R. Meyer J. Köhler A. Homburg Explosives

Underwater Detonations
2. Shock wave
The adjacent layer of water is compressed under the influence of this
high pressure, which in turn transfers that pressure onto the next layer,
and this transfers the pressure onto the next one, and so forth in a
chain reaction.
The velocity of propagation increases with pressure, thus creating a
steeply ascending pressure front, which imparts the nature of a shock
wave to the pressure wave. At the onset, the velocity of propagation
exceeds that of the speed of sound, but deteriorates with increasing
distance, i.e. to approximately 1450 m/s.
The maximum pressure achieved is directly proportional to the cube
root of the charge weight, and inversely proportional to the distance,
resulting in the following approximate formula:
Pmax = C L1/3
e
p: pressure in bar
L: loading weight in kg
e: distance in m
c: empirical factor; ≈500
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3. Gas bubble
As stated previously, the gas formed by the underwater explosion first
enters the small cavity previously occupied by the explosive, thus
creating a gas bubble under a high degree of pressure. The water
surrounding the bubble gives away, and the gas bubble expands. This
causes the water mass to move radially at great velocity away from the
point of explosion. This movement is known as the “thrust”.
The maximum amount of kinetic energy imparted to the water during
an explosion is called the thrust energy.
The increase of expansion of the gas bubble causes a decrease in
pressure on the enclosed gases, which slows down expansion to the
point where all of the kinetic energy is expended. This causes lowering
of pressure in the gas bubble contents, influenced by the static water
pressure, and the water mass engulfs it again. The gases are compressed
again up to a second minimum, at which point another
pressure wave is formed (secondary pressure wave). Oscillation of the
gas bubble can be repeated several times, causing a third, and, under
favorable conditions, further minima. The gas bubble is propelled
upwards towards the surface of the water. The difference in pressure
between the top and the bottom layer of the bubble causes the bottom
layer to move at greater speed, thus forcing it upwards into the bubble.
It is possible for both surfaces to meet. Within a limited area the water
receives an upward thrust, creating the so-called waterhammer (water
jet).