Miroslaw Andrejczuk

Numerical Simulation of Cloud–Clear Air Interfacial Mixing: Homogeneous versus Inhomogeneous Mixing

Abstract This note presents an analysis of several dozens of direct numerical simulations of the cloud–clear air mixing in a setup of decaying moist turbulence with bin microphysics. The goal is to assess the instantaneous relationship between the homogeneity of mixing and the ratio of the time scales of droplet evaporation and turbulent homogenization. Such a relationship is important for developing improved microphysical parameterizations for large-eddy simulation of clouds. The analysis suggests a robust relationship for the range of time scale ratios between 0.5 and 10. Outside this range, the scatter of numerical data is significant, with smaller and larger time scale ratios corresponding to mixing scenarios that approach the extremely inhomogeneous and homogeneous limits, respectively. This is consistent with the heuristic argument relating the homogeneity of mixing to the time scale ratio.

Numerical Simulation of Cloud–Clear Air Interfacial Mixing: Effects on Cloud Microphysics

This paper extends the previously published numerical study of Andrejczuk et al. on microscale cloud– clear air mixing. Herein, the primary interest is on microphysical transformations. First, a convergence study is performed—with well-resolved direct numerical simulation of the interfacial mixing in the limit—to optimize the design of a large series of simulations with varying physical parameters. The principal result is that all conclusions drawn from earlier low-resolution (x 10 2 m) simulations are corroborated by the high-resolution (x 0.25 10 2 m) calculations, including the development of turbulent kinetic energy (TKE) and the evolution of microphysical properties. This justifies the use of low resolution in a large set of sensitivity simulations, where microphysical transformations are investigated in response to variations of the initial volume fraction of cloudy air, TKE input, liquid water mixing ratio in cloudy filaments, relative humidity (RH) of clear air, and size of cloud droplets. The simulations demonstrate that regardless of the initial conditions the evolutions of the number of cloud droplets and the mean volume radius follow a universal path dictated by the TKE input, RH of clear air filaments, and the mean size of cloud droplets. The resulting evolution path only weakly depends on the progress of the homogenization. This is an important conclusion because it implies that a relatively simple rule can be developed for representing the droplet-spectrum evolution in cloud models that apply parameterized microphysics. For the low-TKE input, when most of the TKE is generated by droplet evaporation during mixing and homogenization, an inhomogeneous scenario is observed with approximately equal changes in the dimensionless droplet number and mean volume radius cubed. Consistent with elementary scale analysis, higher-TKE inputs, higher RH of cloud-free filaments, and larger cloud droplets enhance the homogeneity of mixing. These results are discussed in the context of observations of entrainment and mixing in natural clouds.

Laboratory and modeling studies of cloud-clear air interfacial mixing: anisotropy of small-scale turbulence due to evaporative cooling

Small-scale mixing between cloudy air and unsaturated clear air is investigated in numerical simulations and in a laboratory cloud chamber. Despite substantial differences in physical conditions and some differences in resolved scales of motion, results of both studies indicate that small-scale turbulence generated through cloud-clear air interfacial mixing is highly anisotropic. For velocity fluctuations, numerical simulations and cloud chamber observations demonstrate that the vertical velocity variance is up to a factor of two larger than the horizontal velocity variance. The Taylor microscales calculated separately for the horizontal and vertical directions also indicate anisotropy of turbulent eddies. This anisotropy is attributed to production of turbulent kinetic energy (TKE) by buoyancy forces due to evaporative cooling of cloud droplets at the cloud-clear air interface. Numerical simulations quantify the effects of buoyancy oscillations relative to the values expected from adiabatic and isobaric mixing, standardly assumed in cloud physics. The buoyancy oscillations result from microscale transport of liquid water due to the gravitational sedimentation of cloud droplets. In the particular modeling setup considered here, these oscillations contribute to about a fifth of the total TKE production. 5 Author to whom any correspondence should be addressed.

Another Look at Stochastic Condensation for Subgrid Cloud Modeling: Adiabatic Evolution and Effects

The theory of stochastic condensation, which models the impact of an ensemble of unresolved supersaturation fluctuations S on the volume-averaged droplet-size distribution f (r), is revisited in the modern context of subgrid cloud parameterization. The exact transition probability density for droplet radius driven by independent, Gaussian S fluctuations that are periodically renewed is derived and shown to be continuous but not smooth. The Fokker–Planck model follows naturally as the smooth-in-time approximation to this discrete-in-time process. Evolution equations for the moments of f (r) that include a contribution from subgrid S fluctuations are presented; these new terms are easily implemented in moment-based cloud schemes that resolve supersaturation. New, self-consistent expressions for the evolution of f (r) and mean supersaturation S in a closed, adiabatic volume are derived without approximation; quite appropriately, these coupled equations exactly conserve total water mass. The behavior of this adiabatic system, which serves as a surrogate for a closed model grid column, is analyzed in detail. In particular, a new nondimensional number is derived that determines the relative impact of S fluctuations on droplet spectral evolution, and the contribution of fluctuations to S is shown to be negative definite and maximal near the accommodation length and has a direct correspondence to the analysis of Cooper. Observational support for the theory of stochastic condensation is found in cloud droplet spectra from cumulus cloud fields measured during the Rain in the Cumulus over the Ocean (RICO) and Small Cumulus Microphysics Study (SCMS) campaigns. Increasing spectral broadening with increasing spatial scale is discovered and compares well with theoretical predictions. However, the observed spectra show evidence of non-Gaussian S fluctuations and inhomogeneous mixing, processes neglected in the current theory.