Explosive volcanic eruptions often produce large amounts of ash that is transported high into the atmosphere in a turbulent buoyant plume. The ash can be spread widely and is hazardous to aircraft causing major disruption to air traffic. Recent events, such as the eruption of Eyjafjallajokull, Iceland, in 2010 have demonstrated the need for forecasts of ash transport to manage airspace. However, the ash dispersion forecasts require boundary conditions to specify the rate at which ash is delivered into the atmosphere.
Models of volcanic plumes can be used to describe the transport of ash from the vent into the atmosphere. I will show how models of volcanic plumes can be developed, building on classical fluid mechanical descriptions of turbulent plumes developed by Morton, Taylor and Turner (1956), and how these are used to determine the volcanic source conditions. I will demonstrate the strong atmospheric controls on the buoyant plume rise. Typically steady models are used as solutions can be obtained rapidly, but unsteadiness in the volcanic source can be important. I'll discuss very recent work that has developed unsteady models of volcanic plumes, highlighting the mathematical analysis required to produce a well-posed mathematical description.