1. Introduction
Clouds play a central role in Earth’s climate both through their interaction with radiation and through their role in the hydrological cycle. Warm clouds—those in which freezing does not occur—make a large contribution to the planetary albedo especially in the subtropics and produce 30% of the total rainfall globally and 70% of tropical rainfall (Lau and Wu 2003). Both cloud albedo and the rate of rain formation depend crucially on the size distribution of cloud droplets, but fundamental questions remain about the processes controlling the width and shape of this distribution.
When a moist air parcel is adiabatically lifted past its saturation level, water begins to condense around cloud condensation nuclei (CCN). The CCN size (or mass) distribution determines the initial size distribution for the droplets. Further condensational growth of the droplets is inversely proportional to their radius, and this entails an intrinsic tendency for the distribution to become narrower (Pruppacher and Klett 1997). However, observations have long shown that droplet size distributions in warm clouds are broad and often multimodal (Warner 1969). High-resolution observations show that even the narrowest measured distributions are broader than predicted by a conventional adiabatic parcel model (Brenguier and Chaumat 2001).
There is as yet no complete understanding of the processes that counteract condensational narrowing to broaden the distribution. This uncertainty poses a major roadblock in understanding the formation of warm-cloud precipitation (Devenish et al. 2012; Grabowski and Wang 2013). Growth to raindrop size requires collision and coalescence of droplets, which in turn requires significant velocity differences among droplets. Droplet fall speeds—governed by Stokes’s law—increase quadratically with radius, and significant collision rates are only achieved once a substantial subset of droplets has reached a size O(10) μm while those at the lower end of the distribution are still O(1) μm. This “condensation–coalescence bottleneck” in warm clouds remains a major unsolved problem.
Clouds are highly turbulent systems and turbulent stirring, entrainment, and mixing are observed to drive supersaturation and droplet density fluctuations down to centimeter scales (Beals et al. 2015). Turbulence may help overcome the bottleneck by facilitating droplet collisions, both by locally increasing droplet concentration (the inertial clustering effect; Sundaram and Collins 1997) and by generating droplet velocity differences (the sling effect; Falkovich et al. 2002). Here we focus on a different role of turbulence, namely, the broadening of droplet size spectra by differential condensation driven by turbulent supersaturation fluctuations. Droplets caught in the updraft of a turbulent eddy will experience greater supersaturation and will therefore grow faster than those caught in the downdraft (which may even experience subsaturation and evaporative loss). It is plausible that this effect will be stronger for larger eddies with stronger updrafts, so we may expect the resulting broadening to increase with increasing Reynolds number.
Early investigations of this effect relied on simplified stochastic models (Levin and Sedunov 1966; Mazin 1968; Bartlett and Jonas 1972; Srivastava 1989; Cooper 1989). A more recent approach is the so-called large-eddy hopping, which follows the different growth histories of many different droplets arriving at a given point inside a cloud, each experiencing a different supersaturation history as a result of entrainment and mixing (Lasher-Trapp et al. 2005; Cooper et al. 2011; Bewley and Lasher-Trapp 2011). Previous cloud simulations have been performed by means of large-eddy simulations, a numerical technique consisting in modeling cloud turbulence by solving the filtered Navier–Stokes equations. This technique requires a subgrid-scale model for the smallest scales of turbulence. Several LES studies describe the problems of cloud droplet growth by condensation in the atmospheric boundary layers such as Magaritz-Ronen et al. (2014) and Riechelmann et al. (2015). In the last years, increased computing power has enabled brute-force approaches in which direct numerical simulation (DNS) of the Navier–Stokes equations is used to generate turbulent velocity and supersaturation fields within a cubic domain containing a large swarm of droplets that are individually tracked as Lagrangian particles and allowed to interact with the supersaturation field. Such technique aims to capture the effect of turbulence within a small subdomain of the adiabatic (nonentraining) core of a cumulus cloud and it does not require any subgrid model. The first study of this type (Vaillancourt et al. 2002) used 5 × 104 droplets in a domain of about 10 cm3 with a resolution of 803 grid points. The main conclusion of this study was that small-scale turbulence rapidly moves droplets from regions of high and low supersaturation, without a significant increase of the variance of the droplet size spectrum. On the other hand, focusing on the large-scale turbulence fluctuations in a cloud of 100-m size, Celani et al. (2007) found a dramatic broadening of the droplet spectrum, although the dynamics of the small scales was not resolved since the simulation Kolmogorov scale was unrealistically large. The same effect was reported in Paoli and Shariff (2009), where an artificial forcing term was added to the supersaturation equation to mimic the effect of the large-scale eddies.
