On the dynamics of volcanic columns: A comparison of field data with a new model of negatively buoyant jets

Explosive volcanic eruptions propel high-velocity turbulent jets into the atmosphere and are one of the most powerful and dangerous turbulent flows on Earth. Such eruptions are particularly difficult to predict due to their unusual dynamics that allow the jet to form a high buoyant plinian plume or dense pyroclastic flows when the column collapses. A major goal of physical volcanology has been to predict quantitatively the limit between the flow regimes, as a function of exit conditions specified at the vent, which requires a physical model constrained by geologic field data. A first generation of quasi-analytic models, developed over 2030 years although qualitatively successful, has failed to achieve this goal, because they overestimate by more than one order of magnitude the mass flux at the transition. There has been no consensus on whether this mostly reflects poor knowledge of geologic parameters or inadequacies in the physical description of the dynamics. Direct numerical simulations bring considerable advances in the study of unsteady phenomena that occur within the volcanic column, but their complexity makes the deciphering of the underlying dynamics challenging. Here, we present a basis for a new generation of 1D-models that includes a more sophisticated description of the rate of entrainment of air into the jet as a function of its buoyancy. In this framework, we demonstrate that the inconsistency between previous 1 D models and field data is due to the omission of a key ingredient in the modeling of turbulence: reduction of entrainment due to the high density of the volcanic jet. We show that negative buoyancy near the base of the jet reduces the coefficient governing turbulent mixing to much less than the value commonly assumed based on experimental studies of neutrally buoyant jets and positively buoyant plumes. The results of our new model, allowing for variable entrainment as a function of local Richardson number, greatly improve the quantitative prediction of the transition as constrained by field data from a large number of eruptions. (C) 2008 Elsevier B.V. All rights reserved.