WMOD00434

• Title: The Generation of Secondary Ice Particles in Clouds by Crystal-Crystal Collision
• Date: 11/11/1978
• Weather Modification - Doc Type: Report

2171

NOVEMBER 1978

LARRY VARDIMAN

30

From the foregoing characteristics, it is apparent
that Co and. Ko should be maximized to obtain the
greatest effect of secondary particle generation.
In general the solution' to Eq. (17) can only be
found if K (t) is known as a function of time. How-
ever, K (t) will.vary depending on the initial crystal
type and size distributions and on the size distribu-
tions of the fragments which are produced in the
cloud. Therefore, this solution can best be approxi-
mated by numerical methods. A general estimate of
the mag,nitude of secondary particle production can
be obtained by calculating Ko for various crystal
combinations and size distributions. This has been
'done and will be discussed in Section 4.

l
l

r

c. Crystal collisions with a .fixed plate

1) SIMILARITY TO COLLISIONS IN CLOUDS

Various methods of observing or simulating crystal
collisions in a cloud were a.ttempted, including stereo-
photography of collisions between naturally falling ice
crystals and the artificial collision of ice crystals in
an electric field. The observation of collisions between
crystals falling in the atmosphere was found to be
extremely difficult due to the infinitesimal probability
of photographing a collision in a reasonable amount
of time. Collisions of crystals in an electric field was
found to be impractical. Field measurements of crystal
concentrations in space and time wer~attempted
with an airborne ice crystal counter to identify frag-
ment generation zones in and around convective
clouds, but instrumental difficulties and problems in
interpretation led to the abandonment of this line of
investigation.
One frequently suggested method is to catch or
grow an ice crystal, mount it in some manner, and
bombard it with an object of known mass and velocity.
Two main objections may be given' to this method:
1) in catching and mounting the crystal, its properties
may be changed because the most fragile elements
on the crystal may be broken off or sublimated in
the subsaturated environment of the handling equip-
ment; and 2) mounting the crystal is difficult, at
best, and detracts from the reality of collision simi-
larity because the mount will absorb a portion of the
collision energy and affect the collision in unknown
ways.
It was finally decided that a more suitable experi-
ment was to use a high-speed camera to photograph
,the collisions of natural ice crystals falling at terminal
velocity on a fixed plate. The objections cited above
are not present and a large statistical sample of col-
lisions may be obtained. The immediate reaction is
that a collision of an ice crystal with a fixed plate in
no way simulates a, crystal-crystal collision in a cloud
because of the fixed surface and the extreme impact.
A mathematical treatment of the change in momen-
tum, however, shows such a treatment to be possible.

Co= 10/1

C=~
I-CoKo'

Co=5/1

Ko= 0.001 sec-'

25

Co=2/L

Co= I /!

"-
.,

Co=O.lIl

~ 20
~

c
o

~
'E
CD
u
c
o
U

5

00

500

1000

Time (seconds)

FIG. 1. The variation of C as a function of time for various
values of Co and K o.

When the fragmentation is studied.as a function of
the change in momentum the only remaining dif-
ferences are collision orientation, shape effects and
the coefficient of restitution. Shape ~ffects and col-
lision orientation may be different when a falling
crystal hits a fiat plate of infinite extent because the
crystal will tend to take a "double bounce" when it
hits. This is especially true of platelike crystals be-
cause the leading edge may hit first, rotating the
crystal so that the back edge hits before complete
rebound. This is not true of more spherical particles
such as graupel. The shape of the fiat surface is clearly
different than that of another crystal and for spatial
crystals this is probably important. These crystals
have burr-like protrusions which could intermesh with
another crystal but cannot do so on a fiat surface.
This effect would cause spatial crystals to produce
more fragments on a fiat surface than a similar col-
lision with another crystal. The coefficient of restitu-
tion will also be different but will be treated in the
following sections.
These limitations and approximations are estimated
to be of second-order importance when compared to
the. degree of fragmentation in actual collisions.
A sensitivity analysis on the numerical model in
Section 4 will show the effect of overestimate or
underestimate in the fragment generation function.

2) MATHEMATICAL FORMULATION OF THE CHANGE IN
MOMENTUM WITH A FIXED PLATE

The equations for the change in momentum be-
tween two colliding particles were treated in an earlier

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