Lanotte et al. (2009) addressed the issue of the relative roles of small- and large-scale eddies in broadening droplet size spectra. These authors performed a series of DNS simulations progressively increasing the range of resolved scales, keeping the Kolmogorov scale fixed but increasing the external scale up to 70 cm including over 3 × 107 droplets with initially identical sizes. They found that the spectra broadened as the simulation proceeded; crucially, the broadening achieved after a fixed time increased as the domain size (and thus the Reynolds number) increased. They also provided scaling arguments to suggest that this increase in spectral width can be extrapolated to higher Reynolds number as a power law. These results suggest that the broadening effect of large-scale eddies becomes increasingly dominant as Reynolds number increases. Nevertheless, this broadening effect is limited by the value of the quasi-equilibrium supersaturation sqs as described in Grabowski and Wang (2013). In general, supersaturation fluctuations increase with the Reynolds number but cannot be larger than sqs, which weakly depends on the characteristic turbulent scale L of the system (sqs ∝ υrms ∝ L1/3 in the turbulent inertial range, where υrms indicates a characteristic velocity at scale L).
In recent work (Sardina et al. 2015), we focused on the time evolution of the droplet size spectrum. Using a modeling setup similar to Lanotte et al. (2009) but with a domain size up to 3 m and longer simulation times, we found that the width of the droplet spectrum increases continuously in time as t1/2. Further, we found that the broadening rate is linearly dependent on the ratio between the large and the small turbulent scales, that is, proportional to the Reynolds number. We also presented a simple stochastic model that quantitatively predicts the broadening rates in the numerical simulations and can be used to extrapolate to greater Reynolds numbers. A simplified version of our stochastic model, involving just the time evolution of the supersaturation field, was recently tested and experimentally validated in a laboratory cloud chamber (Chandrakar et al. 2016), showing excellent agreement between the model and experimental data. These results imply that the width of the droplet size distribution can become realistically large at any Reynolds number so long as one waits long enough; for realistic cloud Reynolds numbers, the time required is about 20 min. In the same context, new stochastic approaches have been developed more recently. Siewert et al. (2017) extended our stochastic model to the case where droplets are allowed to fully evaporate and also accounting for the variation of the supersaturation relaxation time. Grabowski and Abade (2017) formulated a new stochastic model aimed at improving subgrid-scale modeling in LESs.
For the sake of simplicity, Sardina et al. (2015) made several unrealistic assumptions. In particular, the cloudy parcel was assumed to be stationary, with a domain-mean supersaturation held fixed at zero. Also, the droplets were assumed to be initially monodisperse with a radius of 10 μm. Here, we extend our previous work by relaxing these assumptions, including the effect of a mean updraft velocity and examining activation of CCN of different composition. Given the current computational resources, studies involving CCN activation either include a complete representation of cloud turbulence while using a simple representation of cloud microphysics (Lasher-Trapp et al. 2005; Bewley and Lasher-Trapp 2011) or rely on simple methods for representing cloud turbulence using a more complete representation of the cloud microphysics (Jensen and Nugent 2017). Very few studies have addressed the question in simple homogeneous isotropic turbulence and for computational expedience used two-dimensional DNS (Celani et al. 2008, 2009).
Our modeling setup and assumptions are discussed in section 2. In section 3 we briefly review the results of Sardina et al. (2015) and elucidate the physical mechanisms underlying the time-dependent turbulent broadening. Section 4a considers the effect of a mean updraft velocity on the spectrum evolution of initially large droplets, while in section 4b we study the influence of droplet activation and deactivation by conducting simulations starting from cloud condensation nuclei. Finally, Section 5 presents a discussion and conclusions.
