EFFECTS OF VERTICAL WIND ON STORMS 341 
a given level, from high to low induced pressure, 
and thus to decrease Vz. The force acting on a 
unit slice is DAP, AP being the difference be- 
tween upstream and downstream pressures, aver- 
aged across the cloud diameter D. The accelera- 
tion is given by this force, divided by the mass 
of the slice (prD*/4), being 
dV. ti 4AaP 
dt  pxD 
(3) 
In a coordinate system following the cloud, if 
advective transfer of momentum across storm 
boundaries is neglected 
We Ve FAV, 
a ah ae 
On substitution from (3), 
av. 4AP av. 
Sie aD ap a 
; Pa Oz 
The in-cloud air can be maintained at a constant 
mean velocity different from that in the environ- 
ment, so long as the sum of the two terms on the 
right is zero. 
With strong shear typical of spring squall-line 
situations, it is found [Vewton and Newton, 1959] 
that for large rainstorms (D ~ 30 km), with 
modest mean vertical motions (w ~ 1-3 m/sec), 
balance between the terms in (4) can exist if the 
in-cloud shear is about 1 that in the environ- 
ment (the difference between 0V./02 and dV; /dz 
determines Vz and thusAP, at upper and lower 
levels). In the cases studied, it turned out that 
the estimated difference between mean in-cloud 
and ambient wind velocities was around 10 m/sec 
in lower and upper parts of the cloud. 
This proposition may be illustrated by use of 
observations provided by Malkus and Ronne 
[1954]. Figure 2 shows a comparison of horizontal 
velocities of cloud towers, with winds at a nearby 
station. Cloud turrets penetrating a strong shear 
layer and entering the subtropical jet stream, had 
speeds 9-15 m/sec lower than the environment 
winds. 
From data tabulated by Malkus and Ronne, 
the following mean values are estimated for sev- 
eral towers in the layer 10-12 km: D = 8 km, 
w = 6 m/sec, Ve = 12 m/sec, p = 0.4 X 10° 
em/em’, 0V./dz = 3.5 X 10-% sec. At the ap- 
propriate Reynolds number,AP is about 0.4 mb. 
Substitution of these values gives, for the first 
term on the right in (4), 1.6 em/sec?, and for the 
second term, —2.1 em/sec?. 
Considering the crudity of our estimates from 
their data, this is good agreement, showing that 
vertical transfer of momentum can effectively 
offset the tendency for the cloud to be accelerated 
by outside forces. Furthermore, the close agree- 
ment suggests that the analogy between a vigor- 
ous cloud tower and a rigid obstacle (for which 
the laboratory measurements of P are valid) is 
not a bad one. 
The expression for form drag used by Malkus 
and Scorer [1955] is physically similar to that 
used here. Analogous to (3), their expression 
would be dV./dt = KV;?. The experimental 
values quoted above give K ~ 1/(3R), R being 
the cloud radius. This value for the drag coeffi- 
cient is several times smaller than that derived 
by Malkus and Scorer for cloud bubbles. 
Vertical pressure-gradient forces—Maximum 
values of P on the upstream and downstream 
sides of an obstacle being about pV ,?/2, relative 
motions of the order 10 m/see give a total vertical 
decrement of P, in a case like Figure 1, of about 
1 mb. 
In a typical large thunderstorm, there is a 
radial outflow in lower levels of order 10 m/sec, 
due to thermodynamic processes within the 
storm. When this is superimposed on the mean 
relative motions caused by momentum transfer, 
the total relative motion between ‘in-cloud’ and 
ambient winds on the right flank is double the 
amount estimated above. The vertical decrement 
of pressure can then be 1.5 to 2.56 mb. WithéP = 2 
mb in a layer 500 mb deep, the vertical accelera- 
tion given by the last term of (2) is 4 em/sec?, 
comparable with the buoyancy acceleration if 
AT = 1°C averaged through the whole layer. 
Significance for triggering new convection—Par- 
ticularly because low-level outdrafts decay rap- 
idly with height, most of the hydrodynamic pres- 
sure differential tends to be concentrated in the 
lowest 200 to 300 mb or less. According to (2), a 
200-300-mb layer can be lifted until it is 2-3°C 
cooler than the undisturbed environment, if 
6P = 2 mb. Ina typical mT air mass, the amount 
of lifting involved is enough to set off the existing 
potential instability. 
Lesser lifting, such as provided by the down- 
draft outflow alone, can suffice to trigger new 
convection when the air mass is very unstable 
in lower levels, such as in mid-afternoon. The 
estimates of Vz and P above are characteristic 
