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Article
Article Type:
Research Article

Lagrangian Droplet Dynamics in the Subsiding Shell of a Cloud Using Direct Numerical Simulations

Vincent E. Perrin Delft University of Technology, Delft, Netherlands

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Harmen J. J. Jonker Delft University of Technology, Delft, Netherlands

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Print Publication:
01 Oct 2015
DOI:
https://doi.org/10.1175/JAS-D-15-0045.1
Page(s):
4015–4028
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Abstract

This study investigates the droplet dynamics at the lateral cloud–environment interface in shallow cumulus clouds. A mixing layer is used to study a small part of the cloud edge using direct numerical simulation combined with a Lagrangian particle tracking and collision algorithm. The effect of evaporation, gravity, coalescence, and the initial droplet size distribution on the intensity of the mixing layer and the evolution of the droplet size distribution is studied. Mixing of the droplets with environmental air induces evaporative cooling, which results in a very characteristic subsiding shell. As a consequence, stronger horizontal velocity gradients are found in the mixing layer, which induces more mixing and evaporation. A broadening of the droplet size distribution is observed as a result of evaporation and coalescence. Gravity acting on the droplets allows droplets in cloudy filaments detrained from the cloud to sediment and remain longer in the unsaturated environment. While this effect of gravity did not have a significant impact in this case on the mean evolution of the mixing layer, it does contribute to the broadening of the droplet size distribution and thereby significantly increases the collision rate. Although more but smaller droplets result in more evaporative cooling, more droplets also increase small-scale fluctuations and the production of turbulent dissipation. For the smallest droplets considered with a radius of 10 μm, the authors found that, although a more pronounced buoyancy dip was present, the increase in dissipation rate actually led to a decrease in the turbulent intensity of the mixing layer. Extrapolation of the results to realistic clouds is discussed.

Corresponding author address: Harmen J. J. Jonker, Delft University of Technology, Stevinweg 1, Delft 2628 CN, Netherlands. E-mail: h.j.j.jonker@tudelft.nl

Abstract

This study investigates the droplet dynamics at the lateral cloud–environment interface in shallow cumulus clouds. A mixing layer is used to study a small part of the cloud edge using direct numerical simulation combined with a Lagrangian particle tracking and collision algorithm. The effect of evaporation, gravity, coalescence, and the initial droplet size distribution on the intensity of the mixing layer and the evolution of the droplet size distribution is studied. Mixing of the droplets with environmental air induces evaporative cooling, which results in a very characteristic subsiding shell. As a consequence, stronger horizontal velocity gradients are found in the mixing layer, which induces more mixing and evaporation. A broadening of the droplet size distribution is observed as a result of evaporation and coalescence. Gravity acting on the droplets allows droplets in cloudy filaments detrained from the cloud to sediment and remain longer in the unsaturated environment. While this effect of gravity did not have a significant impact in this case on the mean evolution of the mixing layer, it does contribute to the broadening of the droplet size distribution and thereby significantly increases the collision rate. Although more but smaller droplets result in more evaporative cooling, more droplets also increase small-scale fluctuations and the production of turbulent dissipation. For the smallest droplets considered with a radius of 10 μm, the authors found that, although a more pronounced buoyancy dip was present, the increase in dissipation rate actually led to a decrease in the turbulent intensity of the mixing layer. Extrapolation of the results to realistic clouds is discussed.

Corresponding author address: Harmen J. J. Jonker, Delft University of Technology, Stevinweg 1, Delft 2628 CN, Netherlands. E-mail: h.j.j.jonker@tudelft.nl
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  • Abma, D., T. Heus, and J. P. Mellado, 2013: Direct numerical simulation of evaporative cooling at the lateral boundary of shallow cumulus clouds. J. Atmos. Sci., 70, 2088–2102, doi:10.1175/JAS-D-12-0230.1.

    • Search Google Scholar
    • Export Citation

  • Alduchov, O. A., and R. E. Eskridge, 1996: Improved Magnus form approximation of saturation vapor pressure. J. Appl. Meteor., 35, 601–609, doi:10.1175/1520-0450(1996)035<0601:IMFAOS>2.0.CO;2.

