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mean flow curvature may be obtained using the transverse velocity pro- file. Similar transverse velocity profiles have been established by differ- ent researchers (19,22,25). From the velocity profile developed by Kik- kawa et al. (19), the mean flow curvature, r" is related to the transverse surface velocity and other parameters, i.e. r, =~; (~ -;~ ..A) ........................................ (6) At each time step, the mean flow curvature at each cross section is ob- tained using Eqs. 5 and 6. Accuracy of computation for the finite dif- ference equation (Eq. 5) is maintained if the step size Il.s s 2h, (10). Fol- lowing this criterion, the distance between two adjacent cross sections is divided into smaller increments if necessary. Flow parameters for these increments are interpolated from values known at adjacent cross sec- tions. Computation of Sediment Transport and Sorting.-Sediment trans- port, in the presence of transverse flow, can be considered as consisting of the longitudinal and transverse components. The longitudinal sedi- ment load is computed using a shear-stress type formula, because of the transverse variation in stream bed configuration. For this purpose, the Engelund-Hanson formula (12) is included in the model, but it may be replaced by any other valid formula. The relation for the transverse vari- ation in shear stress developed by Kikkawa et al. (19) has the form T, = pgn'h-l13a'. . . . . . . . . , . . . . . , . . . . . . . . . . . . . . . . . . .. . . . , . , . .. . . , . (7) in which T, = local longitudinal shear stress; p = density of fluid; n = Manning's coefficient; h = local depth; and a = depth-averaged longi- tudinal velocity. Other investigators have developed analytical relationships for the equilibrium transverse bed profile in alluvial channel bends (6,13, 14,19,20,28). In an unsteady flow, the transverse bed profile varies with time, and it is constantly adjusted toward the equilibrium state through scour and deposition, Sediment movement in the transverse direction contributes to the adjustment of transverse bed profile. The transverse bed load can be related to the longitudinal bed load by the direction of near-bed sediment movement (17,19,21). Such a relationship developed by Kikkawa et al. (19), which is employed in the model, can be written in parametric form as tan 8 = (~) - '" (2.) az ......,............................... (8) U" T* iJr in which 8 = angle of deviation of sediment particle path from the lon- gitudinal (tangential) direction; <1>, '" = functions; v, = near-bed trans- verse velocity; u, = near-bed longitudinal velocity, T. = dimensionless shear stress acting on bed = u~/(p, - p)gd; u. = shear velocity; d = diameter of sediment, p, = mass density of sediment; and z = local bed elevation. The near-bed transverse velocity, v" is a function of the cur- vature (19,22,25); it is computed using the mean flow curvature. 647 25