Modelling Of Sediment Transport And Morphodynamics

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Die Küste, 81 (2014), 89-106Modelling of Sediment Transport andMorphodynamicsBert Putzar and Andreas MalcherekSummaryThis article summarizes general concepts for morphodynamic modelling and sedimenttransport in the coastal zone. Firstly, basic concepts with respect to non-cohesive sediments are introduced. The following sections describe techniques to model fractionatedsediment transport and to predict bed forms, as well as the related bed roughness. Thelast section is devoted to the simulation of dredging and dumping activities in the contextof long term morphodynamic simulations.Keywordssediment transport, morphodynamics, bed evolution, coastal zone, fractionated sedimenttransport, dunes, ripples, bed roughness, dredging and dumping, long-term morphodynamic modellingZusammenfassungEs werden die grundlegenden Konzepte der Sohlevolution und des Sedimenttransports nicht-kohäsiverSedimente eingeführt. Anhand von Beispielen werden Ansätze zur Behandlung von Sedimentklassen undzur Prädiktion von Sohlformen vorgestellt. Der Einfluss von Unterhaltungsmaßnahmen in Seeschifffahrtsstraßen auf die langfristige Sohlentwicklung wird im Rahmen eines Langfristmodells aufgezeigt.SchlagwörterSedimenttransport, Morphodynamik, Sohlevolution, Küstenzone, fraktionierter Sedimenttransport, Dünen, Riffel, Sohlrauheit, Unterhaltungsmaßnahmen, roduction .90Fundamental Concepts of Natural Sediment Transport . 90The Bed-Evolution Equation .91Bottom Shear Stress and Transport Initiation .92Bed Load Transport .94Suspended Sediment Transport .95Fractionated Sediment Transport .97Vertical Discretization of the Hydrographic Bed .9789

Die Küste, 81 (2014), 89-1063.2 Sediment Separation in a Tide-affected Bight . 98Prediction of Dunes and Ripples . 994.1 Grain and Bed Roughness . 994.2 Predicted Heights of Bed Forms and Resulting Roughness . 1005Effect of Maintenance Measures on Bed Evolution . 1025.1 Modelling of Maintenance Measures . 1025.2 Long-term Bed Evolution in the Elbe Estuary . 1026References . 10441IntroductionEven today, modelling of the continuous changes in the elevation of the hydrographicbottom and the structure of the corresponding subsurface of coastal waters is a tremendous scientific challenge. Primary cause is the large number of processes involved. Theserange from the different scales of the currents involved, like turbulences, swell, tides andlong-range currents (MALCHEREK 2010a), via the composition of the present sedimentsand biological processes, right up to anthropogenic encroachment like, for instance,dredging and dumping as maintenance measures or resource extraction.This article aims to introduce the approaches established today and implemented inmost current sediment transport models. Emphasis is placed on non-cohesive sediments,which, in coastal regions, are primarily represented through sandy sediment distribution.The multitude of empirical formulations and dedicated models regarding individual processes can and will not be covered. Rather, the emphasis is placed on outlining the premises pertaining to the various process models and their associated problems, limitationsand knowledge deficits.The mechanisms that apply to cohesive sediments are different than those applyingto sandy sediments. An introduction to this topic and further research is given byMALCHEREK (2010b), MALCHEREK and CHA (2011), as well as WEHR and MALCHEREK(2012), in which an isopycnic numerical model for the simulation of cohesive transportprocesses in tidal regions was presented. Sediment mixtures constitute a further field ofresearch. For an introduction to modelling of the interaction of cohesive and noncohesive beds see DONG (2007) and JACOBS et al. (2010).2Fundamental Concepts of Natural Sediment TransportAs a rule, the beds of natural channels consist of a mixture of grains of sediment withvarying properties, as well as miscellaneous biological components. They form a framework whose cavities are filled with in-situ water and whose structural cohesiveness maybe influenced by chemical as well as biological processes. Separation processes and thegeological history of the substratum lead to horizontal as well as vertical structuring.This complex structure cannot be precisely described in a deterministic manner.Therefore, within the numerical model the mobile sediment of the bed and the adjoiningbodies of water will be considered as a continuum (Fig. 1) and its physics described90

Die Küste, 81 (2014), 89-106through mathematical models. Particularly size, shape and the properties of the sedimentparticles, as well as the water content, apply to its specific classification.The most basic case occurs with uniform sediment distribution of spherical sediment particles with a diameter of no more than 64 μm. This presumes a case of non-cohesive sediment, where the electro-chemical forces in relation to the weight force per grain are negligible. This concept forms the basis for the subsequent comments in this paragraph. Sediment particles with varying diameters represent an enlargement on the basic scenario.Sediment fractions can then be developed according to the grain distribution curve andmodels for the physical processes of inhomogeneous sediment distribution can be established. These approaches will be discussed in paragraph 3.Figure 1: Conceptual design of a body of water with mobile bed.2.1 The Bed-Evolution EquationAlmost all morphodynamic numerical models utilize the Bed-Evolution or Exnerequation as a basis for conceptual modelling. It describes the changes in the geodetic location of the bed z B in dependence of the time t through the transport of bed and suspended load:1 nwz BwtG ĭ divqS S(1)USJJGTIn this equation the dimensionless parameter ݊ represents the porosity, qS qSx , qSythe horizontal volumetric bed load transport in [m²/s], ĭS in [kg/m²s] the vertical sediment flow of suspended sediment and ȡS in [kg/m³] the sediment density. The porosityrepresents the relation between water volume and the total volume of water and sedimentand carries an approximate value of 0.3 for sandy sediment. A prediction of this parameter was presented in MALCHEREK and PIECHOTTA (2004). The dry density of the sediment is generally given as ȡS kg/m³.As has been described, the movement of sediment can be differentiated as bed loadtransport and suspended sediment transport. In the former, sediment particles movealong the bed in a rolling or skipping motion. Suspended sediment transport is achievedwhen turbulences near the bed are high enough to prevent the particles from settling.Particles are detached from the bed and transported within the current.To interpret the bed evolution equation, both transport types will be considered separately in a one-dimensional scenario. For bed load transport in direction x the right side91

