A revisit of the role of gas entrapment on the stability conditions of explosive volcanic columns

Explosive volcanic eruptions produce high-velocity turbulent jets that can form either a stable buoyant Plinian column or a collapsing fountain producing pyroclastic density currents (PDC). Determining the source conditions leading to these extreme regimes is a major goal in physical volcanology. Classically, the regime boundary is defined as the critical eruptive mass discharge rate (MDR) before collapse for a given amount of free gas in the eruptive mixture (free gas + pyroclasts) at the vent. Previous studies have shown that an agreement between theory and field data can be achieved in two different frameworks: (i) by accounting for the effect of gas entrapment in large pumice fragments, which lowers the effective gas content, depending on the total grain-size distribution (TGSD) of pyroclastic fragments, or (ii) by accounting for the reduction of turbulent entrainment at the base of the volcanic column due to its negative buoyancy. Here, we aim at combining these two using a 1D model of volcanic column that includes sedimentation to follow the evolution of the TGSD. In powerful (≥ 107 kg s−1) Plinian eruptions, the loss of particles by sedimentation acts as to decrease the load of particles during the plume rise, which favors the formation of a stable column. In this case, we obtain that coarse TGSD promote the formation of stable plumes, a result at odds with the predictions of models considering gas entrapment in large pyroclastic fragments. To interpret this conclusion, we reconsider the effect of gas entrapment and show that in general, it has a dominant role on column collapse compared to particle sedimentation, and hinders the formation of buoyant columns. This drastic effect is reduced when incorporating open porosity, e.g. by considering that some bubbles inside a fragment are connected to the exterior. The characteristics of the PDC produced by column collapse are then predicted as a function of the TGSD and MDR at the source. We further test the model using two well-documented historical events, the ≈186 CE Taupo and 79 CE Vesuvius eruptions. Our model predictions are consistent with the Taupo eruption record, but not with the Vesuvius one. In this latter case, we suggest that the characteristics of the TGSD imply to take into account the thermal disequilibrium between gas and pyroclasts.