A new mathematical model developed to predict behavior of debris flows and avalanches also holds promise for predicting behavior of debris-laden flash floods. The model assumes that debris flows behave as mixtures of interacting Newtonian fluids and Coulomb solids. Solid and fluid constituents obey three-dimensional mass and momentum balances, which are summed and depth-integrated to yield equations that describe shallow flows of the mixture as a whole. An important distinction between these mixture equations and standard shallow-water equations results from strong variation of flow resistance due to interacting solid and fluid forces. Partitioning of flow resistance between solid and fluid components depends on fluid pressure, which evolves as flow evolves. If fluid pressure supports the total weight of the flowing mass, all resistance results from hydrodynamic forces, and the equations reduce to the conventional shallow-water form. If fluid pressure supports none of the weight of the flowing mass, all flow resistance results from Coulomb friction between interacting solids, and the equations describe motion of granular avalanches. A combination of solid and fluid resistance typifies debris flows and debris-laden flash floods. In these flows solid resistance commonly is concentrated at the fronts of advancing bores that may be heavily freighted with rocks and woody debris. Riemann methods provide an effective tool for solving the shallow flow equations numerically and predicting unsteady motion of debris flows and flash floods along paths with arbitrary geometry and inclination.
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