Broadening of Cloud Droplet Spectra through Eddy Hopping: Turbulent Adiabatic Parcel Simulations

Wojciech W. Grabowski
National Center for Atmospheric Research,a Boulder, Colorado, and Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland

Gustavo C. Abade
Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland

Abstract
This paper investigates spectral broadening of droplet size distributions through a mechanism referred to as the eddy hopping. The key idea, suggested a quarter century ago, is that droplets arriving at a given location within a turbulent cloud follow different trajectories and thus experience different growth histories and that this leads to a significant spectral broadening. In this study, the adiabatic parcel model with superdroplets is used to contrast droplet growth with and without turbulence. Turbulence inside the parcel is described by two parameters: (i) the dissipation rate of the turbulent kinetic energy ε and (ii) the linear extent of the parcel L. As expected, an adiabatic parcel without turbulence produces extremely narrow droplet spectra. In the turbulent parcel, a stochastic scheme is used to account for vertical velocity fluctuations that lead to local supersaturation fluctuations for each superdroplet. These fluctuations mimic the impact of droplets hopping turbulent eddies in a natural cloud. For L smaller than a few meters, noticeable spectral broadening is possible only for strong turbulence—say, ε > 100 cm2 s−3. For L typical for grid lengths of large-eddy simulation (LES) models (say, L between 10 and 100 m), the impact is significant even with relatively modest turbulence intensities. The impact increases with both L and ε. The representation of eddy hopping developed in this paper can be included in a straightforward way in the subgrid-scale scheme of a Lagrangian LES cloud model and may lead to a significant acceleration of simulated rain development through collision–coalescence.

Keywords: Cloud droplets; Condensation; Numerical analysis/modeling
a The National Center for Atmospheric Research is sponsored by the National Science Foundation.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Wojciech W. Grabowski, grabow@ucar.edu

More deatails: AMS