Entrainment in Resolved, Dry Thermals

Entrainment in cumulus convection remains ill-understood and difficult to quantify. For instance, entrainment is widely believed to be a fundamentally turbulent process, even though Turner (1957) pointed out that dry thermals entrain primarily because of buoyancy (via a dynamical constraint requiring an increase in radius $r$), rather than turbulence. Furthermore, entrainment has been postulated to obey a $1/r$ scaling, but this scaling has not been firmly established. Here, we study the classic case of dry, turbulent thermals in a neutrally stratified environment using fully resolved direct numerical simulation. We combine this with a thermal tracking algorithm which defines a control volume for the thermal at each time, allowing us to directly measure entrainment. We test Turner's argument by varying the Reynolds number Re of our thermals between laminar (Re~600) and turbulent (Re~6000) regimes, finding only a 20% variation in entrainment rate $\epsilon$, supporting the claim that turbulence is not necessary for entrainment. We also directly verify the postulated $\epsilon\sim 1/r$ scaling law.