Buoyancy-Driven Entrainment in Dry Thermals

Turner (1957) proposed that dry thermals entrain because of buoyancy (via a constraint which requires an increase in the radius a ). This however, runs counter to the scaling arguments commonly used to derive the entrainment rate, which rely on either the self-similarity of Scorer (1957) or the turbulent entrainment hypothesis of Morton et al (1956). The assumption of turbulence-driven entrainment was investigated by Lecoanet and Jeevanjee (2018), who found that the entrainment efficiency e varies by less than 20 % between laminar (Re = 630) and turbulent (Re = 6300) thermals. This motivated us to utilize Turner's argument of buoyancy-controlled entrainment in addition to the thermal's vertical momentum equation to build a model for thermal dynamics which does not invoke turbulence or self-similarity. We derive simple expressions for the thermals' kinematic properties and their fractional entrainment rate ɛ and find close quantitative agreement with the values in direct numerical simulations. We then directly validate the role of buoyancy-driven entrainment by running simulations where gravity is turned off midway through a thermal's rise. The entrainment efficiency e is observed to drop to less than 1/3 of its original value in both the laminar and turbulent cases when g = 0 , affirming the central role of buoyancy in entrainment in dry thermals.