Viscoplastic dambreak waves: review of simple computational approaches and comparison with experiments

We investigated the dam-break problem for Herschel-Bulkley fluids: a fixed volume of a viscoplastic material (a polymeric gel called Carbopol ultrez 10) was released and flowed down an inclined flume. Using Particle Image Velocimetry techniques, we measured the velocity profiles far from the sidewalls, the front position as a function of time, and the flow depth evolution at a given place. The experimental data were compared to three models of increasing complexity: the kinematic wave model, an advection diffusion model (lubrication theory), and the one-layer Saint-Venant equations. Surprisingly, the best agreement was obtained with the simplest model (kinematic wave model) even though it could not capture the details of the head profile (regarded as a shock wave, i.e., a discontinuity). Lubrication theory (the advection diffusion model) performed well from a qualitative viewpoint. Computed velocity profiles and depth evolution were in reasonably good agreement with data, but this model overestimated initial acceleration, which resulted in a systematic difference between theoretical and experimental curves of the front position over time. This shortcoming was not fixed when using a more elaborate model (Saint-Venant equations), rather it was exacerbated. The relatively modest performance of the more elaborate models was intriguing (for Newtonian liquids, the best agreement was obtained with the most sophisticated model).