Droplet growth in warm turbulent clouds

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

[1]  V. M. Alipchenkov,et al.  Pair dispersion and preferential concentration of particles in isotropic turbulence , 2003 .

[2]  W. Grabowski,et al.  NOTES AND CORRESPONDENCE Modeling of Subgrid-Scale Mixing in Large-Eddy Simulation of Shallow Convection , 2009 .

[3]  S. Shima,et al.  The super‐droplet method for the numerical simulation of clouds and precipitation: a particle‐based and probabilistic microphysics model coupled with a non‐hydrostatic model , 2007, physics/0701103.

[4]  Shintaro Kawahara,et al.  J an 2 00 7 Super-Droplet Method for the Numerical Simulation of Clouds and Precipitation : a Particle-Based Microphysics Model Coupled with Non-hydrostatic Model , 2008 .

[5]  Alexander Khain,et al.  Effects of in‐cloud nucleation and turbulence on droplet spectrum formation in cumulus clouds , 2002 .

[6]  M. Reeks,et al.  Statistical properties of particle segregation in homogeneous isotropic turbulence , 2011, Journal of Fluid Mechanics.

[7]  P. Vaillancourt,et al.  Review of Particle–Turbulence Interactions and Consequences for Cloud Physics , 2000 .

[8]  Raymond A. Shaw,et al.  Statistics of Small-Scale Velocity Fluctuations and Internal Intermittency in Marine Stratocumulus Clouds , 2010 .

[9]  C. Franklin A Warm Rain Microphysics Parameterization that Includes the Effect of Turbulence , 2008 .

[10]  M. Reeks,et al.  Segregation of particles in incompressible random flows: singularities, intermittency and random uncorrelated motion , 2010, Journal of Fluid Mechanics.

[11]  D. Randall,et al.  Large-Eddy Simulation of Evaporatively Driven Entrainment in Cloud-Topped Mixed Layers , 2006 .

[12]  Hui Meng,et al.  Experimental and numerical investigation of inertial particle clustering in isotropic turbulence , 2008, Journal of Fluid Mechanics.

[13]  Some analytical calculations on the effect of turbulence on the settling and growth of cloud droplets , 2001 .

[14]  J. Turner,et al.  Jets and plumes with negative or reversing buoyancy , 1966, Journal of Fluid Mechanics.

[15]  M. Maxey,et al.  Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence , 1993, Journal of Fluid Mechanics.

[16]  Hanna Pawlowska,et al.  An observational study of drizzle formation in stratocumulus clouds for general circulation model (GCM) parameterizations , 2003 .

[17]  A. Prasad,et al.  Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration , 2005 .

[18]  H. Gerber,et al.  Microphysics of Marine Stratocumulus Clouds with Two Drizzle Modes , 1996 .

[19]  Z. Warhaft,et al.  Intermittency and inertial particle entrainment at a turbulent interface: the effect of the large-scale eddies , 2012, Journal of Fluid Mechanics.

[20]  A. Blyth,et al.  Entrainment in Cumulus Clouds , 1993 .

[21]  Szymon P. Malinowski,et al.  Small scale mixing processes at the top of a marine stratocumulus—a case study , 2007 .

[22]  R. Rogers,et al.  A short course in cloud physics , 1976 .

[23]  A. Wexler,et al.  Statistical mechanical description and modelling of turbulent collision of inertial particles , 1998, Journal of Fluid Mechanics.

[24]  F Toschi,et al.  Heavy particle concentration in turbulence at dissipative and inertial scales. , 2006, Physical review letters.

[25]  Piotr K. Smolarkiewicz,et al.  Numerical Simulation of Cloud–Clear Air Interfacial Mixing: Effects on Cloud Microphysics , 2006 .

[26]  Paul A. Vaillancourt,et al.  Microscopic approach to cloud droplet growth by condensation , 1998 .

[27]  B. Baker Turbulent Entrainment and Mixing in Clouds: A New Observational Approach , 1992 .

[28]  G. Falkovich,et al.  Intermittent distribution of heavy particles in a turbulent flow , 2004 .

[29]  L. Collins,et al.  Preferential Concentration of Cloud Droplets by Turbulence: Effects on the Early Evolution of Cumulus Cloud Droplet Spectra , 1998 .

[30]  S. Twomey,et al.  The nuclei of natural cloud formation part II: The supersaturation in natural clouds and the variation of cloud droplet concentration , 1959 .

