On pyroclastic flow emplacement

In this note I investigate some theoretical characteristics of pyroclastic flow deposits, assuming that these flows are Bingham fluids, probably the simplest non-Newtonian fluids. Pyroclastic flows are modeled as laminar debris flows moving on an inclined plane, and their physics is discussed within the classical framework of lubrication theory. Using general hydrodynamics methods, I show that the arrestment and emplacement of pyroclastic flows may be seen as the time-asymptotic limit of their equations of motion. This limit is found to be a nonlinear ordinary differential equation, whose solution gives the shape of pyroclastic flow deposits. The model suggests that these flows stop when the supply of material from the source is depleted; deposit thickness is controlled principally by the flow yield stress tau(z), a parameter characteristic of Bingham fluids, while deposit length, a measure of flow mobility, depends on tau(z), on the source flux qo, and on the slope theta of the solid substrate. Even in this simple model, theoretical analysis shows a complex correlation between flow parameters and deposit profiles.