Papers › Buoyancy-Driven Entrainment in Dry Thermals
Buoyancy-Driven Entrainment in Dry Thermals
Brett McKim, Nadir Jeevanjee, Daniel Lecoanet
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\citet{turner1957} 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 \citet{scorer1957} or the turbulent entrainment hypothesis of \citet{morton1956}. The assumption of turbulence-driven entrainment was investigated by \citet{lecoanet2018}, 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 ϵ and find close quantitative agreement with the values in direct numerical simulations. In particular, our expression for entrainment rate is consistent with the parameterization 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 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.
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