[31]  J. Deardorff Cloud Top Entrainment Instability , 1980 .

[32]  J C Vassilicos,et al.  Rapid growth of cloud droplets by turbulence. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  J. Broadwell,et al.  A simple model of mixing and chemical reaction in a turbulent shear layer , 1982, Journal of Fluid Mechanics.

[34]  K. Shariff,et al.  Turbulent Condensation of Droplets: Direct Simulation and a Stochastic Model , 2009 .

[35]  B. Stevens,et al.  Elements of the microphysical structure of numerically simulated nonprecipitating stratocumulus , 1996 .

[36]  James G. Hudson,et al.  Entrainment, Mixing, and Microphysics in Trade-Wind Cumulus , 2008 .

[37]  Anthony S. Wexler,et al.  Droplets to Drops by Turbulent Coagulation , 2005 .

[38]  R. C. Srivastava Growth Of Cloud Drops by Condensation: A Criticism of Currently Accepted Theory and a New Approach , 1989 .

[39]  L. Collins,et al.  Relationship between the intrinsic radial distribution function for an isotropic field of particles and lower-dimensional measurements , 2002, Journal of Fluid Mechanics.

[40]  Alan Gadian,et al.  Cloud‐aerosol interactions for boundary layer stratocumulus in the Lagrangian Cloud Model , 2010 .

[41]  G. Csanady Turbulent Diffusion of Heavy Particles in the Atmosphere , 1963 .

[42]  H. Jonker,et al.  Subsiding Shells Around Shallow Cumulus Clouds , 2008 .

[43]  Roddam Narasimha,et al.  Direct numerical simulation of turbulent flows with cloud-like off-source heating , 1999 .

[44]  Robert Bingham Cloud droplet growth , 2001 .

[45]  B. Morton,et al.  Buoyant plumes in a moist atmosphere , 1957, Journal of Fluid Mechanics.

[46]  Karl W. Jenkins,et al.  Direct numerical simulation of turbulent flame kernels , 1999 .

[47]  R. A. Shaw,et al.  Can We Understand Clouds Without Turbulence? , 2010, Science.

[48]  W. Grabowski,et al.  Effective radius and droplet spectral width from in‐situ aircraft observations in trade‐wind cumuli during RICO , 2009 .

[49]  Thijs Heus,et al.  Mixing in Shallow Cumulus Clouds Studied by Lagrangian Particle Tracking , 2008 .

[50]  I. Paluch,et al.  The Entrainment Mechanism in Colorado Cumuli , 1979 .

[51]  M. Dubey,et al.  The potential impacts of pollution on a nondrizzling stratus deck : Does aerosol number matter more than type? , 2008 .

[52]  Bogdan Rosa,et al.  Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 1. Results from direct numerical simulation , 2008 .

[53]  T. Elperin,et al.  On the collision rate of particles in turbulent flow with gravity , 2002 .

[54]  Harm J. J. Jonker,et al.  On the Combined Effects of Turbulence and Gravity on Droplet Collisions in Clouds: A Numerical Study , 2009 .

[55]  J. Putaud,et al.  Aerosol activation in marine stratocumulus clouds: 2. Köhler and parcel theory closure studies , 2003 .

[56]  D. Randall,et al.  Conditional instability of the first kind upside-down. [in stratocumulus clouds] , 1980 .

[57]  J. Brenguier,et al.  Cumulus Entrainment and Cloud Droplet Spectra: A Numerical Model within a Two-Dimensional Dynamical Framework , 1993 .

[58]  Analysis of Tools Used to Quantify Droplet Clustering in Clouds , 2010 .

[59]  K. Beard Terminal Velocity and Shape of Cloud and Precipitation Drops Aloft , 1976 .

[60]  J. Abrahamson Collision rates of small particles in a vigorously turbulent fluid , 1975 .

[61]  T. J. Hanratty,et al.  Free‐flight mixing and deposition of aerosols , 1994 .

[62]  S. Oncley,et al.  Acceleration intermittency and enhanced collision kernels in turbulent clouds , 2001 .

[63]  R. Narasimha,et al.  A volumetrically heated jet: large-eddy structure and entrainment characteristics , 1996, Journal of Fluid Mechanics.

[64]  R. Shaw PARTICLE-TURBULENCE INTERACTIONS IN ATMOSPHERIC CLOUDS , 2003 .

