Flying through gigantic volcanic eruption clouds

Abstract: 

Volcanic plumes ascend high into the stratified atmosphere where they form intrusions about the level of neutral buoyancy. Sufficiently powerful eruptions or eruptions in a weak wind form umbrella clouds, which can spread in all directions. The talk demonstrates that volcanic intrusions are governed by buoyancy in the near field, which results in a rapid thinning with radial distance. We will discuss theoretical, numerical and observational evidence to show that buoyancy spreading is almost always dominant even at relatively large distances, hundreds to thousands of kilometres from source, over atmospheric turbulent diffusion, currently the favoured model of the UK Met Office and others, using the numerical advection-diffusion program NAME.  Possibly the most interesting part of the talk from a mathematical point of view is that we shall show how to determine a spreading law from essentially dimensional analysis with a result that agrees with balancing terms in the governing partial differential equations, but, surprisingly, does NOT agree with the actual solution, determined partly numerically, which has a quite different structure.  Why this is so will be explained.