  We study entrainment in dry thermals in neutrally and unstably stratified
ambients, and moist thermals in dry-neutrally stratified ambients using direct
numerical simulations (DNS). We find, in agreement with results of Lecoanet and
Jeevanjee \tb{[J. Atmos. Sci. 76(12), 3785-3801, (2019)]} that turbulence plays
a minor role in entrainment in dry thermals in a neutral ambient for Reynolds
numbers $Re \lesssim 10^4$. We then show that the net entrainment rate
increases when the buoyancy of the thermals increases, either by condensation
heating or because of an unstably stratified ambient. This is in contrast with
the findings of Morrison et al. [J. Atmos. Sci. 78(3), 797-816, (2021)]. We
also show that the role of turbulence is greater in these cases than in dry
thermals and, significantly, that the combined action of condensation heating
and turbulence creates intense small scale vorticity, destroying the {coherent}
vortex ring that is seen in dry and moist laminar thermals. These findings
suggest that fully resolved simulations at Reynolds numbers significantly
larger than the mixing transition Reynolds number $Re=10^4$ are necessary to
understand the role of turbulence in the entrainment in growing cumulus clouds,
which consist of a series of thermals rising and decaying in succession.