[65]  Jiang Lu,et al.  Clustering of settling charged particles in turbulence: theory and experiments , 2010 .

[66]  B. Goswami,et al.  Microphysics of Premonsoon and Monsoon Clouds as Seen from In Situ Measurements during the Cloud Aerosol Interaction and Precipitation Enhancement Experiment (CAIPEEX) , 2011 .

[67]  T. Clark,et al.  Cloud-Environment Interface Instability: Part II: Extension to Three Spatial Dimensions , 1993 .

[68]  Raymond A. Shaw,et al.  Homogeneous and Inhomogeneous Mixing in Cumulus Clouds: Dependence on Local Turbulence Structure , 2009 .

[69]  Jorgen B. Jensen,et al.  A Study of the Source of Entrained Air in Montana Cumuli , 1988 .

[70]  G. Falkovich,et al.  Intermittent distribution of inertial particles in turbulent flows. , 2001, Physical review letters.

[71]  Wojciech W. Grabowski,et al.  Diffusional and accretional growth of water drops in a rising adiabatic parcel: effects of the turbulent collision kernel , 2008 .

[72]  Piotr K. Smolarkiewicz,et al.  Laboratory and modeling studies of cloud–clear air interfacial mixing: anisotropy of small-scale turbulence due to evaporative cooling , 2008 .

[73]  Ka-Ming Lau,et al.  Warm rain processes over tropical oceans and climate implications , 2003 .

[74]  M. Shapiro,et al.  Collision Efficiency of Drops in a Wide Range of Reynolds Numbers: Effects of Pressure on Spectrum Evolution , 2001 .

[75]  A. Sterkin,et al.  Investigation of Droplet Size Distributions and Drizzle Formation Using a New Trajectory Ensemble Model. Part I: Model Description and First Results in a Nonmixing Limit , 2008 .

[76]  Manfred Wendisch,et al.  Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer , 2006 .

[77]  J. Turner,et al.  Buoyancy Effects in Fluids , 1973 .

[78]  Turbulence effects on the collision kernel. II: Increase of the swept volume of colliding drops , 1997 .

[79]  S. Jennings,et al.  The mean free path in air , 1988 .

[80]  Andrzej A. Wyszogrodzki,et al.  Activation of cloud droplets in bin-microphysics simulation of shallow convection , 2011 .

[81]  Ryo Onishi,et al.  Influence of gravity on collisions of monodispersed droplets in homogeneous isotropic turbulence , 2009 .

[82]  W. Cooper,et al.  Effects of Variable Droplet Growth Histories on Droplet Size Distributions. Part I: Theory , 1989 .

[83]  Szymon P. Malinowski,et al.  Spatial distribution of cloud droplets in a turbulent cloud‐chamber flow , 2005 .

[84]  H. Tennekes Simple Model for the Small‐Scale Structure of Turbulence , 1968 .

[85]  W. C. SWINBANK,et al.  Collisions of Cloud Droplets , 1947, Nature.

[86]  S. Corrsin,et al.  Free-Stream Boundaries of Turbulent Flows , 1955 .

[87]  Sonia Lasher-Trapp,et al.  Broadening of droplet size distributions from entrainment and mixing in a cumulus cloud , 2005 .

[88]  J. Seinfeld,et al.  On the representation of droplet coalescence and autoconversion: Evaluation using ambient cloud droplet size distributions , 2009 .

[89]  Wojciech W. Grabowski,et al.  The role of air turbulence in warm rain initiation , 2009 .

[90]  J. Brenguier,et al.  Droplet Spectra Broadening in Cumulus Clouds. Part II: Microscale Droplet Concentration Heterogeneities , 2001 .

[91]  T. Clark,et al.  Cloud-Environment Interface Instability. Part III: Direct Influence of Environmental Shear , 1993 .

[92]  S. Ayyalasomayajula,et al.  Modeling inertial particle acceleration statistics in isotropic turbulence , 2008 .

[93]  H. Gerber,et al.  Holes and Entrainment in Stratocumulus , 2005 .

[94]  Raymond A. Shaw,et al.  FLUCTUATIONS AND LUCK IN DROPLET GROWTH BY COALESCENCE , 2005 .

[95]  R. Wattenbarger,et al.  Effects of turbulence , 1967 .

[96]  J. C. R. Hunt,et al.  Settling of small particles near vortices and in turbulence , 2001, Journal of Fluid Mechanics.

