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in which A ~ porosity. Written in finite difference form with a forward difference for q; (7), Eq. 10 becomes _ 4.t 2 ';+IQ;,+1 - 'iq:; tJ.zi - - . . , ., ... .., .. . ... .., ... . , . ., . . .. (11) 1 - ^ '; + 'i+l ',+1 - '; in which j ~ radial (transverse) coordinate index. Eq. 11 provides the changes in channel bed elevation for a time step, tJ./, due to transverse sediment movement. These transverse changes, as well as the longitu- dinal changes, are applied to the stream bed at each time step. Stream bed profile evolution is simulated by repeated iteration along successive time steps. SAN loRENZO RIVER STUDY The FLUVIAL-12 model described herein was tested by simulating flow and bed profile changes in the San Lorenzo River (see Figs. 1 and 2), which drains into the Santa Cruz Harbor on the Pacific coast through the Oty of Santa Cruz, California. A field study, sponsored by the San Francisco District of the U.S. Army Corps of Engineers, was made dur- ing the February 1980 flood for the purpose of analyzing river bed scour- fill processes during the flood (23). This river reach, which has several channel bends near the mouth, is protected by riprap on its bank slopes. The lower two-mile reach of the San Lorenzo River was simulated us- ing the mathematical model for the February 1980 flood. Hydrographs for this flood event and tidal variation at the harbor used in the simu- lation are shown in Fig. 3. The 9O-hr flood duration was computed using 800 time steps. Initial bed materials in the river varied from very coarse sand (median diameter ~ 1.05 nun) at the upstream end to coarse sand (median diameter ~ 0.64 mm) at the mouth. Sediment load consisted primarily of bed load during the flow period. Selected results obtained from this simulation are shown in Figs. 4-6 for the curved reach where significant river bed changes are predicted. These results are compared with measurements made at the gaging sta- tions (G2-G6 in Fig. 1) on February 19, 1980, around the time of 78.5 hr on the hydrograph. Simulated water surface profiles at the time of the peak flood and at the time of measurement (time ~ 78.5 hr) are shown in Fig. 4(b) with the simulated profile of minimum river bed el- evation at the time of measurement. These results compare favorably with measurements. The simulated river bed profile is closely related to the streamwise variation in the mean flow curvature shown in Fig. 4(c), characterized by an increase in curvature as the flow enters a bend and a decrease in curvature after leaving the bend exit. Upon entering a bend, the rate of increase in flow curvature is more rapid initially and then it slows down gradually. In a long bend, the flow curvature will approach the channel curvature, and thus, the transverse circulation becomes fully developed. Such a condition is predicted at Sections 10, 11, 19 and 22. The transverse flow, as predicted, is not fully developed in other shorter bends where the flow curvature remains less than the channel curva- ture. Upon leaving a bend, the flow curvature decreases following an exponential decay curve, and it persists for a considerable distance downstream, consistent with the experimental findings by Ippen and 649 27