96 IV-3. 3-D SEDIMENT TRANSPORT MODEL Sediment transport in the water column is described by an advection–di?usion equation: ??? ?? + ? ??? ?????? = ? ??? ??? ??? ??? ? +??? ??? ??? (IV-8) where Cj is the volume concentration of suspended sediment of class j; ui are velocity components, ki are eddy di?usivity coe?cients and Wsj is the settling velocity of suspended sediment of class j. The exchange of sediment between the bed and the ?ow is modelled using sink and source terms acting on the bottom computational cell. These terms represent the processes of sediment entering the ?ow due to erosion ?ux and the sediment settling down due to the depositional ?ux. Total ?ux is the di?erence between erosion and deposition ?uxes and it is required to define them for each sediment size class. Bottom boundary conditions are: ?? ??? ?? = ??? + ?? (IV-9) where Dj and Ej are, respectively, the deposition and erosion ?ux of sediments of class j. Non-cohesive sediment ?ux due to sediment deposition is simulated as a ?ux of particles that fall down with settling velocity Wsj: ?? = ?????,?????? (IV-10) where Cj,bottom is the concentration, in the bottom computational cell, of sediments of class j. The erosion ?ux is calculated [IV-4, IV-5]: ?? = ??,?????(1 ? ?)?? ? ?? ???,?(????) ? 1? ?.? ?? ?? > ???,? (IV-11) where dj is the sediment particle diameter; p is porosity; fj is the volume fraction of sediments of class j in the bed; ?b is the bottom shear stress; ?cr,j is the critical shear stress for the sediments of class j; fo is the volume fraction of cohesive sediments in bed composition and a = 3dj is a reference level above the bottom. The erosion rate is defined as: ??,????? = ?? ? ?.????? ???.? (IV-12) with: ?? = ? ?(?? ??? ??) ?? ? ?/? (IV-13) For the cohesive sediments, a deposition ?ux appears only if the shear stress is lower than the critical shear stress for deposition: ?? = ?????? ?1 ? ?? ??? ? ?? ?? < ??? (IV-14)