University of Cambridge > > Institute for Energy and Environmental Flows (IEEF) > Experimental modelling of the Fluid Dynamics of Magma Chambers / Buoyancy induced Taylor dispersion

Experimental modelling of the Fluid Dynamics of Magma Chambers / Buoyancy induced Taylor dispersion

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Experimental modelling of the Fluid Dynamics of Magma Chambers

Determining whether magma chambers convect is of importance for volcanologists and geologists alike. The reason why some solidify to form plutons and others erupt is still uncertain. This study has done mathematical and experimental modeling of a simple analogue basaltic magma chamber to determine the conditions under which convection occurs. The experimental set up used is a tank heated from below and cooled from above, separated into porous and fluid layers with thermal and image data taken. Various regimes are possible, including regimes in which the particles forming the porous layer become entrained into the convecting fluid. Textural analysis of plagioclase aspect ratios in igneous bodies has also been done to determine the solidification histories of various igneous intrusions.

Buoyancy induced Taylor dispersion

We consider the turbulent mixing that occurs due to the injection of a small constant volume flux of dyed salty fluid at the top of a long narrow tank tilted at an angle from the vertical. Using dye and a light attenuation technique, the evolution of the reduced gravity can be extracted throughout the tank, which is initially filled with fluid of lighter density. The injected fluid mixes vigorously with the fluid that initially occupies the tank, and a mixed region of turbulent fluid slowly propagates through the tank due to the unstable density gradient that is set up along the length of the tank. The evolution of the mixing region along the length of the tank can be described as a diffusive process using Prandtl’s mixing length theory; the tilt causes a shear flow that enhances the effective diffusion, in a way analogous to Taylor dispersion for turbulent pipe flow. We show that the solutions to the corresponding nonlinear turbulent diffusion equation match well with our experimental profiles throughout the range of tilt angles tested (0-45 deg.), and that the profiles of reduced gravity along the length of the tank take on a self-similar form. Across the width of the tilted tank, a density gradient is formed throughout the mixed region of dense fluid; we develop a model for the cross-tank profiles of velocity and reduced gravity based on the Navier Stokes equation and the advection-diffusion equation, and show good agreement between our model and our experimental data.

This talk is part of the Institute for Energy and Environmental Flows (IEEF) series.

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