Constraints on the formation of submarine lava flows from numerical model calculations

Abstract To constrain life time and flow rates in a submarine lava tube (pillow), 3D finite-element calculations were carried out for a simplified fixed geometry model tube. The principal parameters included into the model are: a temperature-dependent Newtonian viscosity of the lava, whereby viscosity is also dependent on composition, temperature and crystallinity of the lava, cooling by seawater, and the release of latent heat of crystallization. Time-dependent model runs suggest the longevity of the tube flow is constrained by the competition of advective heat flow along the tube axis and the conduction of heat towards the margins of the flow. In order to keep the lava flowing, a minimum critical pressure gradient along the tube is required. Otherwise, the amount of thermal energy brought in by the influx of hot lava is less than the amount lost at the outer boundaries, and the tube will solidify. Providing an exponentially decaying driving pressure at the tube inlet, this critical pressure gradient has been calculated for different tube lengths and diameters and is compared to critical pressure values resulting from a more simplistic solution, assuming constant viscosity and pure conductive or convective cooling. An analysis of the difference between pressure gradients obtained through the numerical and simplified model is used to derive an appropriate power law for the critical pressure gradient in bodies cooled by convection and conduction including the effect of temperature-dependent viscosity. That gradient scales with the tube radius R as R 3.85 . This law is valid for tube-style lava flows and lava viscosities in the basaltic range.