WMOD00462

• Contract/Permit #: 87-1999
• Title: Development of Empirical Equations of Ice Crystal Growth Microphysics for Modeling Analysis - Final Report
• Date: 9/1/1988
• Weather Modification - Doc Type: Report

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For arbitrarily small time (t-+O), the binomial expansion of the term,
(1 + Co K t) 1 12, modifies Eq. (3.14) to

c(t) := col (1 + COKt/2) -1] = COCOK t /2 oc t, (3.18)

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as t-+O. If the growth time becomes large (t-+oo), then the terms cot> > 1,
Co 1/2 t 1/2 > > 1, and Eq. (3.14) leads to

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c(t) := co( -1 + COK1/2 t21/2 ) = Co COKl/2 tl/2 oc tl/2, (3.19)

as t-+oo. Also, for Eq. (3.13),

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2a(t) := ao COK t/2 oc t ,

(3.20)

as t-+O, and

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2a(t) := ao COK1/2 t1/2 oc t1/2,

(3.21)

as t-+oo. Using similar arguments for Eq. (3.12) gives the results that

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met) :=moCoK3t3oct3,

(3.22)

as t-+O, and

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m (t) == mo COK3/2 t1/2 oc t3/2,

(3.23)

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as t-+oo. The result, met) == moCo K3/2 t3/2 as t-+oo, is the same as
Maxwellian growth theory under the conditions of steady state thermal and
water vapor fields. Thus, these results identify at least two growth regimes :
for small growth time, highly inefficient molecular transportations of heat

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