[97]  Hartmut Höller,et al.  Eddy Dissipation Rates in Thunderstorms Estimated by Doppler Radar in Relation to Aircraft In Situ Measurements , 2001 .

[98]  J. Klett,et al.  Microphysics of Clouds and Precipitation , 1978, Nature.

[99]  C. Jeffery Inhomogeneous cloud evaporation, invariance, and Damköhler number , 2007 .

[100]  Said Elghobashi,et al.  On predicting particle-laden turbulent flows , 1994 .

[101]  Lance R. Collins,et al.  Towards understanding the role of turbulence on droplets in clouds: In situ and laboratory measurements , 2010 .

[102]  Wojciech W. Grabowski,et al.  Comments on “Preferential Concentration of Cloud Droplets by Turbulence:Effects on the Early Evolution of Cumulus Cloud Droplet Spectra” , 1999 .

[103]  A. Soldati,et al.  Measuring segregation of inertial particles in turbulence by a full Lagrangian approach. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[104]  M. Shapiro,et al.  Collisions of Cloud Droplets in a Turbulent Flow. Part IV: Droplet Hydrodynamic Interaction , 2007 .

[105]  Jon M. Reisner,et al.  A Study of Cloud Mixing and Evolution Using PDF Methods. Part I: Cloud Front Propagation and Evaporation , 2006 .

[106]  A. Basu,et al.  Some characteristics of entrainment at a cylindrical turbulence boundary , 2002 .

[107]  B. Stevens Bulk boundary-layer concepts for simplified models of tropical dynamics , 2006 .

[108]  Wojciech W. Grabowski,et al.  Improved Formulations of the Superposition Method , 2005 .

[109]  J. Eaton,et al.  Preferential concentration of particles in homogeneous and isotropic turbulence , 2005 .

[110]  R. Narasimha,et al.  An experimental study of a jet with local buoyancy enhancement , 1995 .

[111]  A. Pumir,et al.  Inertial particle collisions in turbulent synthetic flows: quantifying the sling effect. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[112]  Meheboob Alam Streamwise structures and density patterns in rapid granular Couette flow: a linear stability analysis , 2006, Journal of Fluid Mechanics.

[113]  Raymond A. Shaw,et al.  Supersaturation Intermittency in Turbulent Clouds , 2000 .

[114]  L. Collins,et al.  Measurement of inertial particle clustering and relative velocity statistics in isotropic turbulence using holographic imaging , 2010 .

[115]  P. Dimotakis Two-dimensional shear-layer entrainment , 1986 .

[116]  S. Krueger,et al.  Linear eddy modeling of droplet spectral evolution during entrainment and mixing in cumulus clouds , 1998 .

[117]  B. Stevens Entrainment in stratocumulus‐topped mixed layers , 2002 .

[118]  A. Wexler,et al.  STATISTICAL MECHANICAL DESCRIPTIONS OF TURBULENT COAGULATION , 1998 .

[119]  Michael W. Reeks,et al.  A Lagrangian approach to droplet condensation in atmospheric clouds , 2009 .

[120]  A. Cartellier,et al.  Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence , 2002, Journal of Fluid Mechanics.

[121]  K. Squires,et al.  Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study , 2005, Journal of Fluid Mechanics.

[122]  A. Khain,et al.  Fine Structure of Cloud Droplet Concentration as Seen from the Fast-FSSP Measurements. Part II: Results of In Situ Observations , 2003 .

[123]  M. Maxey The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields , 1987, Journal of Fluid Mechanics.

[124]  J. Brenguier,et al.  Observational Study of the Entrainment-Mixing Process in Warm Convective Clouds , 2007 .

[125]  Zellman Warhaft,et al.  Laboratory studies of droplets in turbulence: towards understanding the formation of clouds , 2009 .

[126]  J. Seinfeld,et al.  Statistical comparison of properties of simulated and observed cumulus clouds in the vicinity of Houston during the Gulf of Mexico Atmospheric Composition and Climate Study (GoMACCS) , 2008 .

[127]  Y. J. Lin,et al.  The entrainment due to a turbulent fountain at a density interface , 2005, Journal of Fluid Mechanics.

[128]  Alexander Khain,et al.  Collisions of Small Drops in a Turbulent Flow. Part I: Collision Efficiency. Problem Formulation and Preliminary Results , 1999 .

