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gitudinal) changing curvature, the developed transverse flow generally occurs over short channel lengths. In addition, the transverse flow lags behind the channel curvature pattern. It is clear that this changing cur- vature and phase lag have important effects on the flow and sediment processes as pointed out by numerous researchers, e.g., Rozovskii (22), Yen and Yen (27), Hooke (16), Bridge and Jarvis (6), Parker et al. (21), and Dietrich and Smith (11). The changing curvature of flow is quanti- fied herein using a recently developed relationship for the growth and decay of transverse flow (10). ANALYTICAL DEVELOPMENT The mathematical model, FLUVlAL-I2, which utilizes analytical equa- tions governing the flow and sediment processes, has the following four major interactive components: (1) Water routing; (2) evaluation of chang- ing flow curvature; (3) computation of sediment transport and sorting; and (4) prediction of stream bed profile changes. It represents an exten- sion of the existing model FLUVlAL-I4 (8) by incorporating the effect of transverse flow on each of these components. Features common to these models are therefore only briefly described. The model employs a space-time domain in which the space domain is represented by discrete cross sections, and the time domain is rep- resented by discrete time steps, Temporal and spatial variations in flow, sediment transport, and stream bed profile are computed following an iterative procedure. Water routing, which is coupled with the changing curvature, is assumed to be uncoupled from the sediment processes. These four components of the model are described as follows. Water Routing.-For an inflow hydrograph, water routing provides temporal and spatial variations of the stage, discharge. energy gradient, and other hydraulic parameters in the channel. The water routing com- ponent has the following two major features: (1) Numerical solution of the continuity and momentum equation for longitudinal flow; and (2) evaluation of flow resistance due to longitudinal and transverse flows. The continuity and momentum equations are aA aQ - + - - q = 0... .. . . . ... ... .. . . . . . .. . .. ... . .. ... . , . . ... . . . ... (1) at as ~ aa~ + g aa~ + ~ :s (~2) + gS - ~2 q = 0........................, (2) in which A = cross-sectional area of flow; t = time; Q = water discharge; s = curvilinear coordinate along channel center line measured from the upstream entrance; q = lateral inflow rate per unit length; g = gravita- tional acceleration; H = stage or water surface elevation; and 5 = energy gradient. Techniques for numerical solution of Eqs. 1 and 2 have been developed by other researchers, This model employs the solution tech- niques and accuracy criteria developed by Fread (15) and by Amein and Chu (2). In a curved channel, the total energy gradient, S, in Eq. 2 can be par- titioned into the longitudinal energy gradient, S', and the transverse en- ergy gradient,S", i.e. 645 23