Two models for roll waves in a mud layer

Abstract

As has been extensively reported by hydraulic engineers in China, the flow of hyperconcentrated fluid mud in rivers is often pulsating and appears roll waves. Two theories for the pulsating flows were reported based on two constitutive laws: the power law and Bingham plastic law. In order to account for the nonlinear bores, convective inertia was kept in the approximate long wave equations, Karman's momentum integral method with an assumed velocity profile was employed. The results of the linearized instability analyses were also discussed. Periodic bores were obtained either as stationary wave solutions or as the long-time limit of unstable disturbance, which are the initially infinitesimal. Implications on bed scour were examined.