Extreme responses of a coupled scalar–particle system during turbulent mixing

Abstract

Extreme responses of a droplet ensemble during an entrainment and mixing process as present at the edge of a cloud are investigated by means of three-dimensional direct numerical simulations in the Euler–Lagrangian framework. We find that the Damköhler number Da, a dimensionless parameter which relates the fluid time scale to the typical evaporation time scale, can capture all aspects of the initial mixing process within the range of parameters accessible in this study. The mixing process is characterized by the limits of strongly homogeneous (Da Lt 1) and strongly inhomogeneous (Da Gt 1) regimes. We explore these two extreme regimes and study the response of the droplet size distribution to the corresponding parameter settings through an enhancement and reduction of the response constant K in the droplet growth equation. Thus, Da is varied while Reynolds and Schmidt numbers are held fixed, and initial microphysical properties are held constant. In the homogeneous limit minimal broadening of the size distribution is observed as the new steady state is reached, whereas in the inhomogeneous limit the size distribution develops strong negative skewness, with the appearance of a pronounced exponential tail. The analysis in the Lagrangian framework allows us to relate the pronounced negative tail of the supersaturation distribution to that of the size distribution.