Waves in a Fluid Mud Layer Flowing Down an Incline

by Ko-Fei Liu, Massachusetts Inst of Technology, Cambridge, United States,
Chiang C. Mei, Massachusetts Inst of Technology, Cambridge, United States,

Document Type: Proceeding Paper

Part of: Hydraulics/Hydrology of Arid Lands (H²AL)


To model the dynamics of fluid mud, lava, or debris with a high concentration of cohesive clay particles, we consider a thin sheet of Bingham plastic fluid flowing down a slope. The Bingham fluid is characterized by a finite yield stress and high viscosity. We first assume long waves and approximate the profile of the local longitudinal velocity by a plug zone on top and a shear zone on the bottom with a parabolic velocity distribution. The instability of a uniform flow to infinitesimal sinusoidal disturbances is then examined. Numerical solutions of the nonlinear post-instability development are discussed. Specifically we present results of periodic bores and finite amplitude waves due to a fluid source at a fixed point upstream of an otherwise uniform flow. The second case resembles the pulsating flow in a muddy river with tributaries. Both can occur beneath a layer of clear water.

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