Three-dimensional turbulent velocity field and air entrainment of the 22 March 1944 Vesuvius eruption plume

Turbulent air entrainment into explosive volcanic jets determines whether an eruption will produce buoyant plumes, pyroclastic density currents, or both. Most previous studies of entrainment consist of numerical models and analog laboratory experiments, with relatively few observations of natural eruptions. The existing observations of entrainment are generally time- and space-averaged measurements, which do not provide information regarding the mechanisms of entrainment. We investigate spatial and temporal variations in entrainment of the March 22 Plinian phase of the 1944 eruption of Mt. Vesuvius using a feature tracking velocimetry (FTV) algorithm applied to film collected by the U.S. Navy and digitized by the U.S. National Archives. We describe a novel technique to estimate the 3D plume morphology from normalized brightness. Projection of the 2D velocity fields from the FTV algorithm onto those 3D surfaces provides 3D velocity fields. The divergence of the velocity fields quantifies local expansion and entrainment and shows that although kilometer scale eddies are present in the plume, entrainment and expansion occur over length scales on the order of hundreds of meters. Integrating the inward directed velocities over the entraining regions quantifies local air entrainment rates. We find that entrainment of 5.4–6.1 × 10⁷ m³s^-1 air occurs over about one-third of the observed plume margins, yielding an average entrainment velocity of ~ 2.8 ms^-1. Extrapolation of those rates to the entire plume indicates total entrainment of 1–3 × 10⁸ m³s^-1. The entrainment velocity has a magnitude ~ 6% of the magnitude of the turbulence intensity along the plume margins, indicating that the latter may approximate the centerline plume velocity and suggesting use of entrainment coefficient of 0.06 for this and similar eruptions, i.e., strong plumes with a relatively high momentum-dominated region.