[129]  A. Wexler,et al.  On the collision rate of small particles in isotropic turbulence. II. Finite inertia case , 1998 .

[130]  J. Latham,et al.  The Evolution of Droplet Spectra and the Rate of Production of Embryonic Raindrops in Small Cumulus Clouds , 1979 .

[131]  S. Kreidenweis,et al.  Stratocumulus processing of gases and cloud condensation nuclei: 1. Trajectory ensemble model , 1998 .

[132]  T. Elperin,et al.  Critical comments to results of investigations of drop collisions in turbulent clouds , 2007 .

[133]  L. Collins,et al.  Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations , 1997, Journal of Fluid Mechanics.

[134]  Wojciech W. Grabowski,et al.  Microscopic approach to cloud droplet growth by condensation , 2001 .

[135]  Raymond A. Shaw,et al.  Towards quantifying droplet clustering in clouds , 2002 .

[136]  Toward the Theory of Stochastic Condensation in Clouds. Part I: A General Kinetic Equation. , 1999 .

[137]  R. G. Corbin,et al.  The influence of entrainment on the evolution of cloud droplet spectra: I. A model of inhomogeneous mixing , 1980 .

[138]  Harry T. Ochs,et al.  Warm-Rain Initiation: An Overview of Microphysical Mechanisms. , 1993 .

[139]  A. P. Siebesma,et al.  Controls on precipitation and cloudiness in simulations of trade‐wind cumulus as observed during RICO , 2011 .

[140]  Piotr K. Smolarkiewicz,et al.  Numerical Simulation of Cloud–Clear Air Interfacial Mixing: Homogeneous versus Inhomogeneous Mixing , 2009 .

[141]  S. S. Shy,et al.  Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements , 2005, Journal of Fluid Mechanics.

[142]  Krishnan Mahesh,et al.  Direct numerical simulation , 1998 .

[143]  A. Prasad,et al.  Evolution of a turbulent jet subjected to volumetric heating , 2004, Journal of Fluid Mechanics.

[144]  Peter Nielsen,et al.  Turbulence Effects on the Settling of Suspended Particles , 1993 .

[145]  Jean-Louis Brenguier,et al.  Droplet Spectra Broadening in Cumulus Clouds. Part I: Broadening in Adiabatic Cores , 2001 .

[146]  J. Warner,et al.  On Steady-State One-Dimensional Models of Cumulus Convection , 1970 .

[147]  B. Geerts,et al.  Dynamics of the Cumulus Cloud Margin: An Observational Study , 2009 .

[148]  T. Clark,et al.  Dynamics of the Cloud-Environment Interface and Entrainment in Small Cumuli: Two-Dimensional Simulations in the Absence of Ambient Shear , 1985 .

[149]  W. Cooper,et al.  Variability of the Supersaturation in Cumulus Clouds. , 1988 .

[150]  A. Wexler,et al.  Modelling turbulent collision of bidisperse inertial particles , 2001, Journal of Fluid Mechanics.

[151]  Caustic activation of rain showers. , 2006, Physical review letters.

[152]  C. Bretherton,et al.  Evaluation of Large-Eddy Simulations via Observations of Nocturnal Marine Stratocumulus , 2005 .

[153]  P. R. Jonas,et al.  Observations of cumulus cloud entrainment , 1990 .

[154]  J. Mellado The evaporatively driven cloud-top mixing layer , 2010, Journal of Fluid Mechanics.

[155]  John Christos Vassilicos,et al.  A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence , 2009 .

[156]  Alexander Khain,et al.  Collisions of small drops in a turbulent flow , 1999 .

[157]  J. Bec,et al.  Multifractal concentrations of inertial particles in smooth random flows , 2004, Journal of Fluid Mechanics.

[158]  Raymond A. Shaw,et al.  Scale-dependent droplet clustering in turbulent clouds , 2001, Journal of Fluid Mechanics.

[159]  P. Sullivan,et al.  Where is the Interface of the Stratocumulus-Topped PBL? , 2005 .

[160]  Wojciech W. Grabowski,et al.  Probability distributions of angle of approach and relative velocity for colliding droplets in a turbulent flow , 2006 .

[161]  L. Biferale,et al.  Acceleration statistics of heavy particles in turbulence , 2006, Journal of Fluid Mechanics.

