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

Abstract

[1] 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.

Solidification dynamics in channeled viscoplastic lava flows

“…The yellow dashed box in the upper figure denotes the domain of the contour figures below. The contour figures show the velocity field and strain rate fields for an isothermal flow with an aspect ratio β = W / H = 2 and a Bingham number of B = τ y / ρg ′ H = 0.27 (reproduced from Robertson and Kerr [2012]). …”

“…The method in Robertson and Kerr [2012, section 6.4] was used to estimate the flow depth, viscosity and yield strength for each flow; Table 3 contains the results. The estimated rheologies agree (within error) with the measurements made by Lyman et al [2005] and Lyman [2006].…”

“…Dimensionless parameters based on the isothermal flow height H and maximum surface velocity U m are used to quantify and scale the solidifying flow results. For each experiment H and U were calculated using the method presented in Robertson and Kerr [2012, section 6.4], given the slurry properties in Table 1 and the measured flow rate Q. …”

“…The second dimensionless parameter is the Bingham number which is the ratio of the yield strength of the fluid τ y to a characteristic viscous stress ρg ′ H. Flows of purely viscous fluids have B = 0, while the yield strength is large enough to prevent flow when B = B ☆ . The value of the critical Bingham number B ☆ is dependent on the channel geometry [ Mosolov and Mjasnikov , 1965; Robertson and Kerr , 2012]. …”

Four-Field Finite Element Solver and Sensitivities for Quasi-Newtonian Flows

“…[5], [34]), lava (see e.g. [44], [21]), etc. Many of these flows involve gravity-driven mass movements and can thus require the modeling of a free-surface moving in time (see e.g.…”