Role of viscous dissipation in the dynamics of lava flows with power-law rheology

Abstract

We model a lava flow as a one-dimensional flow of a pseudoplastic fluid with viscous dissipation. The flow is horizontally unbounded and is driven downslope by the gravity force. We consider a power-law constitutive equation and we take into account the temperature dependence of the rheological parameters. Given an effusion rate and an initial temperature at the eruption vent, the flow is assumed to cool down by heat radiation. We calculate the heat produced by viscous dissipation as a function of lava temperature and effusion rate. The cooling rate is calculated as a function of the surface temperature and flow rate. Viscous dissipation reduces the cooling rate by an amount which is independent of flow rate. We evaluate the effect of viscous dissipation on the flow thickness and velocity. The effect of dissipation is to decrease the flow thickness and to increase the flow velocity. The effect on flow thickness is greater for smaller flow rates, while the effect on velocity is greater for larger effusion rates. In principle, the model provides a method for estimating the flow rate from in-field measurements of distances and temperatures.