[162]  A. Khain,et al.  Collisions of Cloud Droplets in a Turbulent Flow. Part V: Application of Detailed Tables of Turbulent Collision Rate Enhancement to Simulation of Droplet Spectra Evolution , 2008 .

[163]  Wojciech W. Grabowski,et al.  Effects of stochastic coalescence and air turbulence on the size distribution of cloud droplets , 2006 .

[164]  T. Clark,et al.  Cloud-environment interface instability : rising thermal calculations in two spatial dimensions , 1991 .

[165]  Wojciech W. Grabowski,et al.  Theoretical Formulation of Collision Rate and Collision Efficiency of Hydrodynamically Interacting Cloud Droplets in Turbulent Atmosphere , 2005 .

[166]  W. Schubert,et al.  Stability of cloud-topped boundary layers , 1988 .

[167]  Oleg A. Krasnov,et al.  Investigation of Droplet Size Distributions and Drizzle Formation Using A New Trajectory Ensemble Model. Part II: Lucky Parcels , 2009 .

[168]  K. Shinohara Segregation of Particles , 2006 .

[169]  K. Squires,et al.  Particle response and turbulence modification in isotropic turbulence , 1990 .

[170]  N. Malik,et al.  Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes , 1992, Journal of Fluid Mechanics.

[171]  Axel Seifert,et al.  Turbulence effects on warm‐rain autoconversion in precipitating shallow convection , 2010 .

[172]  Steven K. Krueger,et al.  Modeling Entrainment and Finescale Mixing in Cumulus Clouds , 1997 .

[173]  Alain Pumir,et al.  Sling Effect in Collisions of Water Droplets in Turbulent Clouds , 2007 .

[174]  M. Lemone,et al.  Vertical velocity and buoyancy characteristics of coherent echo plumes in the convective boundary layer, detected by a profiling airborne radar , 2005 .

[175]  Lance R. Collins,et al.  Effect of preferential concentration on turbulent collision rates , 2000 .

[176]  S. Ayyalasomayajula,et al.  Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. , 2006, Physical review letters.

[177]  Harm J. J. Jonker,et al.  Size Distributions and Dynamical Properties of Shallow Cumulus Clouds from Aircraft Observations and Satellite Data , 2003 .

[178]  W. Marlow,et al.  Physics of Drop Formation in the Atmosphere , 1974 .

[179]  Jerry Westerweel,et al.  Momentum and scalar transport at the turbulent/non-turbulent interface of a jet , 2009, Journal of Fluid Mechanics.

[180]  Bogdan Rosa,et al.  Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 2. Theory and parameterization , 2008 .

[181]  Lance R. Collins,et al.  Clustering of aerosol particles in isotropic turbulence , 2005, Journal of Fluid Mechanics.

[182]  A. Osiptsov,et al.  Lagrangian Modelling of Dust Admixture in Gas Flows , 2000 .

[183]  J. Warner The Microstructure of Cumulus Cloud. Part II. The Effect on Droplet Size Distribution of the Cloud Nucleus Spectrum and Updraft Velocity , 1969 .

[184]  Jean-Louis Brenguier,et al.  Improvements of Droplet Size Distribution Measurements with the Fast-FSSP (Forward Scattering Spectrometer Probe) , 1998 .

[185]  J. Warner The Microstructure of Cumulus Cloud. Part I. General Features of the Droplet Spectrum , 1969 .

[186]  J. Turner,et al.  An entraining jet model for cumulo-nimbus updraughts , 1962 .

[187]  Lian-Ping Wang,et al.  Reconciling the cylindrical formulation with the spherical formulation in the kinematic descriptions of collision kernel , 2005 .

[188]  Caustics in turbulent aerosols , 2004, cond-mat/0403011.

[189]  W. Grabowski,et al.  A numerical investigation of entrainment and transport within a stratocumulus‐topped boundary layer , 2009 .

[190]  Wojciech W. Grabowski,et al.  Representation of turbulent mixing and buoyancy reversal in bulk cloud models , 2007 .

[191]  James E. Dye,et al.  Evaluation of the Forward Scattering Spectrometer Probe. Part I: Electronic and Optical Studies , 1984 .

[192]  B. Grits,et al.  Collisions of Small Drops in a Turbulent Flow. Part III: Relative Droplet Fluxes and Swept Volumes , 2006 .

[193]  Z. Warhaft,et al.  Entrainment and mixing of water droplets across a shearless turbulent interface with and without gravitational effects , 2011, Journal of Fluid Mechanics.