2. Model description







































In general, droplet dynamics can be described by two different approaches: Lagrangian and Eulerian. In the Lagrangian approach, each droplet is tracked along its motion around the cloud. Equations for their position, velocity, and radius must be numerically solved, and particle–particle interactions and collisions can be described in a natural way (Paoli and Shariff 2009; Lanotte et al. 2009; de Lozar and Muessle 2016). The computational requirements of this approach using realistic droplet numbers can be prohibitive, so the use of a renormalization method or the so-called superdroplet approach is necessary (Shima et al. 2009). Alternatively, the droplet dynamics can be described following the Eulerian approach in terms of a conservation equation for the droplet distribution














We solve the Eulerian equations for the turbulent flow with a pseudospectral method on a uniform grid employing three-dimensional fast Fourier transforms. Time integration is performed with a low-storage third-order Runge–Kutta where the nonlinear terms are computed via an Adam–Bashforth-like approximation and the diffusive terms analytically integrated (Rogallo 1981). Nonlinear terms are classically computed in physical space and dealiased with a standard 2/3 rule. The same time integration scheme is used for the droplet evolution and a three linear interpolation/extrapolation scheme is used to estimate the variables from the Eulerian to the Lagrangian reference frames and vice versa. Droplet velocity and radius are integrated in time with an implicit scheme (predictor–corrector) (Olivieri et al. 2014) to avoid the use of a very small time step associated with a low droplet relaxation time and low values of the droplet radius. Note that, although included, we have verified that the effect of droplet inertia could be safely neglected for our parameter range. [The initial Stokes numbers of the simulations are shown in Table 2. The Stokes number is based on the Kolmogorov time scale
We performed 12 different simulations divided into three groups differing in the chemical composition of the initial salt nuclei. In particular we evolve (i) already-activated droplets with initial radius R0 = 13 μm and no nucleus salt, (ii) (NH4)SO4 salt CCN with initial radius R0 = 0.24 μm, and (iii) NaCl salt CCN with initial radius R0 = 0.022 27 μm. The chemical and physical properties of the three droplet populations are summarized in Table 1. For each droplet family we perform four simulations differing in the updraft velocity W, spanning the range from 0 to 1 m s−1. Each simulation uses a mesh of 2563 grid points with 70 million droplets. A droplet renormalization method is employed to achieve an equivalent concentration of 130 droplets per cubic centimeter and to keep at least 3–6 droplets per computational cell (Lanotte et al. 2009). The renormalization procedure is necessary since we cannot evolve each single droplet inside a 100-m cloud with the actual computational resources (1014 droplets in our case). A renormalization factor of 2 × 106 has been used in our simulations. The use of a renormalization approach is commonly used in the superdroplet method to account the droplet–droplet collisions; the renormalization factor is also called multiplicity. Each simulation is integrated up to a final time of 20 min and is characterized by a root-mean-square turbulent velocity fluctuation of 0.7 m s−1, an integral time scale
Parameters of the numerical simulations for the turbulent gas flow: Lbox, cloud size; Δ, numerical resolution; Reλ, Taylor Reynolds number; ε, turbulent kinetic energy dissipation; υrms, turbulent velocity fluctuations; TL, Eulerian large-eddy turn over time; T0, Lagrangian integral time; 〈s0〉, initial average supersaturation field;
Parameters defining the CCN of the present simulations: critical radius and critical supersaturation depending on the salt composition and initial supersaturation relaxation time.
3. Broadening of the droplet size distribution
In this section, we extend the main results of our previous study (Sardina et al. 2015). In Sardina et al. (2015), we conducted DNSs and LESs using the same model used here (see section 2) with updraft W = 0 and neglecting the Kelvin and Raoult terms in Eq. (11), initializing the simulations with droplets large enough to ensure that they remained well above the critical activation radius at all times. We also derived a simple stochastic model able to accurately reproduce the time evolution of the droplet size spectrum. As in the present work, we did not consider entrainment (Kumar et al. 2014), collisions, or inhomogeneity, so that the size spectrum evolution is driven only by the supersaturation fluctuations.























Equation (28) shows that
Time evolution of the squared radius for 50 different individual droplets obtained with (left) the stochastic model and (right) LES. The black solid lines represent the evolution of the standard deviation.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0241.1
The analytical result above is limited by the droplet size, especially when the droplets are small as shown recently by Siewert et al. (2017). Our theoretical model assumes any possible value for the variable subjected to random walk R2; however, the droplet squared radius cannot become negative by definition and a boundary condition should be included in the model. The quantity R2 can be prescribed to be always positive as in Siewert et al. (2017) or subject to activation/deactivation (the Kölher effect) as we do in the present manuscript. In both cases, the particle size distribution reaches a steady state even without updraft velocity since the continuous broadening by condensation is limited for small values of R2. Our stochastic model can therefore be used as a subgrid-scale model for the unresolved supersaturation in large-eddy simulation using a similar approach developed in Grabowski and Abade (2017).
