Entrainment in Resolved, Turbulent Dry Thermals

Abstract

Entrainment in cumulus convection remains notoriously difficult to quantify. A long-standing conjecture is that the fractional entrainment rate {\epsilon} scales as 1/r, where r is the radius of the convecting parcel, but this has never been directly verified. Furthermore, entrainment rates simulated by large-eddy and cloud-resolving simulations are difficult to interpret, as they depend on both resolution as well as implicit and explicit sub-grid diffusion. Here, we study the classic case of dry, turbulent thermals in a neutrally stratified environment using fully resolved direct numerical simulation (DNS), in conjunction with a thermal tracking algorithm which defines a control volume for the thermal at each time. This allows us to measure a thermal's volume as a function of time, and permits the first direct verification that {\epsilon}~1/r. Also, by using DNS, each simulation has a well-defined Reynolds number Re, so we can explore the dependence of detrainment and entrainment on turbulence in a systematic way. We find that entrainment is predominantly laminar, varying by only 20% between laminar (Re~600) and turbulent (Re~6000) simulations, whereas detrainment is over an order of magnitude smaller than entrainment and predominantly turbulent, increasing by a factor of 10 over the same Re range.