PERIODIC CONFIGURATION OF CHANNELS FORMED ON STEEP SLOPES

Abstract

In this study, we perform a theoretical study on ch annel inception in the case of steep slopes. The co nceptual model for the channelization process under steep sl ope is formulated by considering uniform steady sha llow water flowing in a typically smooth straight ending with upward concave steep slope gradually changing to a very mild slope. The flow on the steep slope is ass umed to be supercritical whereas the flow on mild s lope is assumed to be subcritical in the Froude sense. In t he formulation process, we used two-dimensional depthaveraged shallow water equations. A linear stabilit y analysis is used to study the problem. The proble m is an eigenvalue boundary problem, solved using the spect ral collocation method with the Chebyshev polynomials. Finally, we found a relation between growth rate of perturbation and characteristic wave number for th e case of steep slopes. The dominant wave length is found to be 20 to 29 times the Froude critical depth.