An approximate analytical model of shock waves from underground nuclear explosions

Abstract

We discuss an approximate analytical model for the hydrodynamic evolution of the shock front produced by a spherically symmetric explosion in a homogeneous medium. The model assumes a particular relation between the energy of the explosion, the density of the medium into which the shock wave is expanding, and the particle speed immediately behind the shock front. The assumed relation is exact for shock waves that are strong and self‐similar. Comparison with numerical simulations indicates that the relation is also approximately valid for shock waves that are neither strong nor self‐similar. Using the assumed relation and the Hugoniot of the ambient medium expressed as a relation between the shock speed and the postshock particle speed, one can calculate the radius and other properties of the shock front as a function of time. The model also allows one to investigate how the evolution of the shock wave is influenced by the properties of the ambient medium and how these properties affect the characteristic radius at which the shock wave becomes a low‐pressure plastic wave. The shock front radius versus time curves predicted by the model agree well with numerical simulations of explosions in quartz and wet tuff and with data from four underground nuclear tests conducted in granite, basalt, and wet tuff when the official yields are assumed. When the model is used instead to fit radius versus time data from the hydrodynamic phases of these tests, it gives yields that are within 8% of the official yields when piecewise‐linear approximations to the Hugoniots are used. This accuracy is comparable to the accuracy of other models.

Seismic source functions for explosions in a non-spherical cavity embedded in a scattering environment: application to the regional discrimination of nuclear explosions and earthquakes

“…Lamb, Callen & Sullivan 1992;Glenn 1993). This means that, on the strength of the logic of 'Ockham's razor', non-linearity must not