Dynamics of Lava Domes

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Balmforth0072521 Lava domes are a common geological formation, and theirgeometry sets them apart as one of the more simple types of lavaflow. Moreover, domes often have a relatively low aspect ratioand evolve slowly. These observations can be used as ingredientsin building simple mathematical models of expanding and coolingfluid domes; this proposal surrounds the development of suchmodels. In particular, lava is considered as a solidifying,non-Newtonian fluid with strongly temperature-dependent materialqualities and an intrinsic yield stress. The wide array ofphysical ingredients to the problem make the mathematicalmodelling especially challenging. The project exploits the simplegeometry, slow evolution and low aspect ratio of the dome toasymptotically reduce the governing equations to a simpler form.The reduction furnishes "shallow-lava equations," in much thesame way that the "shallow-ice equations" are derived andextensively used to model ice sheets and glaciers. Differencesarise because of the viscoplastic nature of silicic lava, andbecause solidification creates a solid crust overlying the domethat can contribute significantly to the balance of forces,especially at the disk's edge. The mathematical approach arecomplemented with an experimental one in which laboratory fluidsare used as analogue models of the lava. Both approaches are usedto explore the structure and evolution of the dome, partly withthe aim of learning more about how lava behaves as a fluid. Forexample, some domes lose axisymmetry in what might be anintrinsic morphological instability; this pattern formationprocess is explored in that light. Lava domes occur in many geological settings both on Earthand on many other planets and moons of the solar system. Thesestructures form when crystal-rich silicic magma is pushed upthrough vents onto roughly horizontal surfaces, and often occurinside the craters created by volcanic eruptions. The shape of alava dome is especially simple in comparison to most other lavaflows. Hence, a first step in understanding lava flows in generalis to explore those domes. Moreover, despite their slow growth,domes are natural hazards because they can be the setting ofviolent and dangerous events: domes can rupture and releaseconfined gas in a pyroclastic outflow (an extremely hot andfast-moving current of air and ash), or collapse at theirperipheries to create landslides and debris flows. The proposaloutlines a mathematical and experimental approach to themodelling of lava domes. The purpose is to build models of thedome's structure and evolution, and compare these models with thereal geological structures. By modelling the domes in this way,more will be learned about how lava flows, and ultimately thismay provide insight into the hazards associated with them.