Sensitivity of the dynamics of volcanic eruption columns to their shape

Abstract

This paper presents a one-dimensional steady-state model to investigate the sensitivity of the dynamics of sustained eruption columns to radius variations with height due to thermal expansion of the entrained air, and decreases in atmospheric pressure with height. In contrast to a number of previous models using an equation known as the entrainment assumption, the new model is based on similarity arguments to derive an equation set equivalent to the model proposed by Woods [Bull Volcanol 50:169–193, 1988]. This approach allows investigation of the effect of gas compressibility on the entrainment rate of ambient air, which has been little examined for a system in which a decrease in pressure significantly affects the density stratification of a compressible fluid. The new model provides results that include two end members: one in which the volume change within the eruption columns affects only the radial expansion without changing the vertical motion, and the other is the converse. The Woods [Bull Volcanol 50:169–193, 1988] model can be regarded as being between those two end members. The range of uncertainty arises because the extremely high temperature of discharged materials from a volcanic vent, and the exceptional terminal height of the eruption columns, allow significant expansion of the gas component in the eruption columns, making them behave differently from common turbulent plumes. This study indicates that the maximum height of the eruption columns is affected considerably by this uncertainty, particularly when the eruption columns extend above a height of 10 km, at which the pressure is about one-fourth the pressure at the ground surface. Column collapse may also be suppressed in wider parameter ranges than previously estimated. However, the uncertainty can be reduced by measuring column radii through a vertical profile during actual volcanic eruptions. Accordingly, this paper suggests that appropriate observation of eruption column shapes is essential for improving our understanding of the dynamics of eruption columns.