A three-dimensional dynamical model for channeled lava flow with nonlinear rheology

Recent laboratory studies on the rheology of lava samples from different volcanic areas have highlighted that the apparent viscosity depends on a power of the strain rate. Several authors agree in attributing this dependence to the crystal content of the sample and to temperature. Starting from these results, in this paper we studied the effect of a power law rheology on a gravity‐driven lava flow. The equation of motion is nonlinear in the diffusion term, and an analytical solution does not seem to be possible. The finite volume method has been applied to solve numerically the equation governing the fully developed laminar flow of a power law non‐Newtonian fluid in an inclined rectangular channel. The convergence, the stability, and the order of approximation were tested for the Newtonian rheology case, comparing the numerical solution with the available analytical solution. Results indicate that the assumption on the rheology, whether linear or nonlinear, strongly affects the velocity and/or the thickness of the lava channel both for channels with fixed geometry and for channels with constant flow rate. Results on channels with fixed geometry are confirmed by some simulations for real lava channels. Finally, the study of the Reynolds number indicates that gravity‐driven lava channel flows are always in laminar regime, except for strongly nonlinear pseudoplastic fluids with low fluid consistency and at high slopes.