- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Droplet clustering signatures of entrainment in clouds

Suryadev Pratap Singh*

Michael L. Larsen†

Jesse C. Anderson, Hamed Fahandezh Sadi, Jae Min Yeom, Will Cantrell, and Raymond A. Shaw‡

  • Department of Physics and Astronomy, College of Charleston, Charleston, South Carolina 29424, USA; Laboratory for Fluid Physics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany; and Department of Physics, Michigan Technological University Houghton, Michigan 49931, USA

  • *Contact author: ssingh45@mtu.edu
  • †Present address: Department of Physics and Astronomy, College of Charleston, Charleston, South Carolina 29424, USA.
  • ‡Contact author: rashaw@mtu.edu
PDF

Phys. Rev. Research 8, 033321 – Published 15 September, 2026

DOI: https://doi.org/10.1103/4hrw-nf7t

Abstract

The spatial distribution of cloud droplets is relevant for various microphysical processes, such as condensational growth, collision coalescence, riming and aggregation, and radiative transfer. Cloud droplets and other hydrometeors exhibit clustering at dissipation scales and above due to turbulence-induced preferential concentration. Here, we investigate the role of entrainment in modulating the scale-dependent clustering of cloud droplets and explore how this mechanism differs from inertial clustering. We have performed experiments in the Pi convection-cloud chamber, and imaged 2D droplet fields in the cloud-top region where dry-air entrained through an open cylindrical flange leads to an entrainment-mixing process. Captured images are processed to retrieve instantaneous two-dimensional velocity fields using particle image velocimetry, scale-dependent clustering is explored using the radial distribution function, and spatial nonuniformity is quantitatively identified through the Kolmogorov-Smirnov test. The analysis reveals that the observed droplet clustering is scale dependent and occurs intermittently with enhanced magnitude in the region influenced by entrainment. Furthermore, the strength of clustering and spatial nonuniformity increases with mean entrainment flow. Using a novel bias-mitigation method, we estimate that the strength of clustering (pair-correlation function) roughly doubles in the presence of entrainment (downdraft), compared to no-entrainment (updraft) regimes. Such an entrainment-clustering relationship could be used to help identify and decipher the role of entrainment in modulating localized clustering in natural atmospheric clouds.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (61)

