28 
The initiel upwards velocity of 
the drops thus decreases 
steadily as the horizontal 
abies 2 ia s distance from A increases and 
Ww, 0; leads to a dome-shaped contour. 
lane With the assumption made, the 
R S dome would extend to infinity 
! but the introduction of a finite 
l value for the tension 
at which water cavitates would 
restrict the dome to a finite 
area of surface as observed in 
practice. Further, for a 
finite cavitation tension, the 
Fig.14 - Variation in thickness of thickness of the initial layer 
the initial layer of spray projected at P in fig.i4 will be 
dome greater than at A, the variation 
of thickness with distance A P 
being qualitatively of the shape RDS. As the layer increases in 
thickness a stage will be reached where it no longer breaks up to be 
projected as spray and an edge will be formed to the visible dome. 
78. Beyond the dome there is thus a region in which rupture occurs below 
the surface to form a relatively thick top layer in a state of tension. 
It is observed in practice that the spray dome is surrounded by a "black 
ring", the outer radius of which is fully double that of the dome. If a 
given size of charge is exploded below a certain depth there is no spray 
dome, the maximum pressure being insufficient to cause cavitation in thin 
layers. Empirically, this depth for T.N.T. charges occurs when the maximum 
pressure Py, in the pulse on arrival at the surface is less than about 
1/3 ton per sqe ine Thus, for example, there is no spray dome if a 
300 lb. charge is exploded deeper than about 140 ft. 
The precise mechanism of the surface phenomena has not been finally 
elucidated. Spark photographs of small sub-surface explosions, show that 
the free surface, as it is thrown upwards, breaks into a very large mmber 
of "needles or spikes". The tops of the needles peel off as drops. The 
implication of this result is that an instability of the interface has appeared 
at some early stage in the upward motion. This agrees with some mathematical 
and experimental investigations of G.I. Taylor and D.L. Lewis. They have 
proved that if a system composed of two media, with a common interface 
containing small irregularities (i.e. ripples), is accelerated in the direotion 
from the denser medium to the lighter medium, the irregularities grow 
exponentially with time. The shock wave striking the free surface is a limiting 
case of this phenomenon, in that it causes a finite change in velocity 
instantaneously. The effect is to cause the crests of any small irregularities 
to shoot ahead of the main bulk of the water. 
The initial velocity of the "profile" of these water drops is greater 
than the velocity v, considered in equation (29). Were this not so, 
measurements of the initial velocity distribution of the dome would permit 
one to calculate the exact depth of the explosion, and the peak pressure- 
distance relationship. Such calculations have in fact been made with 
reasonable success; and one must therefore conclude that the instability 
in the very early part of the motion of the dome is soon absorbed in the bulk 
motion, which thereafter proceeds as if the instability had never existed. 
The magnification of surface ripples by the underwater shock decreases 
rapidly with horizontal distance away from the point on the surface above 
the explosion. Cine photographs of the surface show a darkening effeot 
before anything else can be seen (18a). The exact size of this "black ring" 
depends on many factors, especially the lighting conditions, but there can 
be no doubt that the fundamental explanation is to be found in Taylor's 
ideas on the instability of an accelerated interface, in contrast with other 
explanations which relate the darkening to cavitation below the surface. 
