Effects of the curvature of a lava channel on flow dynamics and crust formation

Bends in lava channels are often observed in volcanic fields. The curvature of a channel affects flow dynamics and surface morphology and may be a trigger for the formation of lava tube. We propose a model to describe the effects of curvature on velocity, shear stress and the formation of crust at the flow surface. Lava is described as a Newtonian, homogeneous, isotropic and incompressible fluid. The steady-state solution of the Navier-Stokes equation is found for a unidirectional flow, in cylindrical coordinates. The flow levees are described as arcs of concentric circumferences, with their centres in the origin of the coordinate system. Under the assumption that the gravity force has no radial component, in the bend the fluid moves parallel to the levees. The velocity is assumed to depend on the radial coordinate only. As an effect of curvature, velocity and shear stress are asymmetric with respect to the centre of the channel. The maximum of surface velocity is shifted toward the internal levee, and the shear stress has larger values close to the internal levee. This effect is greater for wider channels. Heat radiation and convection into the atmosphere are considered as the main cooling mechanisms and the temperature distribution along the channel is calculated. Crust formation at the flow surface is considered under the assumption that solid lava is a plastic body. The amount of crust coverage is mainly controlled by the channel width: narrow channels have a greater coverage than wide channels for a given radius of curvature. The effect of a bend is to favour the crust growth toward the internal levee, while the crust coverage toward the external levee decreases. The presence of a bend in a lava channel may favour the formation of a lava tube. The analytical solution will serve as a benchmark for numerical models. Understanding the mechanism of formation of lava tubes is crucial to the simulation of actual lava flows and to evaluation of the associated hazard.