The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the particle inertia (Maxey 1987). Previous numerical results for particles in a random flow field, where the flow dynamics were not considered, showed an increase in the average settling velocity. Direct numerical simulations of the motion of heavy particles in isotropic homogeneous turbulence have been performed where the flow dynamics are included. These show that a significant increase in the average settling velocity can occur for particles with inertial response time and still-fluid terminal velocity comparable to the Kolmogorov scales of the turbulence. This increase may be as much as 50% of the terminal velocity, which is much larger than was previously found. The concentration field of the heavy particles, obtained from direct numerical simulations, shows the importance of the inertial bias with particles tending to collect in elongated sheets on the peripheries of local vortical structures. This is coupled then to a preferential sweeping of the particles in downward moving fluid. Again the importance of Kolmogorov scaling to these processes is demonstrated. Finally, some consideration is given to larger particles that are subject to a nonlinear drag force where it is found that the nonlinearity reduces the net increase in settling velocity.

Motivated by the need to resolve the condensation-coalescence bottleneck in warm rain formation, a significant number of studies have emerged in the past 15 years concerning the growth of cloud droplets by water-vapor diffusion and by collision-coalescence in a turbulent environment. With regard to condensation, recent studies suggest that small-scale turbulence alone does not produce a significant broadening of the cloud-droplet spectrum because of the smearing of droplet-scale fluctuations by rapid turbulent and gravitational mixing. However, different diffusional-growth histories associated with large-eddy hopping could lead to a significant spectral broadening. In contrast, small-scale turbulence in cumulus clouds makes a significant contribution to the collision-coalescence of droplets, enhancing the collection kernel up to a factor of 5, especially for droplet pairs with a low gravitational collision rate. This moderate level of enhancement has a significant impact on warm rain initiation. The multiscale nature of turbulent cloud microphysical processes and open research issues are delineated throughout.

The collision rate of monodisperse solid particles in a turbulent gas is governed by a wide range of scales of motion in the flow. Recent studies have shown that large-scale energetic eddies are the dominant factor contributing to the relative velocity between two colliding particles (the turbulent transport effect), whereas small-scale dissipative eddies can enhance the collision rate significantly by inducing local non-uniform particle distribution (the accumulation effect). The turbulent transport effect is most noticeable when the particle inertial response time τ_p is of the order of the flow integral timescale and the accumulation effect is most pronounced when τ_p is comparable to the flow Kolmogorov time.We study these two contributions separately through direct numerical simulations. The two effects are quantified carefully with a numerical procedure that is independent of the computation of average collision rate. This facilitates the study of not only the statistical description of the collision kernel, but also the relative contributions and modelling of the two physical effects. Simulations at several flow Reynolds numbers were performed to suggest a model for the accumulation effect. The data show that the accumulation effect scales linearly with flow Taylor microscale Reynolds number R_λ, while the theory for fully developed turbulence indicates that the maximum level of the turbulent transport effect scales with R^1/2_λ. Finally, an integrated model has been developed to predict the collision rate at arbitrary flow Reynolds numbers and particle inertia.

In this survey we consider the impact of turbulence on cloud formation from the cloud scale to the droplet scale. We assess progress in understanding the effect of turbulence on the condensational and collisional growth of droplets and the effect of entrainment and mixing on the droplet spectrum. The increasing power of computers and better experimental and observational techniques allow for a much more detailed study of these processes than was hitherto possible. However, much of the research necessarily remains idealized and we argue that it is those studies which include such fundamental characteristics of clouds as droplet sedimentation and latent heating that are most relevant to clouds. Nevertheless, the large body of research over the last decade is beginning to allow tentative conclusions to be made. For example, it is unlikely that small‐scale turbulent eddies (i.e. not the energy‐containing eddies) alone are responsible for broadening the droplet size spectrum during the initial stage of droplet growth due to condensation. It is likely, though, that small‐scale turbulence plays a significant role in the growth of droplets through collisions and coalescence. Moreover, it has been possible through detailed numerical simulations to assess the relative importance of different processes to the turbulent collision kernel and how this varies in the parameter space that is important to clouds. The focus of research on the role of turbulence in condensational and collisional growth has tended to ignore the effect of entrainment and mixing and it is arguable that they play at least as important a role in the evolution of the droplet spectrum. We consider the role of turbulence in the mixing of dry and cloudy air, methods of quantifying this mixing and the effect that it has on the droplet spectrum. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

The fundamental hypotheses underlying Kolmogorov-Oboukhov (1962) turbulence theory (K62) are examined directly and quantitutivezy by using high-resolution numerical turbulence fields. With the use of massively parallel Connection Machine-5, we have performed direct Navier-Stokes simulations (DNS) at 512³ resolution with Taylor microscale Reynolds number up to 195. Three very different types of flow are considered: free-decaying turbulence, stationary turbulence forced at a few large scales, and a 256³ large-eddy simulation (LES) flow field. Both the forced DNS and LES flow fields show realistic inertial-subrange dynamics. The Kolmogorov constant for the k^−5/3 energy spectrum obtained from the 512³ DNS flow is 1.68 ±.15. The probability distribution of the locally averaged disspation rate ε_r, over a length scale r is nearly log-normal in the inertial subrange, but significant departures are observed for high-order moments. The intermittency parameter p, appearing in Kolmogorov's third hypothesis for the variance of the logarithmic dissipation, is found to be in the range of 0.20 to 0.28. The scaling exponents over both ε_r, and r for the conditionally averaged velocity increments $\overline{\delta_ru|\epsilon_r}$ are quantified, and the direction of their variations conforms with the refined similarity theory. The dimensionless averaged velocity increments $(\overline{\delta_ru^n|\epsilon_r})/(\epsilon_rr)^{n/3}$ are found to depend on the local Reynolds number Re_εr = ε^1/3_rr^4/3/ν in a manner consistent with the refined similarity hypotheses. In the inertial subrange, the probability distribution of δ_ru/(ε_rr)^1/3 is found to be universal. Because the local Reynolds number of K62, R_εr = ε^1/3_rr^4/3/ν, spans a finite range at a given scale r as compared to a single value for the local Reynolds number R_r = ε^−1/3r^4/3/ν in Kolmogorov's (1941a,b) original theory (K41), the inertial range in the K62 context can be better realized than that in K41 for a given turbulence field at moderate Taylor microscale (global) Reynolds number R_λ. Consequently universal constants in the second refined similarity hypothesis can be determined quite accurately, showing a faster-than-exponential growth of the constants with order n. Finally, some consideration is given to the use of pseudo-dissipation in the context of the K62 theory where it is found that the probability distribution of locally averaged pseudo-dissipation ε^′_r deviates more from a log-normal model than the full dissipation ε_r. The velocity increments conditioned on ε′_r do not follow the refined similarity hypotheses to the same degree as those conditioned on ε_r.