Broadening of Cloud Droplet Size Distributions by Condensation in Turbulence

• SAITO Izumi

  Department of Physical Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan

• GOTOH Toshiyuki

  Department of Physical Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan

• WATANABE Takeshi

  Department of Physical Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan

Abstract

 To consider the growth of cloud droplets by condensation in turbulence, the Fokker–Planck equation is derived for the droplet size distribution (droplet spectrum). This is an extension of the statistical theory proposed by Chandrakar and coauthors in 2016 for explaining the broadening of the droplet spectrum obtained from the “Π-chamber”, a laboratory cloud chamber. In this Fokker–Planck equation, the diffusion term represents the broadening effect of the supersaturation fluctuation on the droplet spectrum. The aerosol (curvature and solute) effects are introduced into the Fokker–Planck equation as the zero flux boundary condition at R² = 0, where R is the droplet radius, which is mathematically equivalent to the case of Brownian motion in the presence of a wall. The analytical expression for the droplet spectrum in the steady state is obtained and shown to be proportional to Rexp(−cR²), where c is a constant. We conduct direct numerical simulations of cloud droplets in turbulence and show that the results agree closely with the theoretical predictions and, when the computational domain is large enough to be comparable to the Π-chamber, agree with the results from the Π-chamber as well. We also show that the diffusion coefficient in the Fokker–Planck equation should be expressed in terms of the Lagrangian autocorrelation time of the supersaturation fluctuation in turbulent flow.

Journal

• Journal of the Meteorological Society of Japan. Ser. II

  Journal of the Meteorological Society of Japan. Ser. II 97 (4), 867-891, 2019

  Meteorological Society of Japan

Keywords

• cloud droplet size distribution
• turbulence-cloud droplet interaction
• Fokker–Planck equation
• direct numerical simulation

Details

• CRID: 1390845702321388544
• NII Article ID: 130007682340
• NII Book ID: AA00702524
• DOI: 10.2151/jmsj.2019-049
• ISSN: 21869057
• ISSN: 00261165
• NDL BIB ID: 029909160
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I029909160
• Web Site: https://www.jstage.jst.go.jp/article/jmsj/97/4/97_2019-049/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed