Toward a Physical Characterization of Raindrop Collision Outcome Regimes

F. Y. Testik Civil Engineering Department, College of Engineering and Science, Clemson University, Clemson, South Carolina

Search for other papers by F. Y. Testik in
Current site
Google Scholar
PubMed
Close
,
A. P. Barros Civil and Environmental Engineering Department, Pratt School of Engineering, Duke University, Durham, North Carolina

Search for other papers by A. P. Barros in
Current site
Google Scholar
PubMed
Close
, and
L. F. Bliven NASA GSFC Wallops Flight Facility, Wallops Island, Virginia

Search for other papers by L. F. Bliven in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A comprehensive raindrop collision outcome regime diagram that delineates the physical conditions associated with the outcome regimes (i.e., bounce, coalescence, and different breakup types) of binary raindrop collisions is proposed. The proposed diagram builds on a theoretical regime diagram defined in the phase space of collision Weber numbers We and the drop diameter ratio p by including critical angle of impact considerations. In this study, the theoretical regime diagram is first evaluated against a comprehensive dataset for drop collision experiments representative of raindrop collisions in nature. Subsequently, the theoretical regime diagram is modified to explicitly describe the dominant regimes of raindrop interactions in (We, p) by delineating the physical conditions necessary for the occurrence of distinct types of collision-induced breakup (neck/filament, sheet, disk, and crown breakups) based on critical angle of impact consideration. Crown breakup is a subtype of disk breakup for lower collision kinetic energy that presents distinctive morphology. Finally, the experimental results are analyzed in the context of the comprehensive collision regime diagram, and conditional probabilities that can be used in the parameterization of breakup kernels in stochastic models of raindrop dynamics are provided.

Corresponding author address: Dr. Firat Y. Testik, 110 Lowry Hall, Civil Engineering Department, Clemson University, Clemson, SC 29634–0911. E-mail: ftestik@clemson.edu

Abstract

A comprehensive raindrop collision outcome regime diagram that delineates the physical conditions associated with the outcome regimes (i.e., bounce, coalescence, and different breakup types) of binary raindrop collisions is proposed. The proposed diagram builds on a theoretical regime diagram defined in the phase space of collision Weber numbers We and the drop diameter ratio p by including critical angle of impact considerations. In this study, the theoretical regime diagram is first evaluated against a comprehensive dataset for drop collision experiments representative of raindrop collisions in nature. Subsequently, the theoretical regime diagram is modified to explicitly describe the dominant regimes of raindrop interactions in (We, p) by delineating the physical conditions necessary for the occurrence of distinct types of collision-induced breakup (neck/filament, sheet, disk, and crown breakups) based on critical angle of impact consideration. Crown breakup is a subtype of disk breakup for lower collision kinetic energy that presents distinctive morphology. Finally, the experimental results are analyzed in the context of the comprehensive collision regime diagram, and conditional probabilities that can be used in the parameterization of breakup kernels in stochastic models of raindrop dynamics are provided.

Corresponding author address: Dr. Firat Y. Testik, 110 Lowry Hall, Civil Engineering Department, Clemson University, Clemson, SC 29634–0911. E-mail: ftestik@clemson.edu
Save
  • Adam, J. R., N. R. Lindblad, and C. D. Hendricks, 1968: The collision, coalescence, and disruption of water droplets. J. Appl. Phys., 39, 51735180.

    • Search Google Scholar
    • Export Citation
  • Andsager, K., N. F. Laird, and N. F. Laird, 1999: Laboratory measurements of axis ratios for large raindrops. J. Atmos. Sci., 56, 26732683.

    • Search Google Scholar
    • Export Citation
  • Ashgriz, N., and J. Y. Poo, 1990: Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech., 221, 183204.

  • Barros, A. P., O. P. Prat, P. Shrestha, F. Y. Testik, and L. F. Bliven, 2008: Revisiting Low and List (1982): Evaluation of raindrop collision parameterizations using laboratory observations and modeling. J. Atmos. Sci., 65, 29832993.

    • Search Google Scholar
    • Export Citation
  • Barros, A. P., O. P. Prat, and F. Y. Testik, 2010: Size distribution of raindrops. Nat. Phys., 6, 232.

  • Beard, K. V., 1977: On the acceleration of large water drops to terminal velocity. J. Appl. Meteor., 16, 10681071.

