A three‐dimensional Bingham model for channeled lava flows

Abstract

We propose a three‐dimensional (3‐D) Bingham model for channeled lava flow. Unlike from the 3‐D Newtonian models, this model can be applied also far from the vent where the Bingham rheology cannot be neglected as a consequence of the lava cooling. We assume the lava to be an isothermal Bingham liquid flowing in a rectangular channel down a constant slope. The flow velocity is calculated by solving semianalytically the steady state Navier‐Stokes equation together with the 3‐D Bingham constitutive equation. The flow vorticity is evaluated and used to define the plug shape and position for different flows: a completely filled conduit, a partially filled conduit, and an open channel. Each component of the flow vorticity vector satisfies the Laplace equation and has been evaluated by using the relaxation method. The mass flow rate is evaluated for different values of the yield stress; it appears that the Bingham rheology causes a significant reduction in flow rate as the yield stress increases. For the highest yield stress values the plug in the center of the flow welds with the plugs in the flow corners, suggesting a possible rheological mechanism for the lava tube formation.