  • Allen, P., and D. J. Tildesley, 1987: Computer Simulation of Liquids. Clarendon Press, 408 pp.

  • Andrejczuk, M., W. W. Grabowski, S. P. Malinowski, and P. K. Smolarkiewicz, 2004: Numerical simulation of cloud–clear air interfacial mixing. J. Atmos. Sci., 61, 1726–1739, doi:10.1175/1520-0469(2004)061<1726:NSOCAI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Andrejczuk, M., W. W. Grabowski, S. P. Malinowski, and P. K. Smolarkiewicz, 2006: Numerical simulation of cloud–clear air interfacial mixing: Effects on cloud microphysics. J. Atmos. Sci., 63, 3204–3225, doi:10.1175/JAS3813.1.

    • Search Google Scholar
    • Export Citation

  • Andrejczuk, M., W. W. Grabowski, S. P. Malinowski, and P. K. Smolarkiewicz, 2009: Numerical simulation of cloud–clear air interfacial mixing: Homogeneous versus inhomogeneous mixing. J. Atmos. Sci., 66, 2493–2500, doi:10.1175/2009JAS2956.1.

    • Search Google Scholar
    • Export Citation

  • Arabas, S., and S.-i. Shima, 2013: Large-eddy simulations of trade wind cumuli using particle-based microphysics with Monte Carlo coalescence. J. Atmos. Sci., 70, 2768–2777, doi:10.1175/JAS-D-12-0295.1.

    • 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, 183–204, doi:10.1017/S0022112090003536.

    • Search Google Scholar
    • Export Citation

  • Ayala, O., B. Rosa, and L. P. Wang, 2008: Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 2. Theory and parameterization. New J. Phys., 10, 075016, doi:10.1088/1367-2630/10/7/075016.

    • Search Google Scholar
    • Export Citation

  • Babkovskaia, N., M. Boy, S. Smolander, S. Romakkaniemi, U. Rannik, and M. Kulmala, 2015: A study of aerosol activation at the cloud edge with high resolution numerical simulations. Atmos. Res., 153, 49–58, doi:10.1016/j.atmosres.2014.07.017.

    • Search Google Scholar
    • Export Citation

  • Caporaloni, M., F. Tampieri, F. Trombetti, and O. Vittori, 1975: Transfer of particles in nonisotropic air turbulence. J. Atmos. Sci., 32, 565–568, doi:10.1175/1520-0469(1975)032<0565:TOPINA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Chen, M., K. Kontomaris, and J. B. McLaughlin, 1999: Direct numerical simulation of droplet collisions in a turbulent channel flow. Part I: Collision algorithm. Int. J. Multiphase Flow, 24, 1079–1103, doi:10.1016/S0301-9322(98)00007-X.

    • Search Google Scholar
    • Export Citation

  • Deardorff, J. W., 1980: Cloud top entrainment instability. J. Atmos. Sci., 37, 131–147, doi:10.1175/1520-0469(1980)037<0131:CTEI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Devenish, B. J., and Coauthors, 2012: Droplet growth in warm turbulent clouds. Quart. J. Roy. Meteor. Soc., 138, 1401–1429, doi:10.1002/qj.1897.

    • Search Google Scholar
    • Export Citation

  • Falkovich, G., and A. Pumir, 2007: Sling effect in collisions of water droplets in turbulent clouds. J. Atmos. Sci., 64, 4497–4505, doi:10.1175/2007JAS2371.1.

    • Search Google Scholar
    • Export Citation

  • Falkovich, G., A. Fouxon, and M. G. Stepanov, 2002: Acceleration of rain initiation by cloud turbulence. Nature, 419, 151–154, doi:10.1038/nature00983.

    • Search Google Scholar
    • Export Citation

  • Gatignol, R., 1983: The Faxén formulas for a rigid particle in an unsteady non-uniform Stokes-flow. J. Mec. Theor. Appl., 2, 143–160.

  • Grabowski, W. W., 1989: Numerical experiments on the dynamics of the cloud–environment interface: Small cumulus in a shear-free environment. J. Atmos. Sci., 46, 3513–3541, doi:10.1175/1520-0469(1989)046<3513:NEOTDO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Grabowski, W. W., and L.-P. Wang, 2013: Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech., 45, 293–324, doi:10.1146/annurev-fluid-011212-140750.

