A mathematical model of volcanic plumes : submitted to the Institute of Natural and Mathematical Sciences in partial fulfillment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New Zealand
Volcanic plumes and the resultant tephra fallout are of signi cant concern to nations the
world over. Several recent large-scale eruptions have caused such disruption to air traffic
that huge proportions of European commerce have been severely compromised. The plumes
of such eruptions exist beyond any human recourse and must simply be left to extinguish
themselves in time.
Currently, separate models do exist for plume dynamics and the atmospheric transport of
particles, with a mixture of qualitative and quantitative results. In this thesis we develop a
mathematical model with some similarities and some differences to those already in use.
The model has its core in the conservation equations of mass, momentum and energy for
the plume's driving gases and suspended particles. While these equations are non-linear
and diffcult (if not impossible) to solve analytically, we can solve the equations numerically
using a discretisation along the central vertical axis.
Initially these equations are provided with full time-dependency, with a view to pursuing
such results in the future. However, the numerical results contained here are limited to a
flow model of an established and sustained, buoyant plume.