A Numerical Model for Flow and Sediment Transport in Alluvial-River Bends

Abstract

The principal features of the numerical model developed herein for calculation of flow and sediment-transport distributions in alluvial-river bends may be summarized as follows: i. The secondary-flow strength and the bed topography are uncoupled from the calculation of distributions of lateral shift velocity and streamwise velocity. This is accomplished by, first, calculating the secondary-flow strength on the basis of conservation of flux of moment-of-momentum, and, second, determining the bed topography on the basis of radial force equilibrium of the moving bed layer. ii. The distributions of lateral shift velocity and depth-averaged streamwise velocity are calculated, for the warped channel determined as described in step i above, from the depth-integrated equations expressing conservation of mass and momentum. It was concluded that for flows which satisfy (24), it is not necessary to include the third conservation equation, that for radial-direction momentum, or to iterate among three equations to obtain a solution. The numerical scheme utilizes the backward finite-difference method, and evaluates transverse and streamwise distributions of the radial mass-shift velocity and the depth-averaged streamwise velocity. Numerical simulations utilizing the model developed were made for one laboratory flow, two Sacramento River flows, and three different idealized channel bends. The principal conclusions obtained from the simulations are as follows: i. Generally satisfactory agreement between computed and measured results was obtained by utilizing error tolerances of E_U and E_V of 2% and 0.2%, respectively. In the absence of better information, it is recommended that alpha = 1.00 and beta = 3.50 be utilized. In instances where actual field data are available on the rate of development and equilibrium values of S_T, alpha and beta should be adjusted on the basis of the data. ii. The most cost-effective square-grid size is approximately equal to the mean flow depth. iii. The computer program is capable of simulating flow in multiple-bend channels with stepwise-varying radius of curvature. On the basis of the numerical simulations, it was found that the maximum permissible stepwise change of centerline curvature for which the program will run is about 2.5% in the case of increasing Rc and about 10% for decreasing Rc.