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

To constrain life time and flow rates in a submarine lava tube (pillow), 3D finite-element calculations were carried out for a simplified fixed geomet ry model tube. The principal parameters included into the model are: a temp erature-dependent Newtonian viscosity of the lava, whereby viscosity is als o dependent on composition, temperature and crystallinity of the lava, cool ing by seawater, and the release of latent heat of crystallization. Time-de pendent model runs suggest the longevity of the tube flow is constrained by the competition of advective heat flow along the tube axis and the conduct ion of heat towards the margins of the flow. In order to keep the lava flow ing, a minimum critical pressure gradient along the tube is required. Other wise, 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 solidi fy. Providing an exponentially decaying driving pressure at the tube inlet, this critical pressure gradient has been calculated for different tube len gths and diameters and is compared to critical pressure values resulting fr om a more simplistic solution, assuming constant viscosity and pure conduct ive or convective cooling. An analysis of the difference between pressure g radients obtained through the numerical and simplified model is used to der ive an appropriate power law for the critical pressure gradient in bodies c ooled by convection and conduction including the effect of temperature-depe ndent viscosity. That gradient scales with the tube radius R as R-3.85. Thi s law is valid for tube-style lava flows and lava viscosities in the basalt ic range. (C) 1999 Elsevier Science B.V. All rights reserved.