4. Results
In this section we examine how the results described in the previous section change when a constant mean updraft W > 0 is introduced and when the droplet radii are allowed to drop below the critical radius so that droplet activation and deactivation become important.
a. Effect of mean updraft velocity
The presence of a mean updraft velocity induces several changes in the numerical and theoretical results shown in the previous section. The most obvious difference is that a mean updraft induces positive mean supersaturation inside the parcel and consequently a growing mean droplet radius. The top row of Fig. 2 shows the time evolution of the mean supersaturation field and of the mean radius for the sequence of runs initialized with a monodisperse droplet population (top row in Table 2). In all cases with W > 0, after an initial transient adjustment the mean supersaturation settles on a positive steady value in which the production of supersaturation by mean ascent [second term on the rhs of Eq. (5)] is balanced in the mean by condensation onto cloud droplets [last term on the rhs of Eq. (5)]. Droplets are on average gaining mass, and their mean radius increases monotonically (Fig. 2, top right). The W = 0 case is a little more subtle. In this case, mean supersaturation settles on a value just above zero; this is because the curvature term in the Köhler equation [Eq. (11)] increases the equilibrium vapor pressure slightly. There is no mean production of supersaturation and there is no mean change in total liquid water. Somewhat surprisingly, however, the mean droplet radius decreases over time.
Temporal evolution of (top left) mean cloud supersaturation, (top right) mean droplet radius, (bottom left) supersaturation standard deviation, and (bottom right) ratio between mean and standard deviation supersaturation for the largest droplets.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0241.1
The bottom panels of Fig. 2 show the time behavior of the supersaturation standard deviation (bottom left) and the ratio between mean and standard deviation of the supersaturation distribution (bottom right). For the chosen parameters, the supersaturation standard deviation depends weakly on the updraft velocity, decreasing slightly with the intensity of the updraft. This decrease is consistent with the stochastic model. The last term on the right-hand side of Eq. (25) is responsible of this small difference. Nonetheless, the quasi-steady approximation












(top left) Squared droplet radii pdf after 20 min of simulation for the largest droplets. Temporal evolution of squared droplet radius (top right) standard deviation, (bottom left) skewness, and (bottom right) kurtosis for the largest droplets.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0241.1
Correlation between the squared-radius fluctuations and the supersaturation fluctuations
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0241.1
b. The role of droplet activation/deactivation
In the simulations presented in the previous section, the particles have been assumed to have an initial radius of 13 μm and no droplets came close to the critical activation radius in any of the simulations. Now, we show how the condensation dynamics can change when starting directly from CCN. We analyze two populations: ammonium sulfate [(NH4)SO4] and sodium chloride (NaCl). The two populations differ in chemical and physical properties and, consequently, critical activation radius and critical supersaturation.
The time evolution of the mean supersaturation and mean droplet radius are shown in the top-left and top-right panels of Fig. 5, respectively, for the case of (NH4)SO4. The Kölher terms induce nonlinear effects for small radii, which prevents the droplet to evaporate in a negative supersaturation field in the absence of updraft. The mean radius is almost constant in time, around a value of 2 μm. By increasing the updraft velocity, the mean radius starts to grow similarly to the case without CCN. The time evolution of the supersaturation standard deviation is shown in the bottom-left panel for all simulations. The values plotted in the figure can be roughly estimated by using the quasi-equilibrium prediction
Temporal evolution of (top left) mean cloud supersaturation, (top right) mean droplet radius, (bottom left) supersaturation standard deviation, and (bottom right) ratio between mean and standard deviation supersaturation for (NH4)SO4 salt CCN.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0241.1
