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Atmospheric Research 52 1999 167–176 www.elsevier.comrlocateratmos
Revision and clarification of ‘‘A general hydrodynamic theory for mixed-phase
microphysics’’
Johannes P. Bohm
¨
Swiss Federal Institute for Forest, Snow and Landscape Research, Zurcherstrasse 111, CH-8903 Birmensdorf,
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Switzerland Received 23 February 1999; received in revised form 11 June 1999; accepted 22 June 1999
Abstract
Some problems of the interpretation and the application of previously published general hydrodynamic theory of mixed-phase microphysics are addressed. Some restrictions in the
applicability of the previous work, especially regarding aggregation, are removed using new definitions, and some minor errors are corrected. q 1999 Elsevier Science B.V. All rights
reserved.
Keywords: Precipitation; Microphysics; Hydrodynamics; Semiempirical model; Boundary layer theory
1. Introduction
Ž .
Bohm 1992a,b,c presented a general parameterization for solid and liquid hydrome-
¨
teors along with semiempirical solutions for the hydrodynamics of a mixed population of particles. The solutions are based on boundary layer theory and were supplemented
by a solution from potential flow theory in order to improve the collision efficiencies of Ž
. particles of markedly different size e.g., riming and aerosol impaction, Bohm, 1994 .
¨
The results presented formerly are in close agreement with numerical and experimental results from the literature on fall speeds and collision efficiencies of hydrometeors. In
the meantime, various applications in cloud models revealed that some definitions of the collision efficiencies of particles of complex shapes remain unclear. In the present
contribution, a solution to these problems is presented, and most of the questions that arose in the last few years are answered. A refined approach to the general theory is
presented, especially regarding its application for aggregation. Please see Bohm
¨
0169-8095r99r - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž
. PII: S 0 1 6 9 - 8 0 9 5 9 9 0 0 0 3 3 - 2
Ž .
1992a,b,c for results. His results remain fully valid for the present contribution and, hence, are not reproduced in what follows.
Ž . Ž
. The application of the formulae from Bohm 1992a
henceforth, Part I is clear for
¨
single hydrometeors in free fall, but not quite clear in the case of the hypothetical Ž
. Ž particle involved in the collision efficiencies in Bohm 1992b,c
henceforth, Part II and
¨
. Part III, respectively . In principle, we need all the shape characteristics of the
hypothetical particle in the stopping problem discussed in Part II. The procedures applied in Part II and Part III have not been documented in sufficient detail anywhere,
hence, numerous questions arose during the past few years.
In Section 2, the theory is briefly revised and the new approach presented, clarifying its application in aggregation models. In Section 3, the application of the general theory
is documented step by step, including some numerical considerations in Section 3.5. A short summary is found in Section 4.
2. A brief revision and a new approach
