A dynamical model of lava flows cooling by radiation

The behaviour of a lava flow is reproduced by a two-dimensional model of a Bingham liquid flowing down a uniform slope. Such a liquid is described by two rheological parameters, yield stress and viscosity, both of which are strongly temperature-dependent. Assuming a flow rate and an initial temperature of the liquid at the eruption vent, the temperature decrease due to heat radiation and the consequent change in the rheological parameters are computed along the flow. Both full thermal mixing and thermal unmixing are considered. The equations of motion are solved analytically in the approximation of a slow downslope change of the flow parameters. Flow height and velocity are obtained as functions of the distance from the eruption vent; the time required for a liquid element to reach a certain distance from the vent is also computed. The gross features of observed lava flows are reproduced by the model which allows us to estimate the sensitivity of flow dynamics to changes in the initial conditions, ground slope and rheological parameters. A pronounced increase in the rate of height increase and velocity decrease is found when the flow enters the Bingham regime. The results confirm the observation according to which lava flows show an initial rapid advance, followed by a marked deceleration, while the final length of a flow is such that the Graetz number is in the order of a few hundreds.