Pyroclastic current dynamic pressure from aerodynamics of tree or pole blow-down

The common occurrence of tree and pole blow-down from pyroclastic currents provides an opportunity to estimate properties of the currents. Blow-down may occur by uprooting (root zone rupture), or flexure or shear at some point on the object. If trees are delimbed before blow-down, each tree or pole can be simulated by a cylinder perpendicular to the current. The force acting on a cylinder is a function of flow dynamic pressure, cylinder geometry, and drag coefficient. Treated as a cantilever of circular cross-section, the strength for the appropriate failure mode (rupture, uprooting or flexure) can then be used to estimate the minimum necessary current dynamic pressure. In some cases, larger or stronger standing objects can provide upper bounds on the dynamic pressure. This analysis was treated in two ways: (1) assuming that the current properties are vertically constant; and (2) allowing current velocity and density to vary vertically according to established models for turbulent boundary layers and stratified flow. The two methods produced similar results for dynamic pressure. The second, along with a method to approximate average whole-current density, offers a means to estimate average velocity and density over the height of the failed objects. The method is applied to several example cases, including Unzen, Mount St. Helens, Lamington, and Merapi volcanoes. Our results compare reasonably well with independent estimates. For several cases, we found that it is possible to use the dynamic pressure equations developed for vertically uniform flow, along with the average cloud density multiplied by a factor of 2–5, to determine average velocity over the height of the failed object.