The final droplet size distribution is shown in the top-left panel of Fig. 6. Two completely different behaviors emerge. For the largest updrafts, the pdfs are Gaussian, whereas the distributions depart consistently from the Gaussian distribution for the smallest updrafts. In the latter cases, the pdfs show a “haze peak” in correspondence to the critical CCN radius. The pdf pertaining to the case of zero updraft is qualitatively similar to that found in simulations of two-dimensional turbulence (Celani et al. 2008) and the distribution embraces a scale interval of more than two decades even for an updraft of 0.1 m s−1, with long and persistent tails. For the cases of higher updraft, we observe a saturation in time of the distribution for the 1 m s−1 updraft velocity as revealed by the time evolution of the distribution moments shown below. This can be of fundamental importance to estimate the droplet collision dynamics. We therefore examine the moments of the pdfs and report the standard deviation in the top-right panel of Fig. 6. Interestingly, the case with zero updraft substantially differs from the previous simulation with large droplets. Here, we observe a saturation of the droplet size standard deviation in time rather than a monotonic increase. On the other hand, the monotonic behavior in time can be observed for the intermediate updraft velocities. Since the cases with lower updraft velocities show highly non-Gaussian pdfs, the standard deviation does not give enough information on the droplet size spectrum. Figure 6 also shows the skewness (bottom left) and kurtosis (bottom right) of the size spectrum versus time. The data for the higher updraft values confirm that the droplet sizes have an almost Gaussian distribution since their skewness and kurtosis are about 0 and 3, respectively, like a pure Gaussian distribution. A positively skewed distribution is instead found for the two smaller updrafts examined. The positive value of skewness implies the presence of a right tail in the pdf and the lack of symmetry in the spectrum distribution. After time t ≈ 500 s, the pdf has high kurtosis in the zero-updraft case, revealing the presence of large tails and that the droplet distribution reaches a steady state. The high value of kurtosis is about 3 times bigger than the one of the Gaussian distribution, implying that the pdf tails are persistent and decay slowly compared to the Gaussian one. The presence of this long and not symmetric right tail could be crucial for the following gravitational collisional stage of rain formation.
(top left) Squared droplet radii probability density function pdf after 20 min of simulation for (NH4)SO4 salt CCN. Temporal evolution of squared droplet radius (top right) standard deviation, (bottom left) skewness, and (bottom right) kurtosis for (NH4)SO4 salt CCN.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0241.1
The results for the case of the aerosol marine salt (NaCl) are depicted in Fig. 7: the main findings are consistent with those for the (NH4)SO4 aerosols discussed in Fig. 5. The only exceptions are found for the zero-updraft case where the water droplets are smaller in size and thus more dependent on the chemical composition of their nucleus. However, although the global supersaturation and average radius are similar for the two aerosol populations, the droplet size distribution is completely different, as shown in Fig. 8. The droplet size spectrum is shown in the top-left panel, where it is possible to distinguish three different regions: (i) The haze region around the droplet activation radius shows a very clear peak for all the updrafts considered. The peak is more pronounced and distinguished from that in the case of (NH4)SO4 nuclei and clearly divides the nonactive from the active particles. The pdf of the nonactive droplets decays as a power law when decreasing the droplet dimensions; the exponent of the power law is around 1.5. (ii) An intermediate zone, characterized by a plateau in the size distribution, defines the active droplets up to 2–3 μm. (iii) For larger particles, those less influenced by their nucleus chemical composition, the droplet distribution recovers the behavior of the population considered previously. It is remarkable that, in this case, there is a difference of about six orders of magnitude between the squared radii of the larger and smaller droplets, to which corresponds the same variation in droplet terminal velocity with obvious consequences for collision rates. This broad spectrum appears for all the updraft velocities under consideration, with the larger updrafts showing a more distinct bimodal behavior. The previous observations are reflected in the high values of the rms of R2 reported in the top-right panel of Fig. 8. Since we consider in this case droplets of smaller radius, the zero-updraft distribution has not yet reached the steady state and its standard deviation continues to increase at the final simulation time; we believe the steady state will be reached at a later time. The loss of a quasi-Gaussian pdf at the larger updrafts is measured by the skewness of the distribution (bottom left panel): indeed, larger updrafts show a negatively skewed distribution in the droplet size spectra. High values of the kurtosis are also evident in almost all cases.
