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 ID 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 theological 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 Fronde numbers well below 1. Applications of the code to real debris flow events in the Cortina d'Ampezzo area (Dolomites) are presented and compared with available measured hydrographs. A statistical analysis of debris waves shows that a good representation of wave statistics can be obtained with a proper calibration of theological parameters. Finally, it is shown that a minimum duration of debris event and channel length are required for waves showing up, and an explanation, confirmed both by field data and numerical simulations, is provided.