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transverse flows when the mean channel curvature, rc' is replaced by the mean flow curvature, rf. Upon entering a bend, the mean flow curvature increases with the growth in transverse circulation. In a bend, the transverse flow becomes fully developed if the flow curvature approaches the channel curvature. In the case of exiting from a bend to the downstream tangent in which the channel curvature is zero, the flow curvature decreases wi th the decay of transverse circulation. The reason that the flow curvature lags behind the channel curvature during circulation growth and decay is attributed to the internal turbulent shear that the flow has to overccme in transforming from parallel flow into the spiral pattern and vice versa. From the dynamic equation for the trans- verse velocity, an equation governing the streamwise variation in transverse surface velocity, V, was derived (Chang, 1984). In finite difference form, the change in v over the distance & i.s given by - r", vi+l = lVi + Fl(f) ~ exp(F2(f) ~s) ~sJ exp[-F2(f) ~s] rc (4) where v is the transverse surface velocity along discharge centerline, U is the average velocity of a cross section, i and i+l are s-coordinate indices, Fl and F2 are functions of f (friction factor), and the overbar denotes averaging over the incremental distance between i and i+l. Eg. 4 provides the spatial variation in v, from which the mean flow curvature may be obtained using the transverse velocity profile. From the transverse velocity profile by Kikkawa, et al. (1976), the mean flow curvature, rf, is related to the transverse surface velocity as rf = Dc ~ (~~ _ ~ ~ ff) I( v 3 I( 9J"2 (5) where Dc is the flow depth at discharge centerline (thalweg) and I( is the Karman constant. At each time step, the mean flow curvature at each cross section is obtained using Egs. 4 and 5. Accuracy of computation for the finite difference equation (Eg. 4) is maintained if the step size ~ ~ 2Dc. For this reason, the distance between two adjacent cross sections is divided into snaller increments if necessary. Flow parameters for these increments are interpolated from values known at adjacent cross sections. 12