Journal of Conference Abstracts

Laminar and Turbulent Flows in Channels with Phase Transitions: Numerical Modeling of Magma Transport in Dikes

Yuri Fialko (fialko@geo.princeton.edu) & Allan Rubin (allan@geo.princeton.edu)

Dept. of Geosciences, Guyot Hall, Princeton University, 08544, U.S.A.

We consider numerical models of heat and mass transfer associated with lateral magma flow in self-induced fissures (dikes). Forces available to drive the flow include an excess fluid pressure at the magma source, a regional topographic slope and a variation in the horizontal ("tectonic") stresses in the crust. For typical meter-wide basaltic dikes that accrete the Earth's crust at mid-ocean ridges and volcanic rift zones, the flow is likely to be laminar and may be described using lubrication theory. We simplify the problem by neglecting the elastic response of the dike walls to pertrubations in the magma pressure due to magma freezing, and calculate time-dependent temperature and velocity fields associated with the magma flow in a rigid-wall channel having infinite extent in the flow direction. Evolution of the solid-liquid interface is governed by a Stefan-type boundary condition. We calculate "thermal arrest" distances for the laterally propagating dikes for the range of geophysically reasonable parameters. We also identify the critical values of the Brinkman number corresponding to the onset of "thermal runaway" that occurs when the heat generated by viscous dissipation in the fluid exceeds the conductive heat loss to the ambient solid. However, we find that for most geological flows the effects of viscous dissipation may be neglected. In the latter case, thermal erosion associated with lateral dike propagation is likely to be confined to a small region very near the magma source. For a dike that erupts at its downrift end, sufficient supply of melt at the source may cause eventual meltback of the dike walls all the way from the source to the eruption site. If magma supply continues, the flow will become turbulent and the thermal erosion rate will significantly increase. We quantify some effects of the turbulent meltback to explain abnormally large dike thicknesses (tens to hundreds of meters) observed in the so-called giant dike swarms (e.g., the MacKenzie swarm in Canada). Extremely high magma supply rates required for the emplacement of giant dike swarms may be related to mantle plume head arrivals. Our calculations indicate that an order of magnitude (from 10 to 100 m) increase in the dike aperture due to thermal erosion corresponds to 10³ - 10⁴ km³ of erupted lava, which favorably agrees with estimated volumes of the largest continental flood basalts.