284 
Ss ] 
2.4 6 8 lOcm 
XN 
10 
eat Nrel SIZE DISTRIBUTION 
3 OF OSCILLATING 
RAINDROPS 
3 
10 r=1mm 
N{&m-3] 
dr=Imm_ 9 RAINDROP SIZE 
10 DISTRIBUTION 
BEST 1950 
10! 
i 5mm/h 
10° n 1 (ao 
fe) 0.5 1.0 15 20mm 
—> RADIUS r 
Fie. 7—Size distribution of oscillating rain- 
drops, evaluation of a photograph, compared with 
averaged size spectra 
105 
Ww 
4 
S$ 
o 
: 10 4H BEST LENARD S 
= tmm/h Nr.133.6mm/h = S 
: 5Smm/h Nr. loa = 
Ss 4 
asec 25mm/h Netoey 20m M/A fldiy 
m z| “dr 
E ° 
= 
s a 
wi02 2 10 
a % 
o (=) 
3 10! wl 
z a 
a a 
9 & 
0 10° a 
° 0.5 
FRIEDRICH E. VOLZ 
As the drop size increases, eddy frequency in- 
creases rapidly while the oscillation frequency 
of the drop falls. Only the questionable as- 
sumption that the proper vibrations of drops 
larger than 0.6 mm may excite turbulent eddies 
of the same frequency can lead to a source of 
eddying energy which may maintain the damped 
droplet oscillations. It is possible that small- 
scale atmospheric turbulence can excite the os- 
cillations. In this case the amplitude and number 
of oscillating drops should be influenced by the 
factors which control the Austausch coefficient. 
Depending upon the orientation of the os- 
cillations, the rainbow can be affected in a way 
analogous to that caused by the flattening, dis- 
cussed previously. With the Lenard type of os- 
cillation (ellipsoidal with elongation and flatten- 
ing in the vertical) and the Sun near the horizon, 
3 
6 
LAMB 
1°, 
Shower 
Thunder4 
storm 
Cold 
Front 
Warm 
Front 
RELATIVE EFFICIENCY FOR RAINBOW INTENSITY 
ie) 0.5 
1.0 LS 2.0mm 
1.0 1Smm 
r 
Fra. 8. (a) and (b)—Measured size distributions of rain drops; (c) relative efficiency of drops for rain- 
bow intensity 
the wake of the drops, or are they excited by 
atmospheric turbulence which exists independ- 
ently of the falling droplets? How large are the 
oscillations and what is their form ? 
The eddy frequencies behind rigid spheres 
falling in water were measured by Moeller [1938] 
for varying Reynolds’ numbers (Vz). In Figure 
5 the frequencies for raindrops are shown using 
the relation between Reynolds’ number and drop 
size given by Gunn and Kinzer [1949]. In Moel- 
ler’s experiments regular eddies first appear for 
Np = 400 to 600; only in this region, when the 
droplet radius is near 0.6 mm the frequencies of 
eddies and drop oscillations are equal. This agrees 
with sideward shipping of drops of 0.5 mm radius 
observed by Gunn [1949] and with the observed 
lower limit of 0.4 to 0.6 mm for oscillating drops. 
the rainbow will not be affected m a sideways 
direction, but it will be broadened or missing at 
the top thus reinforcing the effect of droplet 
flattening. 
Raindrop size distribution and the rainbow— 
Up to now relative intensities of color distribu- 
tion in the rainbow have been calculated only 
for uniform drop size. However we know that 
raindrops range in size from 0.2 to 1.5 or even 
3 mm. Figure Sa shows average size distributions 
for various rainfall intensities by Best [1950] 
and Figure Sb shows distributions for typical 
kinds of rain measured by Lamb [1958]. In the 
following we will take the raindrops to be spheri- 
eal, thus neglecting flattening and oscillations. 
The results are therefore only valid for the rain- 
bow near to the horizon. 
