Effect of bottom curvature on mudflow dynamics: Theory and experiments

Abstract

A one‐dimensional mathematical model of mudflow dynamics is formulated assuming mud to behave rheologically as a Herschel‐Bulkley fluid. Novel features of the present contribution regard the propagation of mudflows over a curvilinear bottom. A set of nonlinear partial differential equations is found to govern the unsteady, nonuniform flow of such fluids. Following the approach of Huang and Garcìa (1998), a depth‐integrated form of the continuity equation and shear‐integrated and plug‐integrated forms of the momentum equations are derived. A perturbation analysis is also carried out under the assumption of “slender” flow. The leading‐order problem takes the form of a kinematic wave equation. One straightforward application of this simplified model is the evaluation of the maximum run‐out extension of a mud which flows over a bed with a variable topography. This solution is obtained by solving the steady state problem. Dynamics information are obtained by numerically solving the hyperbolic conservative equation by means of a free oscillating numerical method. The effects of bottom curvature either on the equilibrium solution or mudflow dynamics are analyzed. Experiments are also performed releasing a given volume of kaoline and water mixture from a reservoir into both a constant slope and an upward concave channel. Comparisons between the numerical solution and the experimental data are generally satisfactory, though suggesting limitations typical of any approach that neglects convective accelerations and assumes gradually varied flow.