Particle-size distributions and their effect on entrainment in turbulent buoyant plumes

Explosive volcanic eruptions produce turbulent, buoyant jets that contain entrained particles. In these flows, turbulent entrainment of ambient air controls the ultimate rise height and spread of the jet. Volcanic jets are a natural example of these dilute particle-gas systems and the particles they contain can strongly control the dynamics of the bulk flow through the coupling between themselves and the surrounding fluid. The metric for the type of particle-fluid coupling is the Stokes number, St, which measures the timescale for the particles inertia against the timescale for the flow field, typically the overturn time of an eddy. We show that particles that are critically coupled to the flow (St=O(1)) change the turbulent structure of the flow by eddy stretching leading to energy cascades which are anisotropic in the horizontal and vertical directions. Crucially, flows laden with such particles carry considerably more energy in the stream-wise direction than particle-free flows which leads to a decrease in entrainment. This behaviour suggests that turbulent entrainment can effectively be shut down under critical St, giving rise to collapsing fountains whereas particle-free flows under the same source conditions would produce buoyant plumes. Changes in entrainment rates in volcanic jets are also manifested in readily observable features such as the rise height. We may therefore infer entrainment rates and their evolution over the course of an eruption from the maximum height and neutral buoyancy level.