Isothermal dynamics of channeled viscoplastic lava flows and new methods for estimating lava rheology

Abstract

This study analyses the influence of a viscoplastic lava rheology on the dynamics of lava flows. Using a multigrid-based augmented Lagrangian scheme, we find a numerical solution for the flow of a Bingham fluid in a rectangular channel. The numerical results show that an internal viscoplastic rheology significantly modifies the velocity distribution within a lava flow through the development of plug regions whose size is determined by the magnitude of the yield strength. The flow rate, maximum surface velocity and central plug dimensions are determined as functions of the channel geometry and fluid rheology, and comparisons between these and several limiting analytical solutions confirm the accuracy of the numerical method used. The results are also compared to incorrect models which have been proposed previously in the literature. Several algorithms that extend the results to different sets of measured initial parameters are outlined; these calculate: (1) the flow depth when the fluid rheology (viscosity and yield strength) and downstream flow rate are given, (2) the flow depth when the fluid rheology and maximum downstream surface velocity are given, (3) the flow rate and fluid rheology when the flow depth, maximum surface velocity and surface plug width are given, and (4) the flow depth and rheology when the flow rate, maximum surface velocity and surface plug width are given. The use of these algorithms is demonstrated by considering the dynamics of a typical lava flow on Mount Etna, using measured rheological parameters and field observations.