    • Search Google Scholar
    • Export Citation

  • Grabowski, W. W., M. Andrejczuk, and L. P. Wang, 2011: Droplet growth in a bin warm-rain scheme with Twomey CCN activation. Atmos. Res., 99, 290–301, doi:10.1016/j.atmosres.2010.10.020.

    • Search Google Scholar
    • Export Citation

  • Hall, W. D., 1980: A detailed microphysical model within a two-dimensional dynamic framework: Model description and preliminary results. J. Atmos. Sci., 37, 2486–2507, doi:10.1175/1520-0469(1980)037<2486:ADMMWA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Heus, T., and H. J. J. Jonker, 2008: Subsiding shells around shallow cumulus clouds. J. Atmos. Sci., 65, 1003–1018, doi:10.1175/2007JAS2322.1.

    • Search Google Scholar
    • Export Citation

  • Heus, T., C. F. J. Pols, H. J. J. Jonker, H. E. den Akker, and D. H. Lenschow, 2009: Observational validation of the compensating mass flux through the shell around cumulus clouds. Quart. J. Roy. Meteor. Soc., 135, 101–112, doi:10.1002/qj.358.

    • Search Google Scholar
    • Export Citation

  • Heus, T., and Coauthors, 2010: Formulation of the Dutch Atmospheric Large-Eddy Simulation (DALES) and overview of its applications. Geosci. Model Dev., 3, 415–444, doi:10.5194/gmd-3-415-2010.

    • Search Google Scholar
    • Export Citation

  • Jonas, P. R., 1996: Turbulence and cloud microphysics. Atmos. Res., 40, 283–306, doi:10.1016/0169-8095(95)00035-6.

  • Jones, W. P., S. Lyra, and A. J. Marquis, 2010: Large eddy simulation of a droplet laden turbulent mixing layer. Int. J. Heat Fluid Flow, 31, 93–100, doi:10.1016/j.ijheatfluidflow.2009.10.001.

    • Search Google Scholar
    • Export Citation

  • Jonker, H. J. J., T. Heus, and P. P. Sullivan, 2008: A refined view of vertical mass transport by cumulus convection. Geophys. Res. Lett., 35, L07810, doi:10.1029/2007GL032606.

    • Search Google Scholar
    • Export Citation

  • Jonker, H. J. J., M. van Reeuwijk, P. P. Sullivan, and E. G. Patton, 2013: On the scaling of shear-driven entrainment: A DNS study. J. Fluid Mech., 732, 150–165, doi:10.1017/jfm.2013.394.

    • Search Google Scholar
    • Export Citation

  • Katzwinkel, J., H. Siebert, T. Heus, and R. a. Shaw, 2014: Measurements of turbulent mixing and subsiding shells in trade wind cumuli. J. Atmos. Sci., 71, 2810–2822, doi:10.1175/JAS-D-13-0222.1.

    • Search Google Scholar
    • Export Citation

  • Khain, A., M. Pinsky, T. Elperin, N. Kleeorin, I. Rogachevskii, and A. Kostinski, 2007: Critical comments to results of investigations of drop collisions in turbulent clouds. Atmos. Res., 86, 1–20, doi:10.1016/j.atmosres.2007.05.003.

    • Search Google Scholar
    • Export Citation

  • Khain, A., and Coauthors, 2015: Representation of microphysical processes in cloud-resolving models: Spectral (bin) microphysics versus bulk parameterization. Rev. Geophys., 53, 247–322, doi:10.1002/2014RG000468.

    • Search Google Scholar
    • Export Citation

  • Korczyk, P., S. P. Malinowski, and T. A. Kowalewski, 2006: Mixing of cloud and clear air in centimeter scales observed in laboratory by means of Particle Image Velocimetry. Atmos. Res., 82, 173–182, doi:10.1016/j.atmosres.2005.09.009.

    • Search Google Scholar
    • Export Citation

  • Korolev, A., M. Pinsky, and A. Khain, 2013: A new mechanism of droplet size distribution broadening during diffusional growth. J. Atmos. Sci., 70, 2051–2071, doi:10.1175/JAS-D-12-0182.1.

    • 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, 235–244, doi:10.1175/BAMS-86-2-235.

    • Search Google Scholar
    • Export Citation

  • Kumar, B., J. Schumacher, and R. A. Shaw, 2013: Cloud microphysical effects of turbulent mixing and entrainment. Theor. Comput. Fluid Dyn., 27, 361–376, doi:10.1007/s00162-012-0272-z.

    • Search Google Scholar
    • Export Citation

  • Kumar, B., J. Schumacher, and R. A. Shaw, 2014: Lagrangian mixing dynamics at the cloudy–clear air interface. J. Atmos. Sci., 71, 2564–2580, doi:10.1175/JAS-D-13-0294.1.

    • Search Google Scholar
    • Export Citation

  • Lanotte, A. S., A. Seminara, and F. Toschi, 2009: Cloud droplet growth by condensation in homogeneous isotropic turbulence. J. Atmos. Sci., 66, 1685–1697, doi:10.1175/2008JAS2864.1.

    • Search Google Scholar
    • Export Citation

  • Lasher-Trapp, S. G., W. A. Cooper, and A. M. Blyth, 2005: Broadening of droplet size distributions from entrainment and mixing in a cumulus cloud. Quart. J. Roy. Meteor. Soc., 131, 195–220, doi:10.1256/qj.03.199.

    • Search Google Scholar
    • Export Citation

  • Lee, J., Y. Noh, S. Raasch, T. Riechelmann, and L.-P. Wang, 2014: Investigation of droplet dynamics in a convective cloud using a Lagrangian cloud model. Meteor. Atmos. Phys., 124, 1–21, doi:10.1007/s00703-014-0311-y.

    • Search Google Scholar
    • Export Citation

  • Lehmann, K., H. Siebert, and R. A. Shaw, 2009: Homogeneous and inhomogeneous mixing in cumulus clouds: Dependence on local turbulence structure. J. Atmos. Sci., 66, 3641–3659, doi:10.1175/2009JAS3012.1.

    • Search Google Scholar
    • Export Citation

  • Maxey, M. R., and J. J. Riley, 1983: Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids, 26, 883–889, doi:10.1063/1.864230.

    • Search Google Scholar
    • Export Citation

  • Mellado, J. P., 2010: The evaporatively driven cloud-top mixing layer. J. Fluid Mech., 660, 5–36, doi:10.1017/S0022112010002831.

  • Mellado, J. P., B. Stevens, H. Schmidt, and N. Peters, 2009: Buoyancy reversal in cloud-top mixing layers. Quart. J. Roy. Meteor. Soc., 135, 963–978, doi:10.1002/qj.417.

    • Search Google Scholar
    • Export Citation

  • Perrin, V. E., and H. J. J. Jonker, 2014: Preferred location of droplet collisions in turbulent flows. Phys. Rev., 89E, 33005, doi:10.1103/PhysRevE.89.033005.

    • Search Google Scholar
    • Export Citation

  • Pinsky, M. B., and A. P. Khain, 2002: Effects of in-cloud nucleation and turbulence on droplet spectrum formation in cumulus clouds. Quart. J. Roy. Meteor. Soc., 128, 501–533, doi:10.1256/003590002321042072.

    • Search Google Scholar
    • Export Citation

  • Pinsky, M. B., A. P. Khain, and M. Shapiro, 1999: Collisions of small drops in a turbulent flow. Part I: Collision efficiency. Problem formulation and preliminary results. J. Atmos. Sci., 56, 2585–2600, doi:10.1175/1520-0469(1999)056<2585:COSDIA>2.0.CO;2.

  • Pinsky, M. B., 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, 742–764, doi:10.1175/1520-0469(2001)058<0742:CEODIA>2.0.CO;2.

  • Pinsky, M. B., I. P. Mazin, A. Korolev, and A. Khain, 2013: Supersaturation and diffusional droplet growth in liquid clouds. J. Atmos. Sci., 70, 2778–2793, doi:10.1175/JAS-D-12-077.1.

    • Search Google Scholar
    • Export Citation

  • Pruppacher, H. R., and J. D. Klett, 1978: Microphysics of Clouds and Precipitation. Springer, 714 pp.

