Hostname: page-component-7dd5485656-dk7s8 Total loading time: 0 Render date: 2025-10-29T23:06:35.256Z Has data issue: false hasContentIssue false
  • English
  • Français

Droplet dynamics and fine-scale structure in a shearless turbulent mixing layer with phase changes

Published online by Cambridge University Press:  08 February 2017

Paul Götzfried ,
Bipin Kumar ,
Raymond A. Shaw  and
Jörg Schumacher
Paul Götzfried*
Affiliation:
Institut für Thermo- und Fluiddynamik, Postfach 100565, Technische Universität Ilmenau, D-98684 Ilmenau, Germany
Bipin Kumar
Affiliation:
Indian Institute of Tropical Meteorology, Dr Homi Bhaba Road, Pashan, Pune 411008, Maharashtra, India
Raymond A. Shaw
Affiliation:
Department of Physics, Michigan Technological University, Houghton, MI 49931, USA
Jörg Schumacher
Affiliation:
Institut für Thermo- und Fluiddynamik, Postfach 100565, Technische Universität Ilmenau, D-98684 Ilmenau, Germany
*
†Email address for correspondence: paul.goetzfried@tu-ilmenau.de
Get access Rights & Permissions [Opens in a new window]

Abstract

Three-dimensional direct numerical simulations of a shearless mixing layer in a small fraction of the cloud–clear air interface are performed to study the response of an ensemble of cloud water droplets to the turbulent entrainment of clear air into a cloud filament. The main goal of this work is to understand how mixing of cloudy and clear air evolves as turbulence and thermodynamics interact through phase changes, and how the cloud droplets respond. In the main simulation case, mixing proceeds between a higher level of turbulence in the cloudy filament and a lower level of turbulence in the clear air environment – the typical shearless mixing layer set-up. Fluid turbulence is driven solely by buoyancy, which incorporates feedbacks from the temperature, the vapour content and the liquid water content fields. Two different variations on the core set of shearless mixing layer simulations are discussed, a simulation in a larger domain and a simulation with the same turbulence level inside the filament and its environment. Overall, it is found that, as evaporation occurs for the droplets that enter subsaturated clear air regions, buoyancy comes to dominate the subsequent evolution of the mixing layer. The buoyancy feedback leads initially to downdraughts at the cloudy–clear air interface and to updraughts in the bulk regions. The strength of the turbulence after initial transients depends on the domain size, showing that the range of scales is an important parameter in the shearless mixing layer set-up. In contrast, the level of turbulence in the clear air is found to have little effect on the evolution of the mixing process. The distributions of cloud water droplet size, supersaturation at the droplet positions and vertical velocity are more sensitive to domain size than to the details of the turbulence profile, suggesting that the evolution of cloud microphysics is more sensitive to large-scale as opposed to small-scale properties of the flow.

JFM classification

Phase change: Condensation/evaporation Multiphase and Particle-laden Flows: Particle/fluid flow Mixing: Turbulent mixing