  • Blanchard, D. C., 1948: Observations on the behavior of water drops at terminal velocity in air. Occasional Rep. 7, Project Cirrus, General Electric Research Laboratory, 15 pp.

    • Search Google Scholar
    • Export Citation
  • Blanchard, D. C., 1949: Experiments with water drops and the interaction between them at terminal velocity in air. Occasional Rep. 17, Project Cirrus, General Electric Research Laboratory, 29 pp.

    • Search Google Scholar
    • Export Citation
  • Bliven, L. F., and T. M. Elfouhaily, 1993: Presenting the Rain–Sea Interaction Facility. NASA Ref. Pub. 1322, 51 pp.

  • Brazier-Smith, P. R., S. G. Jennings, and J. Latham, 1972: The interaction of falling water drops: Coalescence. Proc. Roy. Soc. London, 326A, 393408.

    • Search Google Scholar
    • Export Citation
  • Gotaas, C., P. Havelka, H. A. Jacobsen, H. F. Svendsen, M. Hase, N. Roth, and B. Weigand, 2007: Effect of viscosity on droplet–droplet collision outcome: Experimental study and numerical comparison. Phys. Fluids, 19, 102106, doi:10.1063/1.2781603.

    • Search Google Scholar
    • Export Citation
  • Gunn, R., 1965: Collision characteristics of freely falling water drops. Science, 150, 695701.

  • Jones, B. K., J. R. Saylor, and F. Y. Testik, 2010: Raindrop morphodynamics. Rainfall—The State of the Science, F. Y. Testik and M. Gebremichael, Eds., Amer. Geophys. Union, 7–28.

    • Search Google Scholar
    • Export Citation
  • Langmuir, I., 1948: The production of rain by a chain reaction in cumulus clouds at temperatures above freezing. J. Meteor., 5, 175192.

    • Search Google Scholar
    • Export Citation
  • Lhermitte, R., 1990: Attenuation and scattering of millimeter wavelength radiation by clouds and precipitation. J. Atmos. Oceanic Technol., 7, 464479.

    • Search Google Scholar
    • Export Citation
  • List, R., and D. M. Whelpdale, 1969: A preliminary investigation of factors affecting the coalescence of colliding water drops. J. Atmos. Sci., 26, 305308.

    • Search Google Scholar
    • Export Citation
  • List, R., and G. M. McFarquhar, 1990: The evolution of three-peak raindrop size distributions in one-dimensional shaft models. Part I: Single-pulse rain. J. Atmos. Sci., 47, 29963006.

    • Search Google Scholar
    • Export Citation
  • List, R., C. F. MacNeil, and J. D. McTaggart-Cowan, 1970: Laboratory investigations of temporary collisions of raindrops. J. Geophys. Res., 75, 75737580.

    • Search Google Scholar
    • Export Citation
  • Low, T. B., and R. List, 1982a: Collision, coalescence and breakup of raindrops. Part I: Experimentally established coalescence efficiencies and fragment size distributions in breakup. J. Atmos. Sci., 39, 15911606.

    • Search Google Scholar
    • Export Citation
  • Low, T. B., and R. List, 1982b: Collision, coalescence and breakup of raindrops. Part II: Parameterization of fragment size distributions. J. Atmos. Sci., 39, 16071618.

    • Search Google Scholar
    • Export Citation
  • Magano, C., and T. Nakamura, 1959: On the behavior of water droplets during collision with a large water drop. J. Meteor. Soc. Japan, 37, 124127.

    • Search Google Scholar
    • Export Citation
  • Magarvey, R. H., and J. W. Geldart, 1962: Drop collisions under conditions of free fall. J. Atmos. Sci., 19, 107113.

  • McFarquhar, G. M., 2004: A new representation of collision-induced breakup of raindrops and its implications for the shapes of raindrop size distributions. J. Atmos. Sci., 61, 777794.

    • Search Google Scholar
    • Export Citation
  • McTaggart-Cowan, J. D., and R. List, 1975: Collision and breakup of water drops at terminal velocity. J. Atmos. Sci., 32, 14011411.

  • Menchaca-Rocha, A., F. Huidobro, A. Martinez-Davalos, K. Michaelian, A. Perez, V. Rodriguez, and N. Carjan, 1997: Coalescence and fragmentation of colliding mercury drops. J. Fluid Mech., 346, 291318.

