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A stochastic model of ice particle multiplication by drop splintering
Author(s) -
Chisnell R. F.,
Latham J.
Publication year - 1974
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49710042504
Subject(s) - supercooling , drop (telecommunication) , ice formation , particle number , range (aeronautics) , population , particle (ecology) , mechanics , meteorology , materials science , environmental science , mathematics , thermodynamics , physics , atmospheric sciences , geology , demography , computer science , telecommunications , oceanography , volume (thermodynamics) , sociology , composite material
A stochastic model is developed which describes the increase in ice particle concentrations resulting from the splintering of supercooled drops on freezing. Analysis of the experimental evidence suggests that significant splintering occurs at least for drops with diameters in the range 50 to 200 μm. At time t = 0 one such drop freezes and ejects r ice splinters. Each of these splinters may be captured by another water drop in the same size range at any subsequent time, which in turn will freeze and eject a further r splinters, and so on. Consideration of the probability that a particular capture will take place at a particular time yields an expression for m(t) , the estimated number of particles existing at time t , m(t) = ( r 2 e ( r ‐1) t /τ − 1)/( r − 1), Where τ is the mean lifetime of an ice splinter. It is stressed that by considering the probability of a collision occurring at any time after the birth of a splinter, far higher estimates of the population are obtained than from a non‐stochastic model. Calculations show that the largest ice particle multiplication factors measured by Mossop et al. (1972), of order 10 4 , can be produced in the available time if the value of r for the splintering size range is 5 or 6. Analysis of the experimental evidence suggests that such a value for r is possible.