The fluid dynamics and thermodynamics of eruption columns
A new model for Plinian eruption columns is derived from first principles and investigated numerically. The dynamics particular to the momentum-driven basal ‘gas-thrust region’ and the upper buoyancy-driven convective region are treated separately. The thermal interactions in the column are modelled by the steady-flow-energy equation. The main results of the present paper are that: (1) the basal gas-thrust region model predicts a very rapid initial expansion of the material on leaving the vent; (2) the gas-thrust region height decreases with initial temperature, inital gas content of the erupted material and initial velocity, but increases with vent radius; (3) the total column height increases with initial temperature, initial velocity and vent radius, but decreases with initial gas content; (4) column collapse occurs for initial velocities of the order of 100 m/s; the precise value increases as the initial gas content in the erupted material decreases; (5) for large vent radii or low initial gas content of the erupted material, the velocity in the column can increase with height once in the buoyancy-driven region instead of decaying to zero monotonically; (6) the interaction of the potential energy with the enthalpy is found to be the dominant thermal interaction in the upper part of the column. Previous models of eruption columns involve inconsistencies and simplifications; these are shown to lead to significant differences in the results in comparison to the present model.