[194]  J. I. MacPherson,et al.  Turbulent Characteristics of Some Canadian Cumulus Clouds , 1977 .

[195]  R. L. Reed,et al.  Laboratory studies of the effects of mixing on the evolution of cloud droplet spectra , 1977 .

[196]  Piotr K. Smolarkiewicz,et al.  Numerical Simulation of CloudClear Air Interfacial Mixing , 2004 .

[197]  Jorgen B. Jensen,et al.  Microphysical and short‐wave radiative structure of stratocumulus clouds over the Southern Ocean: Summer results and seasonal differences , 1998 .

[198]  B. Stevens,et al.  Buoyancy reversal in cloud‐top mixing layers , 2009 .

[199]  S. Caughey,et al.  A field study of nocturnal stratocumulus II Turbulence structure and entrainment , 1982 .

[200]  L. Mahrt Penetrative convection at the top of a growing boundary layer , 1979 .

[201]  C. Bretherton,et al.  Buoyancy reversal and cloud‐top entrainment instability , 1990 .

[202]  Z. Levin,et al.  The role of the inertia of cloud drops in the evolution of the spectra during drop growth by diffusion , 1999 .

[203]  J. Riley,et al.  Equation of motion for a small rigid sphere in a nonuniform flow , 1983 .

[204]  G. Falkovich,et al.  Acceleration of rain initiation by cloud turbulence , 2002, Nature.

[205]  J. Warner,et al.  The Water Content of Cumuliform Cloud , 1955 .

[206]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[207]  Geoffrey Ingram Taylor,et al.  Turbulent gravitational convection from maintained and instantaneous sources , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[208]  A. Cartellier,et al.  Preferential concentration of heavy particles: A Voronoï analysis , 2010 .

[209]  Wojciech W. Grabowski,et al.  Comments on “Droplets to Drops by Turbulent Coagulation” , 2006 .

[210]  H. Fernando,et al.  How turbulence enhances coalescence of settling particles with applications to rain in clouds , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[211]  Wojciech W. Grabowski,et al.  Growth of Cloud Droplets by Turbulent Collision–Coalescence , 2006 .

[212]  P. Squires Penetrative Downdraughts in Cumuli , 1958 .

[213]  S. Krueger Linear Eddy Modeling of Entrainment and Mixing in Stratus Clouds , 1993 .

[214]  Gregory Falkovich,et al.  Droplet condensation in turbulent flows , 2005 .

[215]  R. Breidenthal,et al.  Laboratory experiments on the cloud-top entrainment instability , 1990, Journal of Fluid Mechanics.

[216]  Paul A. Vaillancourt,et al.  Statistics and Parameterizations of the Effect of Turbulence on the Geometric Collision Kernel of Cloud Droplets , 2007 .

[217]  John Christos Vassilicos,et al.  Self-similar clustering of inertial particles and zero-acceleration points in fully developed two-dimensional turbulence , 2006 .

[218]  M. Wendisch,et al.  Probing Finescale Dynamics and Microphysics of Clouds with Helicopter-Borne Measurements , 2006 .

[219]  Armann Gylfason,et al.  Inertial clustering of particles in high-Reynolds-number turbulence. , 2008, Physical review letters.

[220]  A. Kostinski Simple approximations for condensational growth , 2009 .

[221]  F. Toschi,et al.  Cloud Droplet Growth by Condensation in Homogeneous Isotropic Turbulence , 2009 .

[222]  Bogdan Rosa,et al.  Turbulent collision efficiency of heavy particles relevant to cloud droplets , 2008 .

[223]  P. Saffman,et al.  On the collision of drops in turbulent clouds , 1956, Journal of Fluid Mechanics.

[224]  A. Khain,et al.  Fine Structure of Cloud Droplet Concentration as Seen from the Fast-FSSP Measurements. Part I: Method of Analysis and Preliminary Results , 2001 .

[225]  J. Brenguier,et al.  Microphysical properties of stratocumulus clouds , 2000 .

[226]  Alexei Korolev,et al.  Supersaturation of Water Vapor in Clouds , 2003 .

[227]  H. Pruppacher,et al.  A Wind Tunnel Study of the Effects of Turbulence on the Growth of Cloud Drops by Collision and Coalescence , 1999 .

[228]  B. J. Mason,et al.  The physics of clouds , 1971 .