  1. L. Pan, P. Padoan, J. Scalo, A. G. Kritsuk, and M. L. Norman, Turbulent clustering of protoplanetary dust and planetesimal formation, Astrophys. J. 740, 6 (2011).
  2. M. Borgnino, J. Arrieta, G. Boffetta, F. De Lillo, and I. Tuval, Turbulence induces clustering and segregation of non-motile, buoyancy-regulating phytoplankton, J. R. Soc. Interface 16, 20190324 (2019).
  3. F. Azam and F. Malfatti, Microbial structuring of marine ecosystems, Nat. Rev. Microbiol. 5, 782 (2007).
  4. L. Schmidt, I. Fouxon, and M. Holzner, Inertial particles distribute in turbulence as Poissonian points with random intensity inducing clustering and supervoiding, Phys. Rev. Fluids 2, 074302 (2017).
  5. J. Krüger, N. E. Haugen, D. Mitra, and T. Løvås, The effect of turbulent clustering on particle reactivity, Proc. Combust. Inst. 36, 2333 (2017).
  6. A. B. Kostinski and R. A. Shaw, Scale-dependent droplet clustering in turbulent clouds, J. Fluid Mech. 434, 389 (2001).
  7. H. R. Pruppacher and J. D. Klett, Microphysics of Clouds and Precipitation: Reprinted 1980 (Springer Science & Business Media, Dordrecht, Netherlands, 2012).
  8. M. L. Larsen, R. A. Shaw, A. B. Kostinski, and S. Glienke, Fine-scale droplet clustering in atmospheric clouds: 3D radial distribution function from airborne digital holography, Phys. Rev. Lett. 121, 204501 (2018).
  9. R. Srivastava, Growth of cloud drops by condensation: A criticism of currently accepted theory and a new approach, J. Atmos. Sci. 46, 869 (1989).
  10. W. W. Grabowski and L.-P. Wang, Growth of cloud droplets in a turbulent environment, Annu. Rev. Fluid Mech. 45, 293 (2013).
  11. A. B. Kostinski, On the extinction of radiation by a homogeneous but spatially correlated random medium, J. Opt. Soc. Am. A 18, 1929 (2001).
  12. R. A. Shaw, A. B. Kostinski, and D. D. Lanterman, Super-exponential extinction of radiation in a negatively correlated random medium, J. Quant. Spectrosc. Radiat. Transfer 75, 13 (2002).
  13. M. L. Larsen and A. S. Clark, On the link between particle size and deviations from the Beer–Lambert–Bouguer law for direct transmission, J. Quant. Spectrosc. Radiat. Transfer 133, 646 (2014).
  14. C. D. Packard, M. L. Larsen, W. H. Cantrell, and R. A. Shaw, Light scattering in a spatially-correlated particle field: Role of the radial distribution function, J. Quant. Spectrosc. Radiat. Transfer 236, 106601 (2019).
  15. H. Siebert, S. Gerashchenko, A. Gylfason, K. Lehmann, L. Collins, R. Shaw, and Z. Warhaft, Towards understanding the role of turbulence on droplets in clouds: In situ and laboratory measurements, Atmos. Res. 97, 426 (2010).
  16. E.-W. Saw, R. A. Shaw, J. P. Salazar, and L. R. Collins, Spatial clustering of polydisperse inertial particles in turbulence: II. Comparing simulation with experiment, New J. Phys. 14, 105031 (2012).
  17. K. Matsuda, R. Onishi, M. Hirahara, R. Kurose, K. Takahashi, and S. Komori, Influence of microscale turbulent droplet clustering on radar cloud observations, J. Atmos. Sci. 71, 3569 (2014).
  18. S. Glienke, A. B. Kostinski, R. A. Shaw, M. L. Larsen, J. P. Fugal, O. Schlenczek, and S. Borrmann, Holographic observations of centimeter-scale nonuniformities within marine stratocumulus clouds, J. Atmos. Sci. 77, 499 (2020).
  19. S. K. Krueger, C.-W. Su, and P. A. McMurtry, Modeling entrainment and finescale mixing in cumulus clouds, J. Atmos. Sci. 54, 2697 (1997).
  20. A. Cimarelli and G. Boga, Numerical experiments on turbulent entrainment and mixing of scalars, J. Fluid Mech. 927, A34 (2021).
  21. F. Yang, Y. M. Sua, Z. Zheng, J. Anderson, H. F. Sadi, J. M. Yeom, S. P. Singh, P. Hou, W. H. Cantrell, E. R. Lewis, et al., High-resolution lidar observations of sedimentation-induced size sorting of droplets near a laboratory cloud top, Proc. Natl. Acad. Sci. USA 122, e2505421122 (2025).
