A model for the formation of lava tubes by the growth of the crust from the levees

We propose a model to explain lava tube formation by the growth of crust slabs from the levees of a channel toward its center, involving solid surface fragments. The flow dynamics are described with the steady state solution of the Navier-Stokes equation in a rectangular channel, for a Newtonian, homogeneous, isotropic and incompressible fluid. The cooling of a lava flow is described by the mechanism of heat conduction into the atmosphere. The presence of levees is taken into account both in the dynamical and in the thermal model. As long as the flow cools, a solid layer forms at the surface, much thicker near the levees than at the center of the channel. The crust that has formed breaks under the effects of the applied stresses. Solid blocks slow the fluid down, the shear stress at the interface between crust and fluid lava increases and the flow thickens. Using the thin elastic plate approximation, we determine conditions allowing a crust to resist both the action of the shear stress due to the drag of the underlying fluid and the tensile stress due to the weight of the crust itself, detecting the required crust thickness and distances from the eruptive vent where the tube can form