PERIODIC CONFIGURATION OF CHANNELS FORMED ON STEEP SLOPES

In this study, we perform a theoretical study on channel inception in the case of steep slopes. The conceptual model for the channelization process under steep slope is formulated by considering uniform steady shallow 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 assumed to be supercritical whereas the flow on mild slope is assumed to be subcritical in the Froude sense. In the formulation process, we used two-dimensional depth-averaged shallow water equations. A linear stability analysis is used to study the problem. The problem is an eigenvalue boundary problem, solved using the spectral collocation method with the Chebyshev polynomials. Finally, we found a relation between growth rate of perturbation and characteristic wave number for the case of steep slopes. The dominant wave length is found to be 20 to 29 times the Froude critical depth.