A unified model for wind-blown volcanic umbrella clouds

Explosive volcanic eruptions release a rising plume of ash and gas into the atmosphere. Once such a plume reaches its altitude of neutral buoyancy, it spreads into an umbrella cloud, which is then distorted by the surrounding meteorological wind. At least four processes are important in governing the complex evolution of the umbrella cloud: buoyancy-driven spreading, turbulent skin drag, inertial drag at the advancing edge of the cloud, and the momentum of the cloud. Existing models have frequently assumed that just one of these drag forces is dominant. Here we present a model for the spread of an umbrella cloud in a crosswind, which is based on time-dependent partial differential equations that include all four key processes. The model confirms that spread far downstream is driven by a balance between turbulent drag and buoyancy. By including all four processes the transient behaviour of the cloud that occurs upwind of the drag-buoyancy regime can also be investigated. Our findings illustrate the fundamental differences between wind-blown umbrella clouds and those derived from an axisymmetric umbrella cloud approximation, and the consequent importance of accurate physical descriptions of the interaction between wind and umbrella clouds in volcanic ash dispersal models.