Temporal evolution of (top left) mean cloud supersaturation, (top right) mean droplet radius, (bottom left) supersaturation standard deviation, and (bottom right) ratio between mean and standard deviation supersaturation for NaCl salt CCN.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0241.1
(top left) Squared droplet radii probability density function pdf after 20 min of simulation for NaCl salt CCN. Temporal evolution of square droplet radius (top right) standard deviation, (bottom left) skewness, and (bottom right) kurtosis for NaCl salt CCN.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0241.1
For the results just presented, we initially assumed the particle radius to be the radius of the salt condensation nucleus. We did several tests only changing the value of the initial droplet radius, from the activation radius to 5 μm and, surprisingly, obtained the same results. These results are therefore dependent only on the chemical composition of the condensation nuclei and independent on the initial radius distribution. This effect is a consequence of the initial conditions of the supersaturation field. The initial field is generated without the presence of the droplets and it is characterized by a larger standard deviation (1%). When the CCN are injected, many of them are activated instantaneously depending only of the value of c and h and the average radius of the droplet is on the order of 2–3 μm. For these reasons, the effect of the aerosol size is subleading. We understand that the choice of the initial condition can be arbitrary but our initial conditions are not so far from the recent experiments measures by Siebert and Shaw (2017). These authors found that at the early stages of cloud formation the fluctuations of the supersaturation are observed to be approximately normally distributed with standard deviations on the order of 1%. This variability is almost one order of magnitude larger than the steady-state value of the supersaturation as we also find in our numerical results.
5. Discussion and conclusions
A series of LESs of homogeneous isotropic turbulence has been analyzed to illustrate the growth of water droplets via condensation/evaporation in turbulent clouds. The effects of a mean-flow vertical updraft and of the droplet nucleus chemical compositions have been also investigated. In particular, in absence of updraft the droplet squared radii follow a classical random walk behavior, as already described in our previous work (Sardina et al. 2015). The standard deviation of the droplet size distribution increases in time as a power law, t1/2. At fixed time, the standard deviation of the droplet size distribution is bounded by the value of the quasi-equilibrium supersaturation sqs (Grabowski and Wang 2013) and is proportional to the larger turbulent scales of the cloud L2/3. This scenario is modified by the presence of a mean updraft velocity: the power law exponent becomes less than 1/2, and the standard deviation is observed to asymptote to a constant for updraft velocities on the order of 1 m s−1. The overall effect is a reduction of the droplet growth, in agreement with the results from the simulations of Gotoh et al. (2016). We have presented an extended stochastic model that, for the first time, is able to analytically predict this reduction in droplet spectral broadening. The model shows that the steady-state value of the droplet distribution standard deviation is inversely proportional to the square root of the average supersaturation field and directly proportional to the turbulence Reynolds number. This result arises from the fact that a positive average supersaturation field induces a decorrelation of the radius growth from the local resolved supersaturation field.
The power-law behavior observed at zero updraft for large droplets t1/2 is modified also in presence of small droplets on the order of the critical radius inside the cloud domain. When droplets reach the critical radius, their evaporation is blocked by the chemical properties of its salt nucleus and a deviation from a classic random walk behavior is observed. This is associated to the saturation of the droplet growth for the zero-updraft case and reflected in the droplet squared-radius spectra. While for large particles the distribution is purely Gaussian, smaller particles tend to strongly deviate from a Gaussian behavior. The right tail of the distribution tends to resemble a Gaussian behavior while the left tail is characterized by a peak in correspondence of the haze activation radius. The strong deviations of the droplet spectrum from a Gaussian distribution will be crucial for the later stages of droplet growth, which are dominated by droplet collisions. Growth by turbulent and gravitationally induced collisions strongly depends on both droplet size and droplet number distributions. For the NaCl CCN we observe the existence of six orders of magnitude difference between the squared radii of the larger and smaller droplets, associated with a similar difference in droplet terminal velocity. This huge difference in droplet terminal velocity can enhance the efficiency of gravitational collisions. The study of turbulence induced collisions is fundamental to continue the investigation of the size gap in warm-cloud rain formation. Droplet collisions occur at small scales so that an LES technique is not suitable to investigate this phenomenology. Novel highly resolved DNSs are needed to address this phenomenology and to be able to derive new collision kernel and models to be incorporated in an LES. The simulations described in the paper represent a unique dataset to study the effect of CCN activation/deactivation in three-dimensional homogeneous isotropic turbulence and can be used to improve the current microphysical models in the presence of turbulence.
Acknowledgments
This work was supported by the Swedish e-Science Research Centre (SeRC), by the European Research Council Grant ERC-2013-CoG-616186, TRITOS, and by the Swedish Research Council (VR) Grants 621-2014-5319 and 2014-5001. Computer time provided by SNIC (Swedish National Infrastructure for Computing) is gratefully acknowledged. This article is based upon work from COST Action MP1305, supported by COST (European Cooperation in Science and Technology).
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