A numerical study of turbulent mixing in eruption clouds using a three-dimensional fluid dynamics model

The dynamics of eruption clouds in explosive volcanic eruptions are governed by entrainment of ambient air into eruption clouds by turbulent mixing. We develop a new numerical pseudo gas model of an eruption cloud by employing three-dimensional coordinates, a third-order accuracy scheme, and a fine grid size in order to investigate the behavior of entrainment due to turbulent mixing. The quantitative features of entrainment are measured by a proportionality constant relating the inflow velocity at the edge of the flow to the average vertical velocity (i.e., the entrainment coefficient). Our model has successfully reproduced the quantitative features of entrainment observed in the laboratory experiments as well as fundamental features of the dynamics of eruption clouds, such as the generation of eruption columns and/or pyroclastic flows. The value of the entrainment coefficient for eruption clouds is estimated from the column height and critical condition for column collapse by comparing results of our model with those of previous one-dimensional models. It is suggested that the value of the entrainment coefficient for an eruption cloud is approximately constant, although the value estimated from the critical condition for column collapse (k similar to 0.07) is slightly smaller than that based on the column height (k similar to 0.1). This difference reflects the vertical change of flow structure in the eruption cloud. The eruption cloud in the upper region exhibits a meandering instability, which leads to efficient mixing, whereas the cloud near the vent maintains a concentric structure with an inner dense core surrounded by an outer shear region. Our model is consistent with previous one-dimensional models for steady eruption clouds supported by the laboratory experiments, and it is also applicable to unsteady and transient features of actual eruption clouds.