Effects of Entrainment and Mixing on Droplet Size Distributions: Bridging the DNS-LES Gap

The fundamental difficulties that the large-eddy simulation (LES) approach faces when attempting to represent the effects of entrainment and mixing on droplet microphysics include representing the subgrid-scale (SGS) variability of subsaturation and its impact on droplet size distribution (DSD) evolution and accounting for the finite rate of SGS mixing and therefore of droplet evaporation.

Direct numerical simulation (DNS) resolves the smallest scales of fluid motion; therefore DNS is not limited like LES, but it is restricted to domains of less than about one meter in extent. This limits the range of Damkohler (Da) numbers (ratio of a flow time scale to a droplet evaporation [phase relaxation] time scale to values ~1, unless the molecular diffusivity of water vapor is artificially increased (as in Kumar et al. 2012). The two limits, Da ≪ 1 and Da ≫ 1, describe homogeneous and inhomogeneous mixing, respectively.

The EMPM (Explicit Mixing Parcel Model) predicts the evolving in-cloud variability due to entrainment and finite-rate turbulent mixing using a 1D representation of a cloudy parcel. It calculates the growth of tens of thousands of individual cloud droplets based on each droplet's local environment. The 1D formulation allows the model to resolve fine-scale variability down to the smallest turbulent scales (about 1 mm) in large domains (20 to 200 m), thereby bridging the DNS-LES gap, and allowing Da = 100 or more to be achieved.

Recently, B. Kumar, J. Schumacher, and R. Shaw (2012, 2013) performed several DNSs of the response of a droplet population to entrainment and mixing that are ideally suited for evaluating the EMPM. We will compare our EMPM results to their DNS results for identical configurations, and also present results for scenarios that DNS is not presently capable of simulating.