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<br />362 Computational Fluid Dynamics <br /> <br />Total load sediment transport equations were found to be far too sensitive to the <br />now field and yielded physically unreasonable result~. Instead. a 3D suspended sand <br />lield is calculated using a near-bed boundary condition that is a function of iocal <br />boundary shear stress. This combination i~ computationally robust and yields pre- <br />dictions that agree well with measurements. The transport of suspended sand is <br />governed by an advection--<liffusion equation: <br /> <br />. <br /> <br />(C C.ClI (,('\1 cell' C or c ((' (, GC (,C <br />-..J,...-...;..------~---~---~--+Il. -=0 <br />c./ . ex c.y c.: c.x- GX '.I" ,\' c.:" c.: .' c.: <br /> <br />(14.10) <br /> <br />where l' is sand concentration and 11', is sediment settling velocity. The sediment eddy <br />viscosity. E. in equation (14.10) is assumed to be equal to the momentum eddy <br />viscosity represented by equation (14.8). As with equations (l4.IHI4.3), equation <br />114.10) was modified for applications to the lower Tanner and t:pper Unkar <br />reaches, which have signilicant curvature. for application to an orthogonal curvi- <br />linear coordinate system using the metric of Smith and Mclean (1984). <br />Equation (14.10) is solved for a given now field with I I points in the vertical that <br />are concentrated near the water surface and near the bed to resolve the gradients <br />near the boundaries. The sand transport is represented by the median grain size, d,o. <br />The eddy viscosity as a function of: is calculated with equation (14.8). The velocity <br />as a function of: is computed from the logarithmic velocity profile (Keulegan. 1938) <br />from which equation (14. 7) is derived. The numerical method used to solve equation <br />(14.10) is similar to the one used forthe now equations (Patankar, 1980) extended to <br />three dimensions. <br />The lower sediment-concentration boundary condition used in the solution of <br />equation (14.10) is calculated by tirst determining a reference concentration, c" at <br />the top of the bedload layer. where : = :a. The reference concentration, Ca, is <br />determined from the relations of Smith and McLean (I 977): <br /> <br />. <br /> <br />(.b.......'i' <br />c.=- <br />1 + "',IS <br /> <br />(14.11) <br /> <br />where Cb is the bed concentration and" is the normalized excess shear stress; <br /> <br />T., - Tc <br />s=- <br />To <br /> <br />(14.12) <br /> <br />where the subscript >findicates skin friction shear stress and T, is critical shear stress <br />for the initiation of signilicant particle motion (Shields, 1936). The value of the <br />constant~. has been updated to 0.004 by Wiberg (reported by Mclean, 1992). The <br />distance above the bed corresponding to Ca, namely :a' is determined from the <br />expression presented by Dietrich (1982) with coefficients a, and a, as updated by <br />Wiberg and Rubin (i985) <br /> <br />1{JI-:-T. <br />=. = ( <br />. II {I~T <br /> <br />d4.1J1 <br /> <br />- <br /> <br />. <br />