“…The mixing of water, steam, pyroclasts, and lithic debris in the vent region in explosive hydrovolcanic eruptions is complex and may involve effects of shocks, supersonic flow, film boiling, and multiple fragmentation mechanisms (Wohletz et al, 2013;Houghton and Carey, 2015;van Otterloo et al, 2015) that introduce inherently time-dependent and three-dimensional mechanisms for entrainment and mechanical stirring that are not captured in a one-dimensional steady-state integral model. However, following extensive studies of entrainment and mixing into turbulent plumes (Morton et al, 1956;Linden, 1979;Turner, 1986), a recent complementary analysis of water entrainment into supersonic, submerged gas jets (Zhang et al, 2020) and studies of the bulk energetics of interactions between hot pyroclasts and water (Dufek et al, 2007;Mastin, 2007a;Schmid et al, 2010;Sonder et al, 2011;Dürig et al, 2012;Woodcock et al, 2012) we can parameterize these processes to explore effects on total budgets for mass, energy, and buoyancy. Following Morton et al (1956); Kaminski et al (2005); Carazzo et al (2008); Zhang et al (2020), we will relate the radial entrainment speed of water or atmosphere to the local rise speed of a jet and prescribe resulting velocity, pressure and temperature fields.…”