Analysis of Debris Wave Development with One-Dimensional Shallow-Water Equations

The objective of this contribution is to analyze the formation of debris waves in natural channels. Numerical simulations are carried out with a 1D code, based on shallow-water equations and on the weighted averaged flux method. The numerical code represents the incised channel geometry with a power-law relation between local width and flow depth and accounts for all source terms in the momentum equation. The debris mixture is treated as a homogeneous fluid over a fixed bottom, whose rheological behavior alternatively follows Herschel-Bulkley, Bingham, or generalized viscoplastic models. The code is first validated by applying it to dam-break tests on mudflows down a laboratory chute and verifying its efficiency in the simulation of rapid transients. Then, following the analytical method developed by Trowbridge, the stability of a uniform flow for a generalized viscoplastic fluid is examined, showing that debris flows become unstable for Froude numbers well below 1. Applications of the code to real debris...

[1]  Cheng-lung Chen,et al.  Generalized Viscoplastic Modeling of Debris Flow , 1988 .

[2]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[3]  D. Peregrine,et al.  Numerical solution of the shallow water eqns on a beach using the weighted average flux method , 1992 .

[4]  Philippe Coussot,et al.  Numerical modeling of mudflows , 1997 .

[5]  D. Weber,et al.  Murgang-Beobachtungsstationen in der Schweiz , 2001 .

[6]  J. Cunge,et al.  Practical aspects of computational river hydraulics , 1980 .

[7]  R. Blakely,et al.  En masse debris transport in a mountain stream , 1984 .

[8]  Alessandro Simoni,et al.  Field observations of a debris flow event in the Dolomites , 1999 .

[9]  Roll waves simulation using shallow water equations and Weighted Average Flux method , 2002 .

[10]  J. J. Stoker.  Water Waves: The Mathematical Theory with Applications , 1957 .

[11]  Maria Nicolina Papa,et al.  Numerical simulation of real debris-flow events , 2000 .

[12]  Cheng‐lung Chen,et al.  General Solutions for Viscoplastic Debris Flow , 1988 .

[13]  R. Dressler,et al.  Mathematical solution of the problem of roll-waves in inclined opel channels , 1949 .

[14]  Philippe Coussot,et al.  Mudflow Rheology and Dynamics , 1997 .

[15]  S. Orlandini,et al.  Effect of Wind on Precipitation Intercepted by Steep Mountain Slopes , 2000 .

[16]  Dieter Rickenmann,et al.  Empirical Relationships for Debris Flows , 1999 .

[17]  R. Iverson,et al.  U. S. Geological Survey , 1967, Radiocarbon.

[18]  F. Engelund,et al.  Instability of Hyperconcentrated Flow , 1984 .

[19]  D. Fread,et al.  1D modeling of mud/debris unsteady flows , 1999 .

[20]  Fan Chun.  Stability of flow of a generalized Newtonian fluid down an inclined plane , 1982 .

[21]  Lorenzo Marchi,et al.  Debris Flow Monitoring Activities in an Instrumented Watershed on the Italian Alps , 1997 .

[22]  J. Trowbridge.  Instability of concentrated free surface flows , 1987 .

[23]  R. R. Brock,et al.  Development of Roll-Wave Trains in Open Channels , 1969 .

[24]  Exact Riemann Solution and Weighted Average Flux Method for Power-law Channel Section , 2002 .