The instability and the non-linear development of a flow in an inclined alluvial channel

Abstract

In this paper the instability and the non-linear development of a flow in an inclined alluvial channel is investigated. It is shown that in linear case, at the critical value of inclined angle the arbitrary disturbance of the water surface and of velocity will be splinted in three modes. The non-linear differential equations describing the behavior of the modes when the time become large are obtained. Some solutions are analyzed.