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 814 , 10 March 2017 , pp. 452 - 483
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abma, D., Heus, T. & Mellado, P. J. Direct numerical simulation of evaporative cooling at the lateral boundary of shallow cumulus clouds. J. Atmos. Sci. 70, 2088–2102.Google Scholar
Andrejczuk, M., Grabowski, W. W., Malinowski, S. P. & Smolarkiewicz, P. K. 2006 Numerical simulation of cloud–clear air interfacial mixing: effects on cloud microphysics. J. Atmos. Sci. 63, 3204–3225.CrossRefGoogle Scholar
Andrejczuk, M., Grabowski, W. W., Malinowski, S. P. & Smolarkiewicz, P. K. 2009 Numerical simulation of cloud–clear air interfacial mixing: homogeneous versus inhomogeneous mixing. J. Atmos. Sci. 66, 2493–2500.Google Scholar
Atkinson, B. W. & Zhang, J. W. 1996 Mesoscale shallow convection in the atmosphere. Rev. Geophys. 34, 403–431.CrossRefGoogle Scholar
Austin, P. H., Baker, M. B., Blyth, A. M. & Jensen, J. B. 1985 Small-scale variability in warm continental cumulus clouds. J. Atmos. Sci. 42, 1123–1138.Google Scholar
Beals, M. J., Fugal, J. P., Shaw, R. A., Lu, J., Spuler, S. M. & Stith, J. L. 2015 Holographic measurements of inhomogeneous cloud mixing at the centimeter scale. Science 350, 87–90.Google Scholar
Bergougnoux, L., Bouchet, G., Lopez, D. & Guazzelli, É. 2014 The motion of solid spherical particles falling in a cellular flow field at low Stokes number. Phys. Fluids 26, 093302.Google Scholar
Blyth, A. M. 1993 Entrainment in cumulus clouds. J. Appl. Meteorol. 32, 626–641.2.0.CO;2>CrossRefGoogle Scholar
Bodenschatz, E., Malinowski, S. P., Shaw, R. A. & Stratmann, F. 2010 Can we understand clouds without turbulence? Science 327, 970–971.CrossRefGoogle ScholarPubMed
Briggs, D. A., Ferziger, J. H. & Koseff, J. R. 1996 Entrainment in a shear-free turbulent mixing layer. J. Fluid Mech. 310, 215–241.CrossRefGoogle Scholar
Crowe, C., Sommerfeld, M. & Tsuji, Y. 1998 Multiphase Flows With Droplets and Particles. CRC Press.Google Scholar
Gerashchenko, S., Good, G. & Warhaft, Z. 2011 Entrainment and mixing of water droplets across a shearless turbulent interface with and without gravitational effects. J. Fluid Mech. 668, 293–303.Google Scholar
Gerber, E. H., Frick, M. G. & Jensen, J. B. 2008 Entrainment, mixing, and microphysics in trade-wind cumulus. J. Met. Soc. Japan 86A, 87–106.Google Scholar
Gilbert, B. 1980 Diffusion mixing in grid turbulence. J. Fluid Mech. 100, 349–365.CrossRefGoogle Scholar
Good, G. H., Gerashchenko, S. & Warhaft, Z. 2012 Intermittency and inertial particle entrainment at a turbulent interface: the effect of the large-scale eddies. J. Fluid Mech. 694, 371–398.Google Scholar
Gotoh, T., Suehiro, T. & Saito, I. 2016 Continuous growth of cloud droplets in cumulus cloud. New J. Phys. 18, 043042.Google Scholar
Grabowski, W. W. & Wang, L. P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293–324.Google Scholar
Hamlington, P. E., Schumacher, J. & Dahm, W. J. A. 2008 Local and nonlocal strain rate fields and vorticity alignment in turbulent flows. Phys. Rev. E 77, 026303.CrossRefGoogle ScholarPubMed
Heus, T. & Jonker, H. J. J. 2008 Subsiding shells around shallow cumulus clouds. J. Atmos. Sci. 65, 1003–1018.Google Scholar
Holzner, M., Liberzon, A., Nikitin, N., Lüthi, B., Kinzelbach, W. & Tsinober, A. 2008 A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation. J. Fluid Mech. 598, 465–475.CrossRefGoogle Scholar
Ireland, P. J. & Collins, L. R. 2012 Direct numerical simulation of inertial particle entrainment in a shearless mixing layer. J. Fluid Mech. 704, 301–332.Google Scholar
Katzwinkel, J., Siebert, H., Heus, T. & Shaw, R. A. 2014 Measurements of turbulent mixing and subsiding shells in trade wind cumuli. J. Atmos. Sci. 71, 2810–2822.Google Scholar
Knaepen, B., Debliquy, O. & Carati, D. 2004 Direct numerical simulation and large-eddy simulation of a shear-free mixing layer. J. Fluid Mech. 514, 153–172.Google Scholar
Kumar, B., Janetzko, F., Schumacher, J. & Shaw, R. A. 2012 Extreme responses of a coupled scalar-particle system during turbulent mixing. New J. Phys. 14, 115020.Google Scholar
Kumar, B., Schumacher, J. & Shaw, R. A. 2013 Cloud microphysical effects of turbulent mixing and entrainment. Theor. Comput. Fluid Dyn. 27, 361–376.Google Scholar
