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Numerical simulation of sediment mixture deposition part 1 ... - LTHE

Numerical simulation of sediment mixture deposition part 1 ... - LTHE

2 SEDICOUP modeling

done through the presence of β j in equation (1) for transport capacity g v,j *. The bed material sorting equation is: with p the porosity of bed material; w act the width of the "active bed"; e m the mixing layer thickness; G j the total net volumetric sediment discharge of class j; Γ the alluvial bed area with respect to a reference plane; S j a source term (exchanges with suspended load, bank aggradation/degradation, lateral input). β j * is the volumetric fraction of sediment j in exchanges between surface and subsurface (see Figure 1). During sediment deposition, and in the case of a constant mixing layer thickness, material issuing from the mixing layer is progressively buried in the underneath stratum β j * = β j . During erosion, and with this same condition of a constant thickness, the mixing layer is fed with material from the underneath stratum and β j * = volumetric fraction of sediment j in the first stratum under the mixing layer. Fig. 1. ∂ ∂G ---- [( 1– p) β ∂t j w act e m ] + --------+ j ∂x ∂ ---- [( 1 – p) β * ∂t j ( Γ – w act e m )] + S j = 0 Rules for the storage of bed material during aggradation. (4) The appellation "mixing" layer is improper in the sense that it aims at representing different physical situations: (i) The deposition layer, a sort of buffer zone for recording sediment quality. (ii) The mixed-layer, i.e. the bed zone which is stirred and whose sediment may be exposed to flow drag forces. A typical example is the dune whose material is alternatively exposed to erosion on the upstream face and further burden on the lee side. (iii) The surface layer during erosion, with the asymptotic situation of static armor. (iv) The transport layer, for example in the case of sediment transiting over a non-erodible bottom such as a rock outcrop or a concrete lining (Belleudy et al. 1990). One of the difficulties of SEDICOUP modeling is to maintain the continuity of these different meanings of the mixing layer among themselves especially while giving a numerical meaning and respecting constraints of its use as a "control volume". The mixing layer is the layer of bed material taken into account for sediment transport rate calculation and available for erosion. The mixing layer should not be too thin so that it remains the "same" during one time step of calculation; it should not be too large in order to reproduce effective changes of bed composition during the process under simulation. The thickness of the mixing layer may vary with its composition and with flow characteristics (reproducing for example the size of the dunes or the formation of the armor). In the present simulation, it fortunately takes its more simple meaning of a deposition layer. Its grain size distribution is directly linked to sediment transport rate (capacity), and is representative of sediment at the surface of the bed. Because there is no further mixing of deposited material, the depth of this deposition layer is kept constant at the classical value of "the size of the largest grain". Naturally the surface layer rises during deposition. Material which lays on the surface at time t will be buried a little time later and replaced by newly deposited material (the grain size distribution of which may be different). At the same time that a negative gradient of sediment transport feeds the surface layer from above, sediments are exchanged between the surface layer (whose depth is given), and the subsurface. In SEDICOUP modeling, sediment joins the subsurface with the actual size distribution of the mixing layer. This sediment is recorded in the form of strata with a fixed thickness. These strata (and their sediment characteristics) remain available during the simulation in case further erosion takes place. In order to avoid possible numerical instabilities, the process for building successive strata is as illustrated in Figure 1. The modeler fixes the strata reference thickness e str before starting the simulation. When the thickness of the stratum which lies just below the mixing layer (and which receives its excess material) exceeds a* e str , this stratum is split into a stored stratum (whose thickness is e str ), and a new first substratum with initial thickness (1-a)* e str . For the simulation, the mixing layer thickness e m and the strata thickness e str are both equal to 0.05 m (nearly the largest grain size) and parameter a is set to 1.5. 3 Description of simulation conditions Simulation conditions are defined in order to reproduce as closely as possible the conditions of run 3 which is described in Seal’s and Toro-Escobar’s papers. "Standard" numerical options for modeling are selected. Model The channel described by the model is 60 m long. Its typical cross-section is rectangular, 0.305 m wide. Cross-sections of the computational grid are ∆x = 2.5 m apart. The channel floor is horizontal (elevation h = 0, no slope), and covered with gravel (d m = 42.3 mm). A Manning-Strickler relationship is used for regular head-loss calculation. Friction of channel walls is neglected. JOURNAL OF HYDRAULIC RESEARCH, VOL. 38, 2000, NO. 6 419

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