WMOD00289 ‎(2)‎

• Title: Observations and Numerical Simulations of Precipitation Mechanisms in Natural and Seeded Convective Clouds
• Prepared By: Lroen D. Nelson
• Date: 3/1/1979
• State: IL
• Weather Modification - Doc Type: Report

9

Coalescence - Breakup

The coalescence term C(x) is that formulation given by Kovetz and

Olund (1969) as:

1 ~lIf XII
C(x) = 2' J f(x1)f{xIl)!(x1 ,xll)l3(x' ,xxll,x) dxll dx'
o 0

- I co f(x)f(x')f(x,x') dx'
o

where

f(x')
f(xll)
I(x,x') =

= the density function of number at mass x'
= the density function of number as mass XII
the collection kernel given by:

% 2 2
~(X,.XI) = 17' r [y (r,rl)J A V(r,r')
c

where y is the linear collision efficiency and A V is the relative terminal
c

velocity of the two drops

13 (Xl, XII, x) = the redistribution kernel chosen to be non-zero

only for those pairs of droplets which combine to

give rise upon redistribution to droplets of mass x.

13 is chosen to conserve both number and mass

upon redistribution.

The breakup termB(x) is that given by Srivastava (1971) as:

B(x) J cof(xl)K(x' ,x)P(xl) dx' - f(x)P(x)
x

'"

(eq. 5)

(eq. 6)

(eq. 7)