Abstract
At the inception of channeization, gullies are seen to be formed at the downstream end of plateaux. Those gullies migrate upstream to become channels and develop into complex systems of channel network. In this paper, a mathmatical model of gully formation is presented. Velocity and surface profiles of sheet flow over the plateau with the perturbed downstream end are calculated by solving St. Venant shallow water equations with the use of singular perturbation techniques. The calculated results show the tendency of flow concentration into indentations at the downstream end as expected. Applying the “threshold concept” to the results, characteristic wavelength of the order of (depth/plateau slope) is obtained, which is of the same order as that obtained from the “upstream-driven theory”.