  22. R. Paoli and K. Shariff, Turbulent condensation of droplets: Direct simulation and a stochastic model, J. Atmos. Sci. 66, 723 (2009).
  23. K. D. Squires and J. K. Eaton, Preferential concentration of particles by turbulence, Phys. Fluids 3, 1169 (1991).
  24. M. Obligado, T. Teitelbaum, A. Cartellier, P. Mininni, and M. Bourgoin, Preferential concentration of heavy particles in turbulence, J. Turbul. 15, 293 (2014).
  25. J. Chun, D. L. Koch, S. L. Rani, A. Ahluwalia, and L. R. Collins, Clustering of aerosol particles in isotropic turbulence, J. Fluid Mech. 536, 219 (2005).
  26. K. Lehmann, H. Siebert, M. Wendisch, and R. A. Shaw, Evidence for inertial droplet clustering in weakly turbulent clouds, Tellus B: Chem. Phys. Meteorol. 59, 57 (2007).
  27. O. Ayala, B. Rosa, L.-P. Wang, and W. W. Grabowski, Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 1. Results from direct numerical simulation, New J. Phys. 10, 075015 (2008).
  28. E.-W. Saw, J. P. Salazar, L. R. Collins, and R. A. Shaw, Spatial clustering of polydisperse inertial particles in turbulence: I. Comparing simulation with theory, New J. Phys. 14, 105030 (2012).
  29. R. A. Shaw, Particle-turbulence interactions in atmospheric clouds, Annu. Rev. Fluid Mech. 35, 183 (2003).
  30. S. Thomas, M. Ovchinnikov, F. Yang, D. van der Voort, W. Cantrell, S. K. Krueger, and R. A. Shaw, Scaling of an atmospheric model to simulate turbulence and cloud microphysics in the Pi chamber, J. Adv. Model. Earth Syst. 11, 1981 (2019).
  31. E. W. Saw, R. A. Shaw, S. Ayyalasomayajula, P. Y. Chuang, and A. Gylfason, Inertial clustering of particles in high-Reynolds-number turbulence, Phys. Rev. Lett. 100, 214501 (2008).
  32. R. A. Shaw, A. B. Kostinski, and M. L. Larsen, Towards quantifying droplet clustering in clouds, Q. J. R. Meteorol. Soc. 128, 1043 (2002).
  33. M. L. Larsen and R. A. Shaw, A method for computing the three-dimensional radial distribution function of cloud particles from holographic images, Atmos. Meas. Tech. 11, 4261 (2018).
  34. B. Thiede, M. L. Larsen, F. Nordsiek, O. Schlenczek, Y. Kim, E. Bodenschatz, and G. Bagheri, Highly localized droplet clustering in shallow cumulus clouds, Proc. Natl. Acad. Sci. USA 123, e2602976123 (2026).
  35. J. J. D’Alessandro and G. M. McFarquhar, Impacts of drop clustering and entrainment-mixing on mixed phase shallow cloud properties over the Southern Ocean: Results from SOCRATES, J. Geophys. Res.: Atmos. 128, e2023JD038622 (2023).
  36. Y. Liu, J. Yang, G. Zhao, Y. Deng, C. Lu, Y. Yin, X. Jing, and Y. Wang, On the scale of particle clustering induced by inhomogeneous entrainment-mixing in mixed-phase cumulus clouds, Geophys. Res. Lett. 51, e2023GL107645 (2024).
  37. J. J. D’Alessandro, R. Wood, and P. N. Blossey, Drop clustering and drop size correlations from holographic imagery suggest cloud droplet spectral broadening via entrainment-mixing, Atmos. Chem. Phys. 26, 4067 (2026).
  38. K. Chang, J. Bench, M. Brege, W. Cantrell, K. Chandrakar, D. Ciochetto, C. Mazzoleni, L. Mazzoleni, D. Niedermeier, and R. Shaw, A laboratory facility to study gas–aerosol–cloud interactions in a turbulent environment: The π chamber, Bull. Am. Meteorol. Soc. 97, 2343 (2016).
  39. P. J. Ireland, A. D. Bragg, and L. R. Collins, The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects, J. Fluid Mech. 796, 659 (2016).
  40. M. L. Larsen, C. A. Briner, and P. Boehner, On the recovery of 3D spatial statistics of particles from 1D measurements: Implications for airborne instruments, J. Atmos. Ocean. Technol. 31, 2078 (2014).
  41. J. M. Yeom, H. Fahandezh Sadi, J. C. Anderson, F. Yang, W. Cantrell, and R. A. Shaw, Cloud microphysical response to entrainment of dry air containing aerosols, npj Clim. Atmos. Sci. 8, 8 (2025).
