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On the collision of drops in turbulent clouds

Saffman, P. G. and Turner, J. S. (1956) On the collision of drops in turbulent clouds. Journal of Fluid Mechanics, 1 (1). pp. 16-30. ISSN 0022-1120. doi:10.1017/s0022112056000020.

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This paper proposes a theory of collisions between small drops in a turbulent fluid which takes into account collisions between equal drops. The drops considered are much smaller than the small eddies of the turbulence and so the collision rates depend only on the dimensions of the drops, the rate of energy dissipation ε and the kinematic viscosity v. Reasons are given for believing that the collision rate due to the spatial variations of turbulent velocity is shown to be N = 1.30(r_1 + r_2)^2(n_1n_2)(ε | v)^(1/2), valid for r_1|r_2between one and two. A numerical integration has been performed using this expression to show how an initially uniform distribution will change because of collisions. An approximate calculation is then made to take account also of collisions which occur between drops of different inertia because of the action of gravity and the turbulent accelerations. The results are applied to the case of small drops in atmospheric clouds to test the importance of turbulence in initiating rainfall. Estimates of ε are made for typical conditions and these are used to calculate the initial rates of collision, the change in mean properties and the rate of production of large drops. It is concluded that the effects of turbulence in clouds of the layer type should be small, but that moderate amounts of turbulence in cumulus clouds could be effective in broadening the drop size distribution in nearly uniform clouds where only the spatial variations of velocity are important. In heterogeneous clouds the collision rates are increased, and the effects due to the inertia of the drop soon become predominant. The effect of turbulence in causing collisions between unequal drops becomes comparable with that of gravity when ε is about 2000 cm^2 sec^(−3).

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Additional Information:© 1956 Cambridge University Press. (Received 16 November 1955) The authors wish to express their thanks to Dr G. K. Batchelor for his suggestion of this problem, and for many helpful discussions. The work was made possible for one of us (P. G. S.) by the award of a Department of Scientific and Industrial Research maintenance grant, and for the other (J. S. T.) by the tenure of an Exhibition of 1851 Overseas Scholarship.
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Department of Scientific and Industrial Research (UK)UNSPECIFIED
Exhibition of 1851 Overseas ScholarshipUNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20181119-161052336
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Official Citation:Saffman, P., & Turner, J. (1956). On the collision of drops in turbulent clouds. Journal of Fluid Mechanics, 1(1), 16-30. doi:10.1017/S0022112056000020
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91043
Deposited By: George Porter
Deposited On:20 Nov 2018 21:28
Last Modified:16 Nov 2021 03:37

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