Collisions of Cloud Droplets in a Turbulent Flow. Part IV: Droplet Hydrodynamic Interaction

Abstract The paper presents a computationally accurate and efficient method for calculation of cloud droplets’ collision efficiency in a turbulent flow with the properties typical of atmospheric clouds. According to Part III, the statistical properties of a turbulent flow are represented by a set of noncorrelated samples of turbulent velocity gradients and Lagrangian accelerations. Long series of these samples were generated for turbulent parameters typical of different atmospheric clouds. Each sample can be assigned to a certain point of the turbulent flow. Each such point can be surrounded by a small elementary volume with the linear length scale of the Kolmogorov length scale, in which the Lagrangian acceleration and the velocity gradient tensor can be considered uniform in space and invariable in time. For each sample (or an elementary volume), fluxes of droplets of one size onto droplets of another size are calculated both in the presence and absence of hydrodynamical droplet interaction (HDI). In ea...

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

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

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

[4]  Paul A. Vaillancourt,et al.  Collision Rates of Cloud Droplets in Turbulent Flow. , 2005 .

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

[6]  Donald L. Koch,et al.  Coagulation of monodisperse aerosol particles by isotropic turbulence , 2005 .

[7]  M. Shapiro,et al.  A statistical model of strains in homogeneous and isotropic turbulence , 2004 .

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

[9]  R. Hill.  Scaling of acceleration in locally isotropic turbulence , 2001, Journal of Fluid Mechanics.

[10]  G. Voth,et al.  Measurement of particle accelerations in fully developed turbulence , 2001, Journal of Fluid Mechanics.

[11]  A. Pokrovsky,et al.  Collision Rate of Small Graupel and Water Drops , 2001 .

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

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

[14]  G. Voth,et al.  Fluid particle accelerations in fully developed turbulence , 2000, Nature.

[15]  Stavros Tavoularis,et al.  Reynolds number effects on the fine structure of uniformly sheared turbulence , 2000 .

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

[17]  Jeffery.  Effect of particle inertia on the viscous-convective subrange , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Michael Shapiro,et al.  Stochastic effects of cloud droplet hydrodynamic interaction in a turbulent flow , 2000 .

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

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

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

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

[23]  F. Belin,et al.  VELOCITY GRADIENT DISTRIBUTIONS IN FULLY DEVELOPED TURBULENCE : AN EXPERIMENTAL STUDY , 1997 .

[24]  Max Tegmark,et al.  An Icosahedron-based Method for Pixelizing the Celestial Sphere , 1996, The Astrophysical Journal.

[25]  H. Leighton,et al.  The Effect of Turbulence on the Collision Rates of Small Cloud Drops , 1996 .

[26]  A. Khain,et al.  Simulations of drop fall in a homogeneous isotropic turbulent flow , 1996 .

[27]  A. Khain,et al.  A MODEL OF A HOMOGENEOUS ISOTROPIC TURBULENT FLOW AND ITS APPLICATION FOR THE SIMULATION OF CLOUD DROP TRACKS , 1995 .

[28]  R. Antonia,et al.  Reynolds number dependence of high-order moments of the streamwise turbulent velocity derivative , 1981 .

[29]  De Almeida,et al.  The Collisional Problem of Cloud Droplets Moving in a Turbulent Environment–Part II: Turbulent Collision Efficiencies , 1979 .

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

[31]  A. Hamielec,et al.  A Numerical Investigation of the Effect of Electric Charges and Vertical External Electric Fields on the Collision Efficiency of Cloud Drops , 1976 .

[32]  James D. Klett,et al.  Comments on “Collision Efficiency of Water Drops in the Atmosphere" , 1976 .

[33]  S. C. Lee,et al.  Collision Efficiency of Water Drops in the Atmosphere , 1975 .

[34]  T. Gal-Chen,et al.  A numerical study of collision efficiencies and coalescence parameters for droplet pairs with radii up to 300 microns , 1971 .

[35]  M. H. Davis.  The slow translation and rotation of two unequal spheres in a viscous fluid , 1969 .

[36]  J. Sartor,et al.  Theoretical Collision Efficiencies for Small Cloud Droplets in Stokes Flow , 1967, Nature.

[37]  Irving Langmuir,et al.  THE PRODUCTION OF RAIN BY A CHAIN REACTION IN CUMULUS CLOUDS AT TEMPERATURES ABOVE FREEZING , 1948 .

[38]  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 .

[39]  A. Tsinober,et al.  Velocity derivatives in the atmospheric surface layer at Reλ=104 , 2001 .

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

[41]  Alexander Khain,et al.  Formation of inhomogeneity in drop concentration induced by the inertia of drops falling in a turbulent flow, and the influence of the inhomogeneity on the drop‐spectrum broadening , 1997 .

[42]  James D. Klett,et al.  Theoretical Collision Efficiencies of Cloud Droplets at Small Reynolds Numbers , 1973 .