  42. J. M. Yeom, I. Helman, P. Prabhakaran, J. C. Anderson, F. Yang, R. A. Shaw, and W. Cantrell, Cloud microphysical response to entrainment and mixing is locally inhomogeneous and globally homogeneous: Evidence from the lab, Proc. Natl. Acad. Sci. USA 120, e2307354120 (2023).
  43. A. Sofi, M. Shah, and K. Asokan, Structural, optical and electrical properties of ITO thin films, J. Electron. Mater. 47, 1344 (2018).
  44. G. Bradski and K. Adrian, Learning OpenCV: Computer vision with the OpenCV library (O'Reilly Media, Inc., California, USA, 2008).
  45. A. Liberzon, D. Lasagna, M. Aubert, P. Bachant, E. Mahmoodtabar, T. Käufer, Jakirkham, A. Bauer, B. Vodenicharski, C. Dallas, E. Yang, J. Borg, M. M. Farzan, Tomerast, and Ranleu, OpenPIV-Python, Version 0.23.3, Zenodo, 2020, https://doi.org/10.5281/zenodo.4320056.
  46. S. N. Chiu, D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and its Applications (John Wiley & Sons, Chichester, UK, 2013).
  47. F. J. Massey, Jr., The Kolmogorov-Smirnov test for goodness of fit, J. Am. Stat. Assoc. 46, 68 (1951).
  48. J. G. Skellam, The frequency distribution of the difference between two Poisson variates belonging to different populations, J. R. Stat. Soc. 109, 296 (1946).
  49. H. Fahandezh Sadi, E. R. Lewis, K. F. Gali, F. Yang, J. C. Anderson, S. P. Singh, J. M. Yeom, W. Cantrell, and R. A. Shaw, Large aerosol particles favor haze conditions through limitations on water budget and activation kinetics, Geophys. Res. Lett. 53, e2025GL117310 (2026).
  50. T. MacMillan, R. A. Shaw, W. H. Cantrell, and D. H. Richter, Direct numerical simulation of turbulence and microphysics in the Pi chamber, Phys. Rev. Fluids 7, 020501 (2022).
  51. S. Thomas, F. Yang, M. Ovchinnikov, W. Cantrell, and R. A. Shaw, Scaling of turbulence and microphysics in a convection–cloud chamber of varying height, J. Adv. Model. Earth Syst. 15, e2022MS003304 (2023).
  52. J. C. Anderson, S. Thomas, P. Prabhakaran, R. A. Shaw, and W. Cantrell, Effects of the large-scale circulation on temperature and water vapor distributions in the π chamber, Atmos. Meas. Tech. Discuss. 14, 5473 (2021).
  53. S. B. Pope, Turbulent flows, Meas. Sci. Technol. 12, 2020 (2001).
  54. R. Gomes-Fernandes, B. Ganapathisubramani, and J. Vassilicos, Particle image velocimetry study of fractal-generated turbulence, J. Fluid Mech. 711, 306 (2012).
  55. D. Xu and J. Chen, Accurate estimate of turbulent dissipation rate using PIV data, Exp. Therm. Fluid Sci. 44, 662 (2013).
  56. M. A. Yavuz, R. P. J. Kunnen, G. J. F. Van Heijst, and H. J. H. Clercx, Extreme small-scale clustering of droplets in turbulence driven by hydrodynamic interactions, Phys. Rev. Lett. 120, 244504 (2018).
  57. G. L. Holtzer and L. R. Collins, Relationship between the intrinsic radial distribution function for an isotropic field of particles and lower-dimensional measurements, J. Fluid Mech. 459, 93 (2002).
  58. S. P. Singh, M. Larsen, J. Anderson, H. F. Sadi, J. Yeom, W. Cantrell, and R. A. Shaw, Droplet clustering signatures of entrainment in clouds, 2026, Retrieved from: https://digitalcommons.mtu.edu/all-datasets/81.
  59. M. L. Larsen, Scale localization of cloud particle clustering statistics, J. Atmos. Sci. 69, 3277 (2012).
  60. C. Wunsch, The interpretation of short climate records, with comments on the North Atlantic and Southern Oscillations, Bull. Am. Meteorol. Soc. 80, 245 (1999).
  61. J. R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (MIT Press, New York, USA, 2022).

Outline

Information

Phys. Rev. Research 8, 033321– Published 15 September, 2026
  • Received 6 March 2026
  • Accepted 18 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation