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Two case studies of marine stratocumulus (one nocturnal and drizzling, the other daytime and nonprecipitating) are simulated by the UCLA large-eddy simulation model with bin microphysics for comparison with aircraft in situ observations. A high-bin-resolution variant of the microphysics is implemented for closer comparison with cloud drop size distribution (DSD) observations and a turbulent collision–coalescence kernel to evaluate the role of turbulence on drizzle formation. Simulations agree well with observational constraints, reproducing observed thermodynamic profiles (i.e., liquid water potential temperature and total moisture mixing ratio) as well as liquid water path. Cloud drop number concentration and liquid water content profiles also agree well insofar as the thermodynamic profiles match observations, but there are significant differences in DSD shape among simulations that cause discrepancies in higher-order moments such as sedimentation flux, especially as a function of bin resolution. Counterintuitively, high-bin-resolution simulations produce broader DSDs than standard resolution for both cases. Examination of several metrics of DSD width and percentile drop sizes shows that various discrepancies of model output with respect to the observations can be attributed to specific microphysical processes: condensation spuriously creates DSDs that are too wide as measured by standard deviation, which leads to collisional production of too many large drops. The turbulent kernel has the greatest impact on the low-bin-resolution simulation of the drizzling case, which exhibits greater surface precipitation accumulation and broader DSDs than the control (quiescent kernel) simulations. Turbulence effects on precipitation formation cannot be definitively evaluated using bin microphysics until the artificial condensation broadening issue has been addressed.

An open question in cloud physics is how rain forms in warm cumulus as rapidly as it is sometimes observed. In particular, the growth of cloud droplets across the size gap from 10 to 50 μm in radius has not been fully explained. In this paper, the authors investigate the growth of cloud droplets by collision–coalescence, taking into account both the gravitational mechanism and several enhancements of the collision–coalescence rate due to air turbulence. The kinetic collection equation (KCE) is solved with an accurate bin integral method and a newly developed parameterization of turbulent collection kernel derived from direct numerical simulation of droplet-laden turbulent flows. Three other formulations of the turbulent collection kernel are also considered so as to assess the dependence of the rain initiation time on the nature of the collection kernel. The results are compared to the base case using the Hall hydrodynamical–gravitational collection kernel. Under liquid water content and eddy dissipation rate values typical of small cumulus clouds, it is found that air turbulence has a significant impact on the collection kernel and thus on the time required to form drizzle drops. With the most realistic turbulent kernel, the air turbulence can shorten the time for the formation of drizzle drops by about 40% relative to the base case, applying measures based on either the radar reflectivity or the mass-weighted drop size. A methodology is also developed to unambiguously identify the three phases of droplet growth, namely, the autoconversion phase, the accretion phase, and the larger hydrometeor self-collection phase. The important observation is that even a moderate enhancement of collection kernel by turbulence can have a significant impact on the autoconversion phase of the growth.

Riemer and Wexler (2005, henceforth RW05) have utilized the turbulent collision kernel model of Zhou et al. (2001) to study the effect of turbulence on the initiation and development of raindrops from cloud droplets. They concluded that, for a cloud dissipation rate at 300 cm s , turbulent coagulation can move 96% of the droplet mass to sizes over 100 m in radius in 30 min, as compared to only 7% without turbulence. This result shows that turbulence is capable of rapidly transforming droplets to sizes for which the gravitational coagulation can operate effectively, thus overcoming the size-gap bottleneck for rain initiation. Under the assumption that the turbulent collision kernel of Zhou et al. (2001) can be extrapolated to atmospheric Reynolds numbers, RW05 found that the turbulent coagulation kernel is several orders of magnitude larger than the sedimentation kernel for droplets smaller than 100 m. We believe that the effects of turbulence have been grossly overestimated in RW05 for reasons to be discussed below. First, we would like to point out an error in RW05 that led to an overestimation of the rms velocity u by a factor of 3 and thus an overestimation of the Taylor microscale Reynolds number R by a factor of 3. RW05’s estimations were based on the rms velocity u and the average cloud dissipation rate on the in-cloud measurements by MacPherson and Isaac, shown in Table 1 of MacPherson and Isaac (1977). The cloud turbulence is anisotropic and a rough estimate of u for equivalent isotropic turbulence would be

Prediction of the effect of air turbulence on statistics relevant to a collision–coalescence process represents a key challenge in the modeling of cloud microphysics. In this paper, collision-related statistics for gravity-driven motion of droplets are considered and various probability distributions associated with geometric configuration and relative motion of colliding droplets are theoretically derived. The theoretical results agree well with numerical results obtained from direct numerical simulations (DNSs). In the absence of air turbulence, the probability distributions, calculated at the beginning of the time steps used for collision detection, nontrivially depend on the time step size. Next, a novel theory is developed to quantify the effect of turbulence on the angle-of-approach θ and radial relative velocity |wr,c| for colliding pairs. A logical decomposition is used to construct extended collision volumes for a specific level of radial motion caused by air turbulence. It is shown that the inward relative motion due to turbulent fluctuations dominates the effect of turbulence in modifying the probability distributions of θ and |wr,c|. Two key dimensionless parameters are identified in the theory: one measures the effect of finite time step size in numerical collision detection and the second measures the relative magnitude of air turbulence. The theory is compared with 11 numerical experiments from DNS. It is shown that the theory captures the essential physics of the effect of air turbulence and provides a quantitatively good representation of the statistics for θ. For most numerical experiments, the theory predicts 〈θ〉 to within 5%. The probability distribution of |wr,c| is more sensitive to the influence of air turbulence and shows larger intermittency at large |wr,c| than what is assumed in the theory. The theoretical framework developed here may be of value to other problems involving gravitational settling and weak turbulence, such as parameterization of collision kernel and hydrodynamic interactions of droplets in warm rain processes.

A methodology for conducting direct numerical simulations (DNSs) of hydrodynamically interacting droplets in the context of cloud microphysics has been developed and used to validate a new kinematic formulation capable of describing the collision rate and collision efficiency of cloud droplets in turbulent air. The theoretical formulation is formally the same as the formulation recently developed for geometrical collision rate of finite-inertia, nonsettling particles. It is shown that its application to hydrodynamically interacting droplets requires corrections because of a nonoverlap requirement. An approximate method for correcting the kinematic properties has been developed and validated against DNS data. The formulation presented here is more general and accurate than previously published formulations that, in most cases, are some extension to the description of hydrodynamic–gravitational collision. General dynamic and kinematic representations of the properly defined collision efficiency in a turbulent flow have been discussed. In addition to augmenting the geometric collision rate, air turbulence has been found to enhance the collision efficiency because, in a turbulent flow, hydrodynamic interactions become less effective in reducing the average relative radial velocity. The level of increase in the collision efficiency depends on the flow dissipation rate. For example, the collision efficiency between droplets of 20 and 25 μm in radii is increased by 59% and 10% by air turbulence at dissipation rates of 400 and 100 cm2 s−3, respectively. It is also shown that hydrodynamic interactions lead to higher droplet concentration fluctuations. The formulation presented here separates the effect of turbulence on collision efficiency from the previously observed effect of turbulence on the geometric collision rate.

Two formulations of an improved superposition method are proposed for studying droplet–droplet hydrodynamic interactions. The formulations make explicit use of the boundary conditions on the surface of the two interacting droplets. The improved formulations are described through a consistent and rigorous consideration of the relationship between the drag force and representation of disturbance flows. It is demonstrated that the improved formulations are much more accurate than the original implementation of the superposition method. Specifically, for the case of Stokes disturbance flows, the relative errors on the drag force can be reduced by one order of magnitude using the improved formulations, when compared with the original formulation, for situations when the lubrication effect is not dominant. Using the improved superposition method, collision efficiencies of small cloud droplets falling in calm air are also computed and compared with previously published results.

Accurate prediction of heavy particle dispersion in turbulent flows requires a simultaneous consideration of particle's inertia and particle's drift velocity. A mathematically simple and physically comprehensive analysis was developed to solve the dispersion statistics of heavy particles in a homogeneous and isotropic turbulent flow. Normalized particle diffusivity, rms fluctuating velocity, and Lagrangian integral time were related by algebraic equations to three dimensionless parameters: the inertia parameter, the drift parameter, and the turbulence structure parameter. When the drift parameter is large, dispersion scales are very sensitive to the inertia parameter. Heavy particles were found to disperse faster than fluid elements if the inertia parameter controls the dispersion and slower than fluid elements if the drift parameter governs the dispersion. This finding explains previous “contradictory” dispersion data observed in experimental measurements. Not only the particle time respective b...