Buoyancy-driven entrainment in dry thermals

Brett McKim*, Nadir Jeevanjee, Daniel Lecoanet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Over 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.

Original languageEnglish (US)
Pages (from-to)415-425
Number of pages11
JournalQuarterly Journal of the Royal Meteorological Society
Volume146
Issue number726
DOIs
StatePublished - Jan 1 2020
Externally publishedYes

Keywords

  • atmosphere
  • baroclinicity
  • buoyancy
  • convection
  • entrainment
  • theory
  • turbulence
  • vorticity

ASJC Scopus subject areas

  • Atmospheric Science

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