Collision Efficiencies of Ice Crystals at Low–Intermediate Reynolds Numbers Colliding with Supercooled Cloud Droplets: A Numerical Study

Pao K. Wang Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin

Search for other papers by Pao K. Wang in
Current site
Google Scholar
PubMed
Close
and
Wusheng Ji Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin

Search for other papers by Wusheng Ji in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The efficiencies with which ice crystals at low–intermediate Reynolds numbers collide with supercooled cloud droplets are determined numerically. Three ice crystal habits are considered here: hexagonal ice plates, broad-branch crystals, and columnar ice crystals. Their Reynolds numbers range from 0.1 to slightly beyond 100. The size of cloud droplets range from a few to about 100 μm in radius. The collision efficiencies are determined by solving the equation of motion for a cloud droplet under the influence of the flow field of the falling ice crystal. The flow fields of the falling ice crystals were determined previously by numerically solving the unsteady Navier–Stokes equations. Features of these efficiencies are discussed. The computed efficiencies are compared with those obtained by previous investigators and improvements are indicated. New results fit better with the observed riming droplet sizes and cutoff riming ice crystal sizes.

Corresponding author address: Dr. Pao K. Wang, Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, 1225 W. Dayton Street, Madison, WI 53706.

Email: pao@windy.meteor.wisc.edu

Abstract

The efficiencies with which ice crystals at low–intermediate Reynolds numbers collide with supercooled cloud droplets are determined numerically. Three ice crystal habits are considered here: hexagonal ice plates, broad-branch crystals, and columnar ice crystals. Their Reynolds numbers range from 0.1 to slightly beyond 100. The size of cloud droplets range from a few to about 100 μm in radius. The collision efficiencies are determined by solving the equation of motion for a cloud droplet under the influence of the flow field of the falling ice crystal. The flow fields of the falling ice crystals were determined previously by numerically solving the unsteady Navier–Stokes equations. Features of these efficiencies are discussed. The computed efficiencies are compared with those obtained by previous investigators and improvements are indicated. New results fit better with the observed riming droplet sizes and cutoff riming ice crystal sizes.

Corresponding author address: Dr. Pao K. Wang, Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, 1225 W. Dayton Street, Madison, WI 53706.

Email: pao@windy.meteor.wisc.edu

Save
  • Bruntjes, R. T., A. J. Heymsfield, and T. W. Krauss, 1987: An examination of double-plate ice crystals and the initiation of precipitation in continental cumulus clouds. J. Atmos. Sci.,44, 1331–1349.

  • Cotton, W. R., and R. A. Anthes, 1989: Storm and Cloud Dynamics. Academic Press, 880 pp.

  • D’Enrico, R. E., and A. H. Auer, 1978: An observational study of the accretional properties of ice crystals of simple geometric shapes. Preprints, Conf. on Cloud Physics and Atmospheric Electricity, Issaquah, WA, Amer. Meteor. Soc., 114–121.

  • Devulapalli, S. S. N., and J. L. Collett Jr., 1994: The influence of riming and frontal dynamics on winter precipitation chemistry in level terrain. Atmos. Res.,32, 203–213.

  • Harimaya, T., 1975: The timing properties of snow crystals. J. Meteor. Soc. Japan.,53, 384–392.

  • Ji, W., and P. K. Wang, 1989: Numerical simulation of three-dimensional unsteady viscous flow past hexagonal ice crystals in the air—Preliminary results. Atmos. Res.,25, 539–557.

  • ——, and ——, 1991: Numerical simulation of three-dimensional unsteady viscous flow past finite cylinders in an unbounded fluid at low intermediate Reynolds numbers. Theor. Comput. Fluid Dyn.,3, 43–59.

  • ——, and ——, 1999: Ventilation coefficients for falling ice crystals in the atmosphere at low–intermediate Reynolds numbers. J. Atmos. Sci.,56, 829–836.

  • Johnson, D. E., P. K. Wang, and J. M. Straka, 1993: Numerical simulation of the 2 August 1981 CCOPE supercell storm with and without ice microphysics. J. Appl. Meteor.,32, 745–759.

  • ——, ——, and ——, 1994: A study of microphysical processes in the 2 August 1981 CCOPE supercell storm. Atmos. Res.,33, 93–123.

  • Kajikawa, M., 1974: On the collection efficiency of snow crystals for cloud droplets. J. Metetor. Soc. Japan,52, 328–336.

  • Kikuchi, K., and H. Uyeda, 1979: Cloud droplets and rain drops collected and frozen on natural snow crystals. J. Meteor. Soc. Japan,57, 273–281.

  • Lin, H.-M., and P. K. Wang, 1997: A numerical study of microphysical processes in the 21 June 1991 northern Taiwan mesoscale precipitation system. Terr. Atmos. Oceanic Sci.,8, 385–404.

  • Martin, J. J., P. K. Wang, H. R. Pruppacher, and R. L. Pitter, 1981: A numerical study of the effect of electric charges on the efficiency with which planar ice crystals collect supercooled water drops. J. Atmos. Sci.,38, 2462–2469.

  • Miller, N. L., and P. K. Wang, 1989: A theoretical determination of the efficiency with which aerosol particles are collected by falling columnar ice crystals. J. Atmos. Sci.,46, 1656–1663.

  • Ono, A., 1969: The shape and rimimg properties of ice crystals in natural clouds. J. Atmos. Sci.,26, 138–147.

  • Pitter, R. L., 1977: A reexamination of riming on thin ice plates. J. Atmos. Sci.,34, 684–685.

  • ——, and H. R. Pruppacher, 1974: A numerical investigation of collision efficiencies of simple ice plates colliding with supercooled drops. J. Atmos. Sci.,31, 551–559.

  • Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds and Precipitation. 2d ed. Kluwer Academic, 954 pp.

  • Reinking, R., 1979: The onset and steady growth of snow crystals by accretion of droplets. J. Atmos. Sci.,36, 870–881.

  • Sasyo, Y., 1971: Study of the formation of precipitation by the aggregation of snow partices and the accretion of cloud droplets on snowflakes. Pap. Meteor. Geophys.,22, 69–142.

  • ——, and H. Tokuue, 1973: The collection efficiency of simulated snow particles for water droplets (preliminary report). Pap. Meteor. Geophys.,24, 1–12.

  • Schlamp, R. J., H. R. Pruppacher, and A. E. Hamielec, 1975: A numerical investigation of the efficiency with which simple columnar ice crystals collide with supercooled water drops. J. Atmos. Sci.,32, 2330–2337.

  • Wang, P. K., 1983: On the definition of collision efficiency of atmospheric particles. J. Atmos. Sci.,40, 1051–1052.

  • ——, and T. Jaroszczyk, 1991: The grazing collision angle of aerosol particles colliding with infinitely long circular cylinders. Aerosol Sci. Tech.,15, 149–155.

  • ——, and W. Ji, 1997: Simulation of three-dimensional unsteady flow past ice crystals. J. Atmos. Sci.,54, 2261–2274.

  • ——, S. N. Grover, and H. R. Pruppacher, 1978: On the effect of electric charges on the scavenging of aerosol particles by cloud and small rain drops. J. Atmos. Sci.,35, 1735–1743.

  • Wilkins, R. D., and A. H. Auer Jr., 1970: Riming properties of hexagonal ice crystals. Preprints, Conf. on Cloud Physics, Fort Collins, CO, Amer. Meteor. Soc., 81–82.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 651 181 16
PDF Downloads 487 150 15