The dam-break problem for eroding viscoplastic fluids

Natural gravity-driven flows can increase in volume by eroding the bed on which they descend. This process is called basal entrainment and is thought to play a key role in the bulk dynamics of geophysical flows. Although its study is difficult using field measurements, basal entrainment is more easily amenable to analysis using laboratory experiments. We studied basal entrainment by conducting dam-break experiments releasing a fixed amount of viscoplastic fluid (a Herschel-Bulkley fluid) on a sloping, erodible bed of fixed depth. Entrainment was observed continuously, far from the sidewalls, using cameras. Bed material was quickly entrained, which led to flow advancement. Although the slope inclination had clear effects on the entrainment mechanisms, as shown by the internal measurements, this did not translate into faster front progression. Instead, the depth and length of the entrainable material were the most important controlling parameters of front velocity, as the surge scoured out the entrainable layer, pushing the entrainable material downstream and following the rigid bed's geometry. Bulk measurements (front position and flow depth profile) were also compared with predictions from lubrication theory.