The initial stages of explosive volcanic eruptions: insights gained from comparisons between laboratory experiments and numerical models

Explosive volcanic eruptions begin with fragmentation, accompanied by formation of a leading pressure or shock wave and high acceleration of a gas-pyroclast mixture behind that wave. Characterizing and quantifying the details of the initial phases is critical in part because these processes control vent velocity and mass flux, which in turn partially control whether or not an eruption column buoyantly rises or collapses to form pyroclastic density currents. Parameters of particular interest are gas and particle acceleration rate, the degree of coupling between pyroclast and gas phases, particle concentration, shock wave characteristics (which can be measured in the field and interpreted to infer pre-eruption, sub-surface conditions), and characteristics of the rarefaction wave (because its propagation limits the propagation of the fragmentation front). To study these processes, we compared 1D shock tube experiments and equivalent 1D numerical model runs for a range of conditions: initial pressure ratios of 5 to 100, initial particle concentrations of about 40 vol% (air as ambient), and particle sizes of 4 μm to 150 μm. Key parameters of comparison are shock wave strength and velocity and particle flow-front velocity. Rarefaction wave speed and gas velocity behind the shock were calculated using the model, but are difficult to measure in the laboratory and therefore are not an integral part of our study at this time. In general, the experiments and calculations are in reasonable agreement in terms of shock wave characteristics. However, the model over predicts particle velocities by an order of magnitude relative to laboratory measurements. This discrepancy is significant because, as stated above, initial particle velocity is of critical interest to volcanologists when making predictions about plume behavior. We propose two explanations for the difference between calculated and measured particle velocities. 1) Overestimation of the drag coefficient which couples the solid and gas phases in the model. As stated previously in Chojnicki et al. (2006, GRL v.33, L15309), experiments which constrain drag coefficients for dense particle beds are typically conducted under steady conditions, and therefore might not accurately characterize the high-acceleration phases of eruptions (or experiments). 2) Our existing model is formulated for low particle concentrations and therefore excludes a particle-particle interaction term and the effect of pressure gradient on particle acceleration and deceleration. In future work we will add these high-concentration effects, explore different formulations for drag coefficient, and measure gas velocities and rarefaction wave characteristics in additional experiments.