936 
Water formation: 
In the early stages of the water movement the water rises to forma Shape somewhat 
similar to that formed when a oencil is oushed upwards into a Sheet of rubber from beneath. 
This formation is then oartially broken up by a rising soherical disturbance which an early 
arum camera record suggested might be hollow. It is believed that the shock wave first 
aetaches a surface layer of water ana flings It uowards and that the yas bubble then bursts 
through this layer. 
Shock wave: 
Figure 2 shows three successive stages in tne develooment of the shock wave, It 
first rises from the water surface in the for of an arc, then two straight Dranches develop 
and finally a thira wave develops where each straight brancn joins the central arce This 
bifurcation of the shock-wave is shown more clearly in Figure 3. The photograohs only show a 
section of the true shock wave formation, the true shape vejng a dome surmounting a cone, the 
whole formation being symmetrical about a vertical axis. 
The photograohic recora produced by the dome is denser than that given by the cone 
(Figure 3) inaicating that the dome is a more intense shock wave and Is moving at a greater 
sceeo, the pressure and soeed being oossibly greatest at the top of the dome. The dome thus 
becomes more prominent as the shock wave system develoos. The cone arises from the outward 
propagation of the exoloslon along the water surface. Thus if A and W are the velocithes of 
propagation in air and water resoectively then A/w= sina wherea is the angle made by the 
cone and the water surface on a vertical olane througn the centre of the explosion. A mean 
value of @ from several records is 13.8° giving W= 4.214. This is witnin 1 oer cent of the 
ratio of the velocities of sound In air and water: at 13°C (Smithsonian Tables) for sound 
& = 1,110 ft./ second and w = 4,730 ft./second giving W= 4.254. The reasons for the development 
of the bifurcation are not fully understcod. 
"Schliecron® record: velocity of shock wave; 
Figure 4 shows a drum camera “schlieren” record giving the initial vertical velocities 
of the top of the dome and the accomoanyiny shock wave, that is, the velocities of these 
@isturbances In an uoward vertical direction through tne centre of the explosion. It wil) be 
seen that the “schlieren* record igs curved. Measurement of this curvature Shows that the shock 
wave leaves the water surface with a velocity some 50 ver cent jreater than that of sound. 
Tnis matter is dealt with more fully in the following theoretical section. 
10k THEORETICAL 
Introduction. 
In this section an evaluation is made of the intensity and velocity of tne shock wave 
transmitted into air by a shock wave in water incident normally on tne free surface. The 
velocity of the surface is also obtained ano the results are compared with those found 
exoerimentally, The effect of oolique incidence is examined and It is founa that a simple 
reflection theory does not reconcile the experimental results for oblique ano normal Incidence. 
Theory. 
We consider only the case of a olane shock wave. The results should apcly to spherical 
waves or indeed to waves of any form since the effect of attenuation will be infinitesimal In 
comearison with the changes due to reflection and transmission. 
In plane waves of finite amplitude the changes taking olace may be regardeg (1) as que 
to forward prooajation of a quantity P = f(o) + v with velocity c + v ana backward Propagation 
of Q= f(p) — ¥ with velocity c - v, where 
oressure in the medium 
o = 
v = oarticle velocity 
¢ = velocity of sound at point cansiderea 
1 (a )2 : 
f(p) = = (22) 40, i.e. Riemann's Function. 
p ‘3p 
Py 
We snall ceces 
