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

M. Pinsky The Hebrew University of Jerusalem, Jerusalem, Israel

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A. Khain The Hebrew University of Jerusalem, Jerusalem, Israel

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H. Krugliak The Hebrew University of Jerusalem, Jerusalem, Israel

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Abstract

The present study is a continuation of the series of studies dedicated to the investigation of cloud droplet collisions in turbulent flow with characteristics that are typical of real clouds. Detailed tables of collision kernels and collision efficiencies calculated in the presence of hydrodynamic interaction of droplets are presented. These tables were calculated for a wide range of turbulent parameters. To illustrate the sensitivity of droplet size distribution (DSD) evolution to the turbulence-induced increase in the collision rate, simulations of DSD evolution are preformed by solving the stochastic kinetic equation for collisions. The results can be applied to cloud modeling. The tables of collision efficiencies and collision kernels are available upon request. Some unsolved problems related to collisions of droplets and ice hydrometeors in turbulent clouds are discussed in the conclusion.

Corresponding author address: Alexander Khain, Department of the Atmospheric Sciences, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel. Email: khain@vms.huji.ac.il

Abstract

The present study is a continuation of the series of studies dedicated to the investigation of cloud droplet collisions in turbulent flow with characteristics that are typical of real clouds. Detailed tables of collision kernels and collision efficiencies calculated in the presence of hydrodynamic interaction of droplets are presented. These tables were calculated for a wide range of turbulent parameters. To illustrate the sensitivity of droplet size distribution (DSD) evolution to the turbulence-induced increase in the collision rate, simulations of DSD evolution are preformed by solving the stochastic kinetic equation for collisions. The results can be applied to cloud modeling. The tables of collision efficiencies and collision kernels are available upon request. Some unsolved problems related to collisions of droplets and ice hydrometeors in turbulent clouds are discussed in the conclusion.

Corresponding author address: Alexander Khain, Department of the Atmospheric Sciences, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel. Email: khain@vms.huji.ac.il

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  • Almeida, F. C., 1976: The collisional problem of cloud droplets moving in a turbulent environment. Part I: A method of solution. J. Atmos. Sci., 33 , 15711578.

    • Search Google Scholar
    • Export Citation
  • Almeida, F. C., 1979: The collisional problem of cloud droplets moving in a turbulent environment. Part II: Turbulent collision efficiencies. J. Atmos. Sci., 36 , 15641576.

    • Search Google Scholar
    • Export Citation
  • Arenberg, D., 1939: Turbulence as the major factor in the growth of cloud drops. Bull. Amer. Meteor. Soc., 20 , 444448.

  • Beard, K. V., 1976: Terminal velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci., 33 , 851864.

  • Bott, A., 1998: A flux method for the numerical solution of the stochastic collection equation. J. Atmos. Sci., 55 , 22842293.

  • Brenguier, J-L., and L. Chaumat, 2001: Droplet spectra broadening in cumulus clouds. Part I: Broadening in adiabatic cores. J. Atmos. Sci., 58 , 628641.

    • Search Google Scholar
    • Export Citation
  • Chun, J., D. L. Koch, S. L. Rani, A. Ahluwalia, and L. R. Collins, 2005: Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech., 536 , 219251.

    • Search Google Scholar
    • Export Citation
  • Franklin, C. N., P. A. Vaillancourt, M. K. Yau, and P. Bartello, 2005: Collision rates of cloud droplets in turbulent flow. J. Atmos. Sci., 62 , 24512466.

    • Search Google Scholar
    • Export Citation
  • Franklin, C. N., P. A. Vaillancourt, and M. K. Yau, 2007: Statistics and parameterizations of the effect of turbulence on the geometric collision kernel of cloud droplets. J. Atmos. Sci., 64 , 938954.

    • Search Google Scholar
    • Export Citation
  • Grover, S. N., and H. R. Pruppacher, 1985: The effect of vertical turbulent fluctuations in the atmosphere on the collection of aerosol particles by cloud drops. J. Atmos. Sci., 42 , 23052318.

    • Search Google Scholar
    • Export Citation
  • Ivanovsky, A., and I. Mazin, 1960: Turbulent coagulation and its role in drop growth (in Russian). Central Aerol. Obs. Proc., 35 , 2135.

    • Search Google Scholar
    • Export Citation
  • Jonas, P. R., 1996: Turbulence and cloud microphysics. Atmos. Res., 40 , 283306.

  • Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulation. Meteor. Monogr., No. 10, Amer. Meteor. Soc., 84 pp.

    • Search Google Scholar
    • Export Citation
  • Khain, A., M. Ovtchinnicov, M. Pinsky, A. Pokrovsky, and H. Krugliak, 2000: Notes on the state-of-the-art numerical modeling of cloud microphysics. Atmos. Res., 55 , 159224.

    • Search Google Scholar
    • Export Citation
  • Khain, A., M. Pinsky, T. Elperin, N. Kleeorin, I. Rogachevskii, and A. B. Kostinski, 2007: Critical comments to results of investigations of drop collisions in turbulent clouds. Atmos. Res., 86 , 120.

