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Explosive Volcanic Eruptions

Explosive volcanic eruptions can have very high pressures and supersonic velocities at the vent with the formation of a standing shock wave (Mach disk) close to the ground that significantly affects the flow within the eruption column.

We study this problem using a computer program (CFDLib from the Los Alamos National Laboratory) that employs an Arbitrary Lagrangian Eulerian (ALE) scheme using a modified Godunov method (Kashiwa and VanderHeyden 2000). CFDLib solves the Navier-Stokes equations for multiple fluids that can be either incompressible or compressible and can flow at subsonic or supersonic speeds.

Our 2D computer simulations show that a vent pressure well above atmospheric pressure produces an annular profile of the vertical velocity because the vertical flow in the core of the column is drastically reduced as it passes through the Mach disk, whereas the flow at the perimeter passes around the Mach disk, experiencing only an oblique shock. This annular profile is the opposite of the "top-hat" profile typically assumed in parameterized volcanic eruption models. The radial profile of the vertical velocity affects the entrainment of air into the core of the column, which determines whether the plume becomes buoyant or collapses and forms pyroclastic flows (Ogden et al. 2008a). Our simulations also demonstrate how, under certain conditions, a buoyant plume can intermittently collapse and form pyroclastic flows even with a steady constant eruption rate at the vent (Ogden et al. 2008b). This contradicts the common assumption that the eruption rate is the dominant parameter for predicting plume behavior. We are currently testing these results with 3D simulations.

Fig.1 A snapshot of the temperature in a simulated volcanic eruption within the first few seconds of the eruption from a 100 meter radius vent with a pressure 100 times greater than atmospheric.

Kashiwa, B.A. & W.B. VanderHeyden (2000) Toward a general theory for multiphase turbulence. Part I: Development and gauging of the model equations, in Los Alamos National Laboratory Report, pp. 88, Los Alamos National Laboratory, Los Alamos, NM.

Ogden, D.E., Glatzmaier, G.A. & Wohletz, K.H. (2008b) Effects of vent overpressure on buoyant eruption columns: Implications for plume stability Earth Planet. Sci. Lett., 268, 283-292.

Ogden, D.E., Wohletz, K.H., Glatzmaier, G.A. & Brodsky, E.E. (2008a) Numerical simulations of volcanic jets: Importance of vent overpressure J. Geophys. Res., B02204, doi:10.1029/2007JB005133.