3-D numerical simulations of eruption clouds: Effects of the environmental wind on the turbulent mixing

During an explosive volcanic eruption, a mixture of volcanic gas and solid pyroclasts are ejected from a volcanic vent with a high temperature. As it rises, the mixture entrains ambient air owing to turbulent mixing. The entrained air expands by heating from the hot pyroclasts, and the eruption cloud (i.e., the ejected material plus the entrained air) rises as a buoyant plume. Because the plume height is principally determined by the balance between the thermal energy ejected at the vent and the work done in transporting the ejected material plus entrained air through the atmospheric stratification, it is controlled by the efficiency of turbulent mixing; as the amount of entrained air increases, the plume height decreases. In the 1-D models of eruption column (e.g., Woods, 1988), the plume height is calculated on the assumption that the mean inflow velocity across the edge of turbulent jet and/or plume is proportional to the mean vertical velocity (Morton et al., 1956). Experimental studies suggest that the proportionality constant (i.e., entrainment coefficient, k), which represents the efficiency of turbulent mixing, is about 0.10 for pure plumes when there is no wind. When an environmental wind is present, however, the interaction between a buoyant plume and the wind may enhance the entrainment of air and can significantly decrease the plume height (Bursik, 2001). In order to investigate the effects of wind on the vortical structures and the efficiency of turbulent mixing in an eruption cloud, we have carried out 3-D numerical simulations of eruption column which is ejected in a wind field. The simulation results indicate that a buoyant plume vertically rises as a "strong plume" (e.g., Bonadonna et al., 2003) when the wind velocity is low: the cloud reaches the neutral buoyancy level and overshoots until the upward momentum is exhausted. In this case, the plume height is consistent with prediction by the 1-D model with k~0.10. When the wind velocity is high, on the other hand, a "weak plume" develops following a bent-over trajectory as a result of the strong wind advection. In this case, the plume height is lower than that for the no-wind case, which means that the turbulent mixing is more efficient (i.e., the effective value of k is larger than 0.10). The 3-D images of the flows indicate that the vortical structures in the weak plume are affected by the presence of environmental wind; they are largely elongated along the direction of the wind compared with those in the strong plume. The result that the efficiency of turbulent mixing is enhanced by wind is supported by recent observations in the 2011 eruption of Shinmoe-Dake, Japan. The effective values of k are estimated from the relationship between plume height and mass discharge rate on the basis of the 1-D model. The effective value of k is about 0.10 for the March 13 eruption in a calm environment, whereas it is substantially larger than 0.10 (~0.13) in the January 26 - 27 eruptions during which the seasonal wind from west prevailed.