Die Küste, 81 (2014), 89-106of the equation is reduced to wqSx / wx . Accordingly, the bed does not undergo anychanges assuming the bed load transport rate also remains at a constant volume. An equilibrium exists. If, however, qSx increases in the x-vector, less sediment is introduced thandischarged. The bed is degraded. Correspondingly, a deposition scenario results when thebed load transport is decreased and, thus, wqSx / wx is negative. In the case of suspendedsediment, the exchange of sediment between the water column and the bed is decisive. Ifthe sediment flow is balanced, ĭS applies and the bed is not affected. In the case of anegative balance more sediment is discharged than being supplied to the bed. It deepens.The deposition scenario is reinstated when the sediment flow is positive.These observations show that the gradient of sediment transport and the balance ofthe vertical exchange are decisive for bed evolution. In addition, sediment transport cantake place, even without changes in the bed. Therefore, it has to be determined as ofwhich current load sediment is transported and how it may be quantified in terms of bedload transport and suspended sediment transport.2.2 Bottom Shear Stress and Transport InitiationJJGThe interaction between current and the bed is modelled via the bottom shear stress ƴ Bin [N/m²]. Assuming a logarithmic velocity profile and the equivalent bed roughness kS in[m] for hydraulically rough beds, it is formulated as follows:JJGƴBȡț § h · ln kS ¹ G Gu u(2)These are the water density U in [kg/m³], the dimensionless von-Karmann constant N ,Gthe mean flow velocity uux , u yTin [m/s] and the water depth h in [m]. According toNikuradse, the equivalent bed roughness kS can be set in relation to the in-situ sediment.A multitude of formulae exist in regard to their calculation, which essentially depends ona characteristic grain diameter, as well as a scaling factor. One example is the correlationkS 3d . To achieve three-dimensional current modelling, the bottom shear stress needsto be inserted in place of equation 2.Natural channels often exhibit bed forms which dissipate additional flow energies.According to VAN RIJN (1993), the bed roughness may in this case be considered as thesum of grain coarseness kSg and bed form kSf . This will be discussed in more detail inparagraph 4. The stresses acting on the sediment particles are of importance regardingsediment transport. These can be calculated through inserting the grain roughness inplace of the bed roughness in equation 2. Accordingly, the variable for the effective bottom shear stress can be expressed as:JJGƴ 'B92ȡț § h · ln g kS ¹ G Gu u(3)

Die Küste, 81 (2014), 89-106It represents the morphologically active bottom shear stress and is of essential importance for the calculation of sediment transport.The central question concerning transport calculations is, as at what level of bottomshear stress transport of mobile sediment is initiated. A popular approach in morphodynamic modelling is based on research by Shields regarding critical bottom shear stress.It assumes that sediment only becomes mobile after a critical value, the dimensionlessShields-Parameter ƨcr , , has been exceeded. Shields does not supply a functional correlation, presenting his findings graphically in dependence of dimensionless parameters instead. In follow-up articles, this data was supported by curves. A number of functionalcorrelations for the calculation of ƨcr , can be found in the appropriate technical literature.One example, the approach by BROWNLIE (1981), is shown in Fig. 2.The course of the curve or, rather, the Shields diagram is commonly known and hasbeen adequately discussed (BUFFINGTON and MONTGOMERY 1997; VAN RIJN 2007).It should be mentioned that this curve fit naturally represents Shields’ data, but is intended to overestimate ƨcr , , particularly for coarse sediment. Therefore, Figure 2 plots theapproach according to PARKER et al. (2003), scaling the approach by BROWNLIE (1981)to 0.5. This should better represent the initiation of sediment transport. These two formulae alone demonstrate the range necessary to calculate the critical bottom shear stress.In addition, turbulent currents, which can be assumed in natural bodies of water, represent a stochastic process (ZANKE 2002). Stress peaks on single grains caused by turbulentfluctuations are not represented by the functional sequences shown in Figure 2. The approach using ƨ cr has nevertheless been proven successful, as it represents a critical valuewhose exceedance points out that significant amounts of sediment are transported andnot only scant particles.Figure 2: Critical bottom shear stress ƨ cr of the transport initiation in dependence of the GrainReynolds-Number.Fig. 2 displays a further curve. Shown is the partial parameterization according to VANRIJN (1993), which is frequently used in numerical models. It should be noted, that it is a93

Die Küste, 81 (2014), 89-106good reflection of the critical bottom shear stress, while showing discontinuities along thetransitions, though. These could lead to numerical instabilities and should not be applied,according to its authors. Approaches like those by BROWNLIE (1981), PARKER et al.(2003) or ZANKE (2001) are to be preferred.2.3 Bed Load TransportCalculating sediment transport along the bottom is a decisive step toward morphodynamic simulation. Technical literature offers a nearly overwhelming number of more or lessempirically derived formulae, which have been previously examined extensively, forinstance in ZANKE (1982). These have a certain validity based on the data applied, so thatnew approaches regarding different problems are still being published today, for instanceregarding wave and tide influenced transport (CAMENEN and LARSON 2005;MALCHEREK and KNOCH 2005; VAN DER A et al. 2013)