Effect of Mud Rheology on its Inertial Dam-Break Flow

This paper considers the flow generated by the collapse of a dam retainingargillaceous mud when the inertial effects are dominant against the viscous ones, in themomentum balance equation. This flow configuration was studied by Ritter [1892] forinviscid fluids. The more realistic case where the channel is inclined and rough wasconsidered by Su and Barnes [1970] who extended Whitham’s [1955] and Dressler’sapproximate solution [1952; 1954] by using a perturbation series. In this paper, the mud ismodelled using a Herschel-Bulkley rheological equation and the flow develops in ahorizontal smooth channel on the basis of the shallow water assumption. Applying theprinciples of conservation of mass and momentum, an equation of motion is formed in thenon-dimensional form without neglecting any of the stress tensor components, and solvedanalytically in order to point out the effect of the rheological parameters on the dam-breakflow characteristics in the inertial regime. This flow configuration is a scenario of initiationof certain geological flows such as muddy flash floods.