Entrainment in DNS of Turbulent Thermals

Thermals are the result of a finite release of buoyant fluid. Thermals have been studied extensively in the laboratory, and more recently with large eddy simulations (LES). Here we present the first direct numerical simulations (DNS) of thermals; we study both laminar thermals (Re=630) and turbulent thermals (Re=6300) with Pr=1. Our goal is to quantitatively test the entrainment hypothesis of, e.g., Morton, Taylor, & Turner (1956). We use a thermal tracking algorithm based off techniques proposed in atmospheric science, and calculate the entrainment rate as the rate of change of the thermal volume. In line with previous work, we find that the entrainment rate is inversely proportional to the radius of the thermal, d log V/dz = e/r, where e is the entrainment efficiency. The entrainment efficiency for both laminar thermals (e=0.36) and turbulent thermals (e=0.47) is significantly lower than the reported values in laboratory experiments (e~0.75). We suggest this may be due to the use of salt as a source of density perturbations in laboratory experiments, which have Sc~700.