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PARTICLE-LADEN FLOW - ERCOFTAC SERIES Phần 2

Tham khảo tài liệu 'particle-laden flow - ercoftac series phần 2', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Suspended sediment transport 33 du du dw dz d i du st uai waz - g ỉ. dz Av az 2 In these equations x z represent the horizontal and vertical directions and u and w the horizontal and vertical flow velocities. The variable t denotes time z is the water surface elevation g is the constant of gravity and Av is the constant eddy viscosity. Boundary conditions at the bed disallow flow through the bottom equation 3 . Further a partial slip condition compensates for the constant eddy viscosity which overestimates the eddy viscosity near the bed equation 3 . The parameter S denotes the amount of slip with S 0 indicating perfect slip and S TO indicating no slip. At the water surface there is no friction and no flow through the surface equations 4 . dh w u dx 0 seabed Av Su seabed dz 3 du dz . dz I d 0surf ace w dt u d lsurf ace 4 The flow and the sea bed are coupled through the continuity of sediment equation 5 . Sediment is transported in two ways as bed load transport qb and as suspended load transport qs which are modeled separately. Here we use a bed load formulation after 9 equation 6 . dh dt dqb dqs dx dx 5 qb -w ra 6 Grain size and porosity are included in the proportionality constant a Tb is the shear stress at the bottom h is the bottom elevation with respect to the spatially mean depth H and the constant A compensates for the effects of slope on the sediment transport. For more details we refer to 9 or 18 . In order to model suspended sediment transport qs we describe sediment concentration c throughout the water column i.e. a 2DV model. Horizontal diffusion is assumed to be negligible in comparison with the other horizontal influences. The vertical flow velocity w is smaller than the fall velocity for sediment ws and can be neglected in this equation leading to equation 7 . This means that the sediment is suspended only by diffusion from the bed boundary condition equation 12 . As the flow velocity profile is already calculated throughout the vertical direction .