Chapter 5
Spherical Shock Waves: The Self-similar
Solution
5.1 Introduction
Let us now turn our attention in the remaining chapters to some examples of air
motion involving spherical shock waves. This particular chapter deals exclusively
with the effects on the surrounding atmosphere following the sudden release of a
considerable quantity of energy coming essentially from a point source, which was
one of the first attempts to ascertain the propagation of the effects of nuclear weapons
into the surrounding atmosphere. The analysis of this particular problem is known as
the self-similar solution.
5.2 Shock Wave from an Intense Explosion
Nuclear weapons generate very strong shock waves and cause unimaginable destruction over a very wide area. The energy generated is generally measured in tons of
TNT (trinitrotoluene) which is a high-explosive chemical material. The energy unit
for nuclear explosions is measured in terms of the energy released by the chemical
reaction in one ton of TNT which corresponds to the release of 4.2 Â 10
9 Joules of
energy. The fission bombs dropped on the cities of Hiroshima and Nagasaki during
the end of the Second World War generated explosions with energy in the region of
20 kilotons of TNT, while thermonuclear weapons using the fusion of light elements
have their energies measured in megatons (10
6 tons) of TNT. One of the first
estimates of the radius of destruction of a nuclear weapon (that was not yet
developed!) was given in a series of lectures by Robert Serber [1] in April 1943 at
Los Alamos, New Mexico. Serber indicates that if E 0 is the total energy released in
the explosion, then the maximum pressure p in the wave-front varies according to the
relation, p % E 0 /r
3 rather than the usual 1/r
2 dependence because the width of the
strongly compressed region increases in proportion to r (see Sect. 5.4). An estimate
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. Prunty, Introduction to Simple Shock Waves in Air, Shock Wave and High
Pressure Phenomena, https://doi.org/10.1007/978-3-030-63606-7_5
217
Spherical Shock Waves: The Self-similar
Solution
5.1 Introduction
Let us now turn our attention in the remaining chapters to some examples of air
motion involving spherical shock waves. This particular chapter deals exclusively
with the effects on the surrounding atmosphere following the sudden release of a
considerable quantity of energy coming essentially from a point source, which was
one of the first attempts to ascertain the propagation of the effects of nuclear weapons
into the surrounding atmosphere. The analysis of this particular problem is known as
the self-similar solution.
5.2 Shock Wave from an Intense Explosion
Nuclear weapons generate very strong shock waves and cause unimaginable destruction over a very wide area. The energy generated is generally measured in tons of
TNT (trinitrotoluene) which is a high-explosive chemical material. The energy unit
for nuclear explosions is measured in terms of the energy released by the chemical
reaction in one ton of TNT which corresponds to the release of 4.2 Â 10
9 Joules of
energy. The fission bombs dropped on the cities of Hiroshima and Nagasaki during
the end of the Second World War generated explosions with energy in the region of
20 kilotons of TNT, while thermonuclear weapons using the fusion of light elements
have their energies measured in megatons (10
6 tons) of TNT. One of the first
estimates of the radius of destruction of a nuclear weapon (that was not yet
developed!) was given in a series of lectures by Robert Serber [1] in April 1943 at
Los Alamos, New Mexico. Serber indicates that if E 0 is the total energy released in
the explosion, then the maximum pressure p in the wave-front varies according to the
relation, p % E 0 /r
3 rather than the usual 1/r
2 dependence because the width of the
strongly compressed region increases in proportion to r (see Sect. 5.4). An estimate
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. Prunty, Introduction to Simple Shock Waves in Air, Shock Wave and High
Pressure Phenomena, https://doi.org/10.1007/978-3-030-63606-7_5
217