Thermo-viscous fingering of magma flow in volcanic fissures

The stability of hot magma flow through a thin, long volcanic fissure is investigated. Magma flow through the fissure is modeled as a fluid with temperature-dependent viscosity flowing through a narrow slot. The side-walls of the slot are held at a lower temperature, mimicking the colder rock walls surrounding the fissure, thus cooling the magma as it flows. Flow and heat advection equations are averaged across the slot thickness where the averaged model is developed using a weighted-residual integral boundary layer technique. The model accounts for the non-Poiseuille velocity profile in the slot due to temperature-dependent viscosity unlike the Poiseuille flow-based Darcy models used in earlier works. Linear stability analysis reveals that for sufficiently strong temperature-dependence of viscosity, one-dimensional flow of magma undergoes a thermo-viscous fingering type of instability. This usually occurs for parameter values exhibiting a multi-valued relationship between base-state flow rate and pressure-drop. The uniform flow then gives rise to alternate interior bands of low-viscosity fast-moving and high viscosity slow-moving magma. The parametric regions of instability are further investigated and compared with Darcy models.