    • Search Google Scholar
    • Export Citation
  • Kostinski, A. B., and R. A. Shaw, 2005: Fluctuations and luck in droplet growth by coalescence. Bull. Amer. Meteor. Soc., 86 , 235244.

    • Search Google Scholar
    • Export Citation
  • Manton, M. J., 1977: The equation of motion for a small aerosol in a continuum. Pure Appl. Geophys., 115 , 547559.

  • Mazin, I. P., A. Kh Khrgian, and I. M. Imyanitov, 1989: Handbook. of Clouds and Cloudy Atmosphere (in Russian). Gidrometeoizdat, 647 pp.

    • Search Google Scholar
    • Export Citation
  • Panchev, S., 1971: Random Fluctuations in Turbulence. Pergamon Press, 256 pp.

  • Pinsky, M., and A. P. Khain, 2003: Fine structure of cloud droplet concentration as seen from the Fast-FSSP measurements. Part II: Results of in situ observations. J. Appl. Meteor., 42 , 6573.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., and A. P. Khain, 2004: Collisions of small drops in a turbulent flow. Part II: Effects of flow accelerations. J. Atmos. Sci., 61 , 19261939.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., A. P. Khain, and M. Shapiro, 1999a: Collisions of small drops in a turbulent flow. Part I: Collision efficiency. Problem formulation and preliminary results. J. Atmos. Sci., 56 , 25852600.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., A. P. Khain, and Z. Levin, 1999b: The role of the inertia of cloud drops in the evolution of the spectra during drop growth by diffusion. Quart. J. Roy. Meteor. Soc., 125 , 553581.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., A. P. Khain, and M. Shapiro, 2000: Stochastic effects on cloud droplet hydrodynamic interaction in a turbulent flow. Atmos. Res., 53 , 131169.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., A. P. Khain, and M. Shapiro, 2001: Collision efficiency of drops in a wide range of Reynolds numbers: Effects of pressure on spectrum evolution. J. Atmos. Sci., 58 , 742764.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., M. Shapiro, A. Khain, and H. Wirzberger, 2004: A statistical model of strains in homogeneous and isotropic turbulence. Physica D, 191 , 297313.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., A. P. Khain, B. Grits, and M. Shapiro, 2006: Collisions of cloud droplets in a turbulent flow. Part III: Relative droplet fluxes and swept volumes. J. Atmos. Sci., 63 , 21232139.

    • Search Google Scholar
    • Export Citation
  • Pinsky, M., A. P. Khain, and M. Shapiro, 2007: Collisions of cloud droplets in a turbulent flow. Part IV: Droplet hydrodynamic interaction. J. Atmos. Sci., 64 , 24642482.

    • Search Google Scholar
    • Export Citation
  • Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds and Precipitation. 2nd ed. Kluwer Academic, 954 pp.

  • Reuter, G. W., R. De Villiers, and Y. Yavin, 1988: The collection kernel for two falling cloud drops subjected to random perturbations in a turbulent air flow: A stochastic model. J. Atmos. Sci., 45 , 765773.

    • Search Google Scholar
    • Export Citation
  • Riemer, N., and A. S. Wexler, 2005: Droplet to drops by turbulent coagulation. J. Atmos. Sci., 62 , 19621975.

  • Saffman, P. G., and J. S. Turner, 1956: On the collision of drops in turbulent clouds. J. Fluid Mech., 1 , 1630.

  • Shaw, R. A., 2003: Particle–turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech., 35 , 183227.

  • Siebert, H., K. Lehmann, and M. Wendisch, 2006: Observations of small-scale turbulence and energy dissipation rates in the cloudy boundary layer. J. Atmos. Sci., 63 , 14511466.

    • Search Google Scholar
    • Export Citation
  • Vaillancourt, P. A., and M. K. Yau, 2000: Review of particle–turbulence interactions and consequences for cloud physics. Bull. Amer. Meteor. Soc., 81 , 285298.

    • Search Google Scholar
    • Export Citation
  • Vohl, O., S. K. Mitra, S. C. Wurzler, and H. R. Pruppacher, 1999: A wind tunnel study on the effects of turbulence on the growth of cloud drops by collision and coalescence. J. Atmos. Sci., 56 , 40884099.

    • Search Google Scholar
    • Export Citation
  • Wang, L-P., O. Ayala, S. E. Kasprzak, and W. W. Grabowski, 2005a: Theoretical formulation of collision rate and collision efficiency of hydrodynamically interacting cloud droplets in turbulent atmosphere. J. Atmos. Sci., 62 , 24332450.

    • Search Google Scholar
    • Export Citation
  • Wang, L-P., O. Ayala, and W. W. Grabowski, 2005b: On improved formulations of the superposition method. J. Atmos. Sci., 62 , 12551266.

    • Search Google Scholar
    • Export Citation
  • Weil, J. C., R. P. Lawson, and A. R. Rodi, 1993: Relative dispersion of ice crystals in seeded cumuli. J. Appl. Meteor., 32 , 10551073.

    • Search Google Scholar
    • Export Citation
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