Marine Geosciences

F. Klingelhoefer, M. Hort, H.-J. Kuempel,  and H.-U. Schmincke

To constrain life time and flow rates in a submarine lava tube (pillow) finite element calculations were carried out for a simplified fixed geometry model tube. Temperature-dependent Newtonian viscosity and density were assumed and latent heat was accounted for by adjusting the specific heat capacity. The principal parameters included into the model are: the viscosity of the lava, cooling by seawater, and the release of latent heat of crystallization, whereby viscosity is in turn dependent on composition, temperature and crystallinity of the lava.

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 analytic solution using constant viscosity and pure conductive or convective cooling.

An analysis of the discrepancy between pressure gradients obtained in both ways 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 to the tube radius R as R^3.85.
This law is valid for for a tube-style lava flows and lava viscosities in the basaltic range.
 
 
 
 

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