    • Search Google Scholar
    • Export Citation
  • Montgomery, D. N., 1971: Collision and coalescence of water drops. J. Atmos. Sci., 28, 291293.

  • Ochs, H. T., III, K. V. Beard, R. R. Czys, N. F. Laird, D. E. Schaufelberger, and D. J. Holdridge, 1995: Collisions between small precipitation drops. Part I: Laboratory measurements of bounce, coalescence, and temporary coalescence. J. Atmos. Sci., 52, 22582275.

    • Search Google Scholar
    • Export Citation
  • Park, R. W., 1970: Behavior of water drops colliding in humid nitrogen. Ph.D. dissertation, University of Wisconsin, 577 pp.

  • Prat, O., and A. P. Barros, 2007a: A robust numerical solution of the stochastic collection–breakup equation for warm rain. J. Appl. Meteor. Climatol., 46, 14801497.

    • Search Google Scholar
    • Export Citation
  • Prat, O., and A. P. Barros, 2007b: Exploring the use of a column model for the characterization of microphysical processes in warm rain: Results from a homogeneous rainshaft model. Adv. Geosci., 10, 145152.

    • Search Google Scholar
    • Export Citation
  • Prat, O., and A. P. Barros, 2009: Exploring the transient behavior of Z–R relationships: Implications for radar rainfall estimation. J. Appl. Meteor. Climatol., 48, 21272143.

    • Search Google Scholar
    • Export Citation
  • Prat, O., and A. P. Barros, 2010: Assessing satellite-based precipitation estimates in the Southern Appalachian Mountains using raingauges and TRMM PR. Adv. Geosci., 25, 143153.

    • Search Google Scholar
    • Export Citation
  • Qian, J., and C. K. Law, 1997: Regimes of coalescence and separation in droplet collision. J. Fluid Mech., 331, 5980.

  • Schlottke, J., W. Straub, K. D. Beheng, H. Gomass, and B. Weigand, 2010: Numerical investigation of collision-induced breakup of raindrops. Part I: Methodology and dependencies on collision energy and eccentricity. J. Atmos. Sci., 67, 557575.

    • Search Google Scholar
    • Export Citation
  • Straub, W., K. D. Beheng, A. Seifert, J. Schlottke, and B. Weigand, 2010: Numerical investigation of collision-induced breakup of raindrops. Part II: Parameterizations of coalescence efficiencies and fragment size distributions. J. Atmos. Sci., 67, 576588.

    • Search Google Scholar
    • Export Citation
  • Testik, F. Y., 2009: Outcome regimes of binary raindrop collisions. Atmos. Res., 94, 389399.

  • Testik, F. Y., and A. P. Barros, 2007: Toward elucidating the microstructure of warm rainfall: A survey. Rev. Geophys., 45, RG2003, doi:10.1029/2005RG000182.

    • Search Google Scholar
    • Export Citation
  • Testik, F. Y., and D. M. Young, 2008: Breakup patterns for binary drop collisions. J. Visualization, 11, 401405, doi:10.1007/BF03181902.

    • Search Google Scholar
    • Export Citation
  • Testik, F. Y., A. P. Barros, and L. F. Bliven, 2006: Field observations of multimode raindrop oscillations by high-speed imaging. J. Atmos. Sci., 63, 26632668.

    • Search Google Scholar
    • Export Citation
  • Tokay, A., P. G. Bashor, E. Habib, and T. Kasparis, 2008: Raindrop size distribution measurements in tropical cyclones. Mon. Wea. Rev., 136, 16691685.

    • Search Google Scholar
    • Export Citation
  • Villermaux, E., and B. Bossa, 2009: Single-drop fragmentation determines size distribution of raindrops. Nat. Phys., 5, 697702.

  • Wang, P. K., and H. R. Pruppacher, 1977: Acceleration to terminal velocity of cloud and raindrops. J. Appl. Meteor., 16, 276280.

  • Yarin, A. L., 1993: Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman, 446 pp.

  • Yarin, A. L., 2006: Drop impact dynamics: Splashing, spreading, receding, bouncing…. Annu. Rev. Fluid Mech., 38, 159192.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 726 182 16
PDF Downloads 507 139 9