Fig. 9: Spatiotemporal evolution of dynamic pressure during flow propagation.
From: Turbulent particle-gas feedback exacerbates the hazard impacts of pyroclastic density currents
a Dynamic pressure as a function of flow distance D. The red circles show time-averaged values of dynamic pressure \({P}_{{dusty\; gas\_ave}}\). The red line is a best-fit powerlaw through the data that yields \({P}_{{dusty\; gas\_ave}}=136{D}^{-1.019}\). The blue square symbols represent the maximum dusty gas pressure \({P}_{{dusty\; gas\_}\max }\). The black circles show measurements of the maximum particle impact pressure \({P}_{{impact\_}\max }\). b The pressure ratio \({P}_{{dusty\; gas\_}\max }/{P}_{{dusty\; gas\_ave}}\) as a function of flow distance (black diamonds). The contour plot shows the particle volume concentration of particles with diameters \( > 125\, {{{{{\rm{\mu m}}}}}}\), associated with the condition \({St}\ge O\left(1\right)\). The vertical red dotted lines demark particle concentrations of, from left to right, 10−3, 10−4, and 10−5. The secondary, non-linear horizontal time axis depicts the times of flow front arrival corresponding to these distances. After formation of a gravity current structure at c. 1.8 m and up until 5.4 m, the pressure ratio increases slightly to maximum values of around 13. The flow duration associated with this increase coincides with the eddy time scale \({t}_{\varepsilon }\) highlighted on the secondary x-axis. Downstream from 5.4 m, the pressure ratio decreases in association with a reduction in the particle concentration of critical Stokes number particles larger than 125 µm. The horizontal dashed line corresponds to the condition predicted by Eq. (8) where the pressure ratio takes a critical value of c. 3.9, when the flow is depleted in particles with \({St}\ge 1\).
