Buoyancy‐driven entrainment in dry thermals

Abstract

AbstractOver 50 years ago it was proposed that dry thermals entrain because of buoyancy (via a constraint which requires an increase in the radius a). However, this runs counter to the scaling arguments commonly used to derive the entrainment rate, which rely on either the self‐similarity or a turbulent entrainment hypothesis. The assumption of turbulence‐driven entrainment has been investigated and it has been 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 the 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 ϵ and find close quantitative agreement with the values in direct numerical simulations. In particular, our expression for entrainment rate is consistent with the parametrization ϵ∼B/w2, for Archimedean buoyancy B and vertical velocity w. We also 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 one third of its original value in both the laminar and turbulent cases when g=0, affirming the central role of buoyancy in entrainment for dry thermals.