@article{de494c8bc18249d78e5af4d3601d2ab0,
title = "Buoyancy-driven entrainment in dry thermals",
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.",
keywords = "atmosphere, baroclinicity, buoyancy, convection, entrainment, theory, turbulence, vorticity",
author = "Brett McKim and Nadir Jeevanjee and Daniel Lecoanet",
note = "Funding Information: BM is supported by the NOAA Hollings Scholarship, DL is supported by a PCTS fellowship and a Lyman Spitzer Jr. fellowship, and NJ is supported by a Harry Hess fellowship from the Princeton Geoscience Department. Computations were conducted with support by the NASA High End Computing (HEC) program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center on Pleiades, as well as GFDL's computing cluster. Open‐Access support was provided by the University of Exeter APC Fund. We would like to thank Leo Donner and Nathaniel Tarshish for helpful discussions at many points throughout the research process and for Spencer Clark's computer support. Funding Information: information This research was supported by the NOAA Hollings Scholarship, PCTS and Lyman Spitzer Jr. fellowships, and a Harry Hess fellowship from the Princeton Geoscience Department.BM is supported by the NOAA Hollings Scholarship, DL is supported by a PCTS fellowship and a Lyman Spitzer Jr. fellowship, and NJ is supported by a Harry Hess fellowship from the Princeton Geoscience Department. Computations were conducted with support by the NASA High End Computing (HEC) program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center on Pleiades, as well as GFDL's computing cluster. Open-Access support was provided by the University of Exeter APC Fund. We would like to thank Leo Donner and Nathaniel Tarshish for helpful discussions at many points throughout the research process and for Spencer Clark's computer support. Publisher Copyright: {\textcopyright} 2019 The Authors. Quarterly Journal of the Royal Meteorological Society published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society.",
year = "2020",
month = jan,
day = "1",
doi = "10.1002/qj.3683",
language = "English (US)",
volume = "146",
pages = "415--425",
journal = "Quarterly Journal of the Royal Meteorological Society",
issn = "0035-9009",
publisher = "John Wiley and Sons Ltd",
number = "726",
}