate the shear rate if theturbulent dissipation ε is not known (e.g. when an algebraic turbulencemodel is used), G can be obtained assuming equilibrium between productionand dissipation of turbulent kinetic energy (4.204) which gives 2rνT M 2 λT N 2(7.47)G νwhere νT , λT are the turbulent diffusion coefficients for respectively momentum and density and M , N the shear and buoyancy frequencies (seeSection 4.4 for details).A similar empirical approach to flocculation, which considers the influenceof the sediment concentration is given in Van Rijn (2007b) αws 4 log10 2c/cgel φf locws,r(7.48)with 1 φf loc 10 and α a user-defined constant with a minimum of 0 anda maximum of 3, whose default value in COHERENS was obtained fromcalibration of flocculation data in the Scheldt and harbour of Zeebrugge. Note2Note that G has a different meaning than in Section 4.4 where it represents thebuoyancy term in the turbulent energy equation.
7.3. SEDIMENT PROPERTIES323that Van Rijn (2007b) suggests α dsand /d50 1, with dsand the diameter ofthe transition from sand to silt (62 µm).It is also possible to combine the effects of these two models in COHERENS.
2 White-Colebrook (7.5) The coe cients Cand M are denoted as the Chezy, respectively Manning coe cients. In case of a rough bed, the roughness length z 0 can be calculated using the following relation: z 0 0:11 u k b 30 ˇ k b 30 (7.6) Here, k b is the roughness height from Nikuradse, the kinematic viscosity and u the friction velocity.
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
sediment transport problem. SRH-2D also provides detailed hydraulic output that can be used to estimate pier and abutment scour potential. 1.1 Background The Cimarron River example used in the SMS "SRH-2D Sediment Transport" tutorial will be use in this tutorial. If needed, review the "SRH-2D Sediment Transport" tutorial
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
CEDEX’s sediment quality criteria (see Table 7.3) aim to control the management of dredged material in Spanish waters. Sediment with 10% fine fraction ( 63µm) are regarded as clean. Sediment with 10% fine fraction require chemical characterisation with regard to the sediment quality criteria identified in Table 7.3. Sediment where .
BMP C241: Temporary Sediment Pond Purpose Sediment ponds remove sediment from runoff originating from disturbed areas of the site. Sediment ponds are typically designed to remove sediment no smaller than medium silt (0.02 mm). Consequently, they usually reduce turbidity only slightly.
the sediment fall velocity (and hence sediment residence time and fate) is critical to both short-term sediment transport predictions and long-term shoreline restoration efforts. However, this parameter can be difficult to measure and it can be complicated by cohesive sediment flocculation. The problem is
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
Cohesive Sediment Transport Processes 1)Suspension and Transport 2)Flocculation and Settling 3)Deposition 4)Bed Consolidation 5)Erosion and Resuspension 12. Division of Water Quality Sediment Transport 13 Source: Ji 2008. Division of Water Quality Flocculation and Settling Key parameter: settling velocity Six options that relate effective .
