The dimensions and dynamics of volcanic eruption columns

Eruption columns can be divided into three regimes of physical behaviour. The basal gas thrust region is characterized by large velocities and decelerations and is dominated by momentum. This region is typically a few hundred metres in height and passes upwards into a much higher convective region where buoyancy is dominant. The top of the convective region is defined by the level of neutral density (heightH_B) where the column has a bulk density equal to the surrounding atmosphere. Above this level the column continues to ascend to a heightH_T due to its momentum. The column spreads horizontally and radially outwards between heightH_T andH_B to form an umbrella cloud. Numerical calculations are presented on the shape of eruption columns and on the relationships between the heightH_B and the mass discharge rate of magma, magma temperature and atmospheric temperature gradients. Spreading rate of the column margins increases with height principally due to the decrease in the atmospheric pressure. The relationship between column height and mass discharge rate shows good agreement with observations. The temperature inversion above the tropopause is found to only have a small influence on column height and, eruptions with large discharge rates can inject material to substantially greater heights than the inversion level. Approximate calculations on the variation of convective velocities with height are consistent with field data and indicate that columns typically ascend at velocities from a few tens to over 200 m/s. In very large columns (greater than 30 km) the calculated convective velocities approach the speed of sound in air, suggesting that compressibility effects may become important in giant columns. Radial velocities in the umbrella region where the column is forced laterally into the atmosphere can be substantial and exceed 55 m/s in the case of the May 18th Mount St. Helens eruption. Calculations on motions in this region imply that it plays a major role in the transport of coarse pyroclastic fragments.