Particle image velocimetry (PIV) experiments have been conducted to study the velocity flow fields in the developing flow region of high-speed jets. These velocity distributions were examined to determine the entrained mass flow over a range of geometric and flow conditions, including overpressured cases up to an overpressure ratio of 2.83. In the region near the jet exit, all measured flows exhibited the same entrainment up until the location of the first shock when overpressured. Beyond this location, the entrainment was reduced with increasing overpressure ratio, falling to approximately 60% of the magnitudes seen when subsonic. Since entrainment ratios based on lower speed, subsonic results are typically used in one-dimensional volcanological models of plume development, the current analytical methods will underestimate the likelihood of column collapse. In addition, the concept of the entrainment ratio normalization is examined in detail, as several key assumptions in this methodology do not apply when overpressured.

[1] Volcanic plumes are often studied using one-dimensional analytical models, which use an empirical entrainment ratio to close the equations. Although this ratio is typically treated as constant, its value near the vent is significantly reduced due to flow development and overpressured conditions. To improve the accuracy of these models, a series of experiments was performed using particle image velocimetry, a high-accuracy, full-field velocity measurement technique. Experiments considered a high-speed jet with Reynolds numbers up to 467,000 and exit pressures up to 2.93 times atmospheric. Exit gas densities were also varied from 0.18 to 1.4 times that of air. The measured velocity was integrated to determine entrainment directly. For jets with exit pressures near atmospheric, entrainment was approximately 30% less than the fully developed level at 20 diameters from the exit. At pressures nearly three times that of the atmosphere, entrainment was 60% less. These results were introduced into Plumeria, a one-dimensional plume model, to examine the impact of reduced entrainment. The maximum column height was only slightly modified, but the critical radius for collapse was significantly reduced, decreasing by nearly a factor of two at moderate eruptive pressures.

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The developing region of high-speed jets is studied using particle image velocimetry methods. Ensemble-averaged and fluctuating velocity profiles were measured at a range of exit pressures, from a subsonic pressure-balanced case to an overpressured condition 3.2 times atmospheric. When pressure-balanced, the mean flow structure showed gradual development to a bell-shaped profile at approximately 8 diameters downstream, but the turbulent Reynolds stresses were far below self-similar levels. When overpressured, the mean structure displayed a series of compressions and expansions, including a normal shock, and the flow was far from Gaussian after 8 downstream diameters. The turbulent stresses were more suppressed than in the pressure-balanced jet, with little change exhibited in the jet core except very near the normal shock. Instantaneous vorticity contours also showed that the shear layer was divided into two bands at overpressure. This suggests that the turbulent eddies driving entrainment in the near-exit region were substantially weaker than in the self-similar region, which would result in lower mass flow from the ambient.