On the concentration distribution in turbulent thermals

Abstract

Turbulent thermals emerge in a wide variety of geophysical and industrial flows, such as atmospheric cumulus convection and pollutant dispersal in oceans and lakes. When a buoyant fluid mass rises, or sinks, heat and mass transfers occur by the engulfment of the fresh surrounding fluid inside the thermal - a process that spans over multiple scales from macroscopic entrainment of ambient fluid to microscopic diffusive processes. Turbulent thermals are typically investigated through their integral properties (radius, depth, entrainment rate). However, mixing processes depend on the internal distribution of concentration or temperature inside a thermal, which remains poorly constrained. Here, we use laboratory fluid dynamics experiments and direct numerical simulations to investigate the mixing of a passive scalar in turbulent thermals with large Reynolds numbers. We track the evolution of the concentration field, computing its moments and the probability density function. The concentration distribution exhibits self-similarity over time, except at high concentrations, possibly because of the presence of undiluted cores. These distributions are well approximated by an exponential probability density function. Although diffusion has a strong effect on the spatial structure of the concentration field, we observe no significant effect of diffusivity on the concentration distributions in the investigated range of Peclet numbers.