  • Qian, J., and C. K. Law, 1997: Regimes of coalescence and separation in droplet collision. J. Fluid Mech., 331, 59–80, doi:10.1017/S0022112096003722.

    • Search Google Scholar
    • Export Citation

  • Riechelmann, T., Y. Noh, and S. Raasch, 2012: A new method for large-eddy simulations of clouds with Lagrangian droplets including the effects of turbulent collision. New J. Phys., 14, 065008, doi:10.1088/1367-2630/14/6/065008.

  • Sedunov, Y. S., and P. Greenberg, 1974: Physics of Drop Formation in the Atmosphere. Wiley, 234 pp.

  • Seifert, A., and K. D. Beheng, 2001: A double-moment parameterization for simulating autoconversion, accretion and selfcollection. Atmos. Res., 59–60, 265–281, doi:10.1016/S0169-8095(01)00126-0.

    • Search Google Scholar
    • Export Citation

  • Seifert, A., L. Nuijens, and B. Stevens, 2010: Turbulence effects on warm-rain autoconversion in precipitating shallow convection. Quart. J. Roy. Meteor. Soc., 136, 1753–1762, doi:10.1002/qj.684.

    • Search Google Scholar
    • Export Citation

  • Shaw, R. A., 2000: Supersaturation intermittency in turbulent clouds. J. Atmos. Sci., 57, 3452–3456, doi:10.1175/1520-0469(2000)057<3452:SIITC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Shaw, R. A., 2003: Particle-turbulence interaction in atmospheric clouds. Annu. Rev. Fluid Mech., 35, 183–227, doi:10.1146/annurev.fluid.35.101101.161125.

    • Search Google Scholar
    • Export Citation

  • Siebert, H., K. Lehmann, M. Wendisch, H. Franke, R. Maser, D. Schell, E. Wei Saw, and R. A. Shaw, 2006: Probing finescale dynamics and microphysics of clouds with helicopter-borne measurements. Bull. Amer. Meteor. Soc., 87, 1727–1738, doi:10.1175/BAMS-87-12-1727.

    • Search Google Scholar
    • Export Citation

  • Tölle, M. H., and S. K. Krueger, 2014: Effects of entrainment and mixing on droplet size distributions in warm cumulus clouds. J. Adv. Model. Earth Syst., 6, 281–299, doi:10.1002/2012MS000209.

    • Search Google Scholar
    • Export Citation

  • Vaillancourt, P. A., M. K. Yau, and W. W. Grabowski, 2001: Microscopic approach to cloud droplet growth by condensation. Part I: Model description and results without turbulence. J. Atmos. Sci., 58, 1945–1964, doi:10.1175/1520-0469(2001)058<1945:MATCDG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Vaillancourt, P. A., M. K. Yau, P. Bartello, and W. W. Grabowski, 2002: Microscopic approach to cloud droplet growth by condensation. Part II: Turbulence, clustering, and condensational growth. J. Atmos. Sci., 59, 3421–3435, doi:10.1175/1520-0469(2002)059<3421:MATCDG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Wallace, J. M., and P. V. Hobbs, 2006: Atmospheric Science: An Introductory Survey. 2nd ed. Elsevier, 504 pp.

  • Wang, Y., and B. Geerts, 2010: Humidity variations across the edge of trade wind cumuli: Observations and dynamical implications. Atmos. Res., 97, 144–156, doi:10.1016/j.atmosres.2010.03.017.

    • Search Google Scholar
    • Export Citation

  • Wilkinson, M., and B. Mehlig, 2005: Caustics in turbulent aerosols. Europhys. Lett., 71, 186, doi:10.1209/epl/i2004-10532-7.

  • Wilkinson, M., B. Mehlig, and V. Bezuglyy, 2006: Caustic activation of rain showers. Phys. Rev. Lett., 97, 048501, doi:10.1103/PhysRevLett.97.048501.

    • Search Google Scholar
    • Export Citation

  • Woittiez, E. J. P., H. J. J. Jonker, and L. M. Portela, 2009: On the combined effects of turbulence and gravity on droplet collisions in clouds: A numerical study. J. Atmos. Sci., 66, 1926–1943, doi:10.1175/2005JAS2669.1.

    • Search Google Scholar
    • Export Citation
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