Kumar, B., Schumacher, J. & Shaw, R. A. 2014 Lagrangian mixing dynamics at the cloudy–clear air interface. J. Atmos. Sci. 71, 2564–2580.Google Scholar
Lanotte, S. A., Seminara, A. & Toschi, F. 2009 Cloud droplet growth by condensation in homogeneous isotropic turbulence. J. Atmos. Sci. 66, 1685–1697.Google Scholar
Lehmann, K., Siebert, H. & Shaw, R. A. 2009 Homogeneous and inhomogeneous mixing in cumulus clouds: dependence on local turbulence structure. J. Atmos. Sci. 66, 3641–3659.Google Scholar
Malinowski, S. P., Andrejczuk, M., Grabowski, W. W., Korczyk, P., Kowalewski, T. A. & Smolarkiewicz, P. K. 2008 Laboratory and modeling studies of cloud–clear air interfacial mixing: anisotropy of small-scale turbulence due to evaporative cooling. New J. Phys. 10, 075020.Google Scholar
Mellado, J. P. 2010 The evaporatively driven cloud–top mixing layer. J. Fluid Mech. 660, 5–36.CrossRefGoogle Scholar
Olivieri, S., Picano, F., Sardina, G., Iudicone, D. & Brandt, L. 2014 The effect of the Basset history force on particle clustering in homogeneous and isotropic turbulence. Phys. Fluids 26, 041704.Google Scholar
Onishi, R., Matsuda, K. & Takahashi, K. 2015 Lagrangian tracking simulation of droplet growth in turbulence enhancement of autoconversion rate. J. Atmos. Sci. 72, 2591–2607.Google Scholar
Perrin, V. E. & Jonker, J. J. H. 2015 Lagrangian droplet dynamics in the subsiding shell of a cloud using direct numerical simulations. J. Atmos. Sci. 72, 4015–4028.CrossRefGoogle Scholar
Rogallo, R. S.1981 Numerical experiments in homogeneous turbulence. NASA Tech. Mem. 81835.Google Scholar
Rogers, R. R. & Yau, M. K. 1989 A Short Course in Cloud Physics. Pergamon.Google Scholar
Sardina, G., Picano, F., Brandt, L. & Caballero, R. 2015 Continuous growth of droplet size variance due to condensation in turbulent clouds. Phys. Rev. Lett. 115, 184501.Google Scholar
Schumacher, J., Eckhardt, B. & Doering, C. R. 2010 Extreme vorticity growth in Navier–Stokes turbulence. Phys. Lett. A 374, 861–865.Google Scholar
Schumacher, J., Götzfried, P. & Scheel, J. D. 2015 Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids. Proc. Natl Acad. Sci. USA 112, 9530–9535.Google Scholar
Schumacher, J., Sreenivasan, K. R. & Yakhot, V. 2007 Asymptotic exponents from low-Reynolds-number flows. New J. Phys. 9, 89.Google Scholar
Shaw, R. A. 2003 Particle turbulence intercations in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227.Google Scholar
Siebert, H., Beals, M., Bethke, J., Bierwirth, E., Conrath, T., Dieckmann, K., Ditas, F., Ehrlich, A., Farrell, D., Hartmann, S. et al. 2013 The fine-scale structure of the trade wind cumuli over Barbados – an introduction to the CARRIBA project. Atmos. Chem. Phys. 13, 10061–10077.Google Scholar
Siebert, H., Lehmann, K., Wendisch, M., Franke, H., Maser, R., Schell, D., Saw, E. W. & Shaw, R. A. Probing finescale dynamics and microphysics of clouds with helicopter-borne measurements. Bull. Am. Meteorol. Soc. 87 (12), 1727–1738.Google Scholar
da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46, 567–590.CrossRefGoogle Scholar
Stevens, B. & Bony, S. 2013 Water in the atmosphere. Phys. Today 66 (6), 29–34.Google Scholar
Tordella, D. & Iovieno, M. 2006 Numerical experiments on the intermediate asymptotics of shear-free turbulent transport and diffusion. J. Fluid Mech. 549, 429–441.Google Scholar
Tordella, D. & Iovieno, M. 2011 Small-scale anisotropy in turbulent shearless mixing. Phys. Rev. Lett. 107, 194501.CrossRefGoogle ScholarPubMed
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.Google Scholar
Vaillancourt, P. A., Yau, M. K. & Grabowski, W. W. 2001 Microscopic approach to cloud droplet growth by condensation. Part I: model description and results without turbulence. J. Atmos. Sci. 58, 1945–1964.Google Scholar
Veeravalli, S. & Warhaft, Z. 1989 The shearless turbulence mixing layer. J. Fluid Mech. 206, 191–229.Google Scholar
Zeff, B. W., Lanterman, D. D., McAllister, R., Roy, R., Kostelich, E. J. & Lathrop, D. P. 2003 Measuring intense rotation and dissipation in turbulent flows. Nature 421, 146–149.Google Scholar
Zonta, F. & Soldati, A. 2014 Effect of temperature-dependent fluid properties on heat transfer in turbulent mixied convection. Trans. ASME J. Heat Transfer 136, 022501.Google Scholar