Cloud Droplet Growth by Condensation in Homogeneous Isotropic Turbulence

Abstract

The growth of cloud droplets by diffusion of water vapor in a three-dimensional homogeneous isotropic turbulent flow is considered. Within a simple model of advection and condensation, the dynamics and growth of millions of droplets are integrated. A droplet-size spectra broadening is obtained and it is shown to increase with the Reynolds number of turbulence by means of two series of direct numerical simulations at increasing resolution. This is a key point toward a proper evaluation of the effects of turbulence for condensation in warm clouds, where the Reynolds numbers typically achieve extreme values. The obtained droplet spectral broadening as a function of the Reynolds number is shown to be consistent with dimensional arguments. A generalization of this expectation to Reynolds numbers not accessible by direct numerical simulation (DNS) is proposed, yielding upper and lower bounds to the actual size spectra broadening. It is argued that the lower bound is the relevant limit at high Reynolds numbers. A further DNS matching the large scales of the system suggests consistency of the picture drawn. The assumptions underlying the model are expected to hold up to spatial scales on the order of 100 m; no direct comparison with in situ measures is possible. Additional effort is needed to evaluate the impact of this effect for condensation in more realistic cloud conditions.

Droplet growth in warm turbulent clouds

“…As the discussion here and in the previous paragraph suggests, there remains some dispute over the importance of gravity in the study of droplets with radii less than 20 µm, with some authors arguing that sedimentation substantially reduces the supersaturation perturbations and consequently the width of the droplet size distribution (Vaillancourt et al, 2001(Vaillancourt et al, , 2002, while others argue that it is not significant (see the discussion in Vaillancourt, 1999, andShaw et al, 1999). Lanotte et al (2009) also considered the condensational growth of droplets in 3-D DNS (for R λ ranging from 40 to 185). Their results show that the standard deviation of the squared droplet radius, σ a 2 , grows linearly with the largeeddy turnover time (for approximately constant ε), from which they argued that σ a 2 ∼ R 5/2 λ .…”

“…This scaling assumes that the standard deviation of the supersaturation, σ s , does not deviate significantly from its initial value. At Reynolds numbers typical of real clouds, for which the large-eddy turnover time will be much larger than in the DNS of Lanotte et al (2009), this assumption may no longer hold. Lanotte et al (2009) argue that a more appropriate scaling follows from assuming that σ s takes its equilibrium value.…”

“…This simplification is frequently applied in numerical models of droplet condensation in turbulence which employ the socalled point-particle approach to describe the evolution of the droplet phase (e.g. Vaillancourt et al, 2002;Celani et al, 2007;Lanotte et al 2009). …”

“…These two scalings then represent respectively lower and upper bounds on the Reynolds number dependence of σ a 2 . Lanotte et al (2009) test their hypothesis by conducting a quasi-LES (DNS that matches typical large-scale cloud parameters but with unrealistic small scales such as η and τ η ) so that the large-eddy turnover time is now much larger than τ s and s tends to s qe . They find that, at large times, σ a 2 is close to its lower bound.…”

“…In such an approach, the Eulerian fluid flow model is coupled to the Lagrangian representation of the thermodynamics (see, for example, Andrejczuk et al, 2008Andrejczuk et al, , 2010Shima et al, 2009). This approach is in the spirit of the pseudo-LES simulations presented in Lanotte et al (2009) and discussed in section 4.1.3.…”