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 pointed out in 1957 that dry thermals entrain primarily because of buoyancy (via a dynamical constraint requiring an increase in radius r). 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 thermals in a neutrally stratified environment using fully resolved direct numerical simulation. We combine this with a thermal tracking algorithm that defines a control volume for the thermal at each time, allowing us to directly measure entrainment. We vary the Reynolds number (Re) of our thermals between laminar (Re’ 600) and turbulent (Re’ 6000) regimes, finding only a 20% variation in entrainment rate «, supporting the claim that turbulence is not necessary for entrainment. We also directly verify the postulated «; 1/r scaling law.