The dam-break problem for eroding viscoplastic fluids

Abstract

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.

Mass exchange between geophysical flows and beds: Idealised computational modelling using a Herschel-Bulkley rheology

“…Authors such as Hu et al [16], Song & Choi [17] and Bates & Ancey [18] have done sterling work to study mechanisms of entrainment using small-scale flume apparatus. In particular, [18] used Carbopol, which can be modelled using a Herschel-Bulkley (non-Newtonian) rheology, to model both flows and nonfixed beds. Non-Newtonian rheologies constitute a reasonable simplification of clay-rich flows and advantageously comprise relatively few parameters.…”

“…In this study, we use results from Bates & Ancey [18] to evaluate a Smoothed Particle Hydrodynamics (SPH) model, into which we implemented a regularised Herschel-Bulkley rheology. The SPH model that we used solves the full 2D Navier-Stokes equations.…”

Modeling the Slump-Type Landslide Tsunamis Part I Developing a Three-Dimensional Bingham-Type Landslide Model

“…Numerically, the slumps and tailings fluid can be considered a viscoplastic material with the yield stress, which is one of the important parameters. Mudflow can be modeled by Bingham model [11][12][13], Herschel-Bulkley model [14,15], and the Coulomb-viscoplastic model [16] by incorporating them with the www.videleaf.com depth-integrated equations models. The viscosity in these models is discontinuous [17].…”

Modeling the Slump-Type Landslide Tsunamis Part I: Developing a Three-Dimensional Bingham-Type Landslide Model

“…Numerically, the slumps and tailings fluid can be considered a viscoplastic material with the yield stress, which is one of the important parameters. Mudflow can be modeled by Bingham model [11][12][13], Herschel-Bulkley model [14,15], and the Coulomb-viscoplastic model [16] by incorporating them with the depth-integrated equations models. The viscosity in these models is discontinuous [17].…”