Bi-directional flows in constrained systems

Abstract

We consider the exchange flow of relatively dense, viscous fluid in a container connected by a vertical pipe to a container beneath it, initially full of relatively light fluid. A non-dimensional value for the flux of dense fluid down the tube is determined experimentally as a function of the ratio of the two viscosities and the Reynolds number. The experimental data are satisfactorily collapsed using dimensional analysis and balancing buoyancy, inertial and viscous forces as appropriate. A theoretical analysis, assuming steady, axisymmetric motion, captures a considerable part, but not all of the processes involved. The paper discusses quantitative applications of the results to the movement of magma in volcanic conduits. The concepts indicate how bi-directional convection in the conduit between a lava lake and a magma reservoir deep in the crust is the essential ingredient in the explanation of the long-standing problem that the amount of degassing of sulphur dioxide from a lava lake in a volcanic crater can exceed by many orders of magnitude that consistent with the amount of lava solidified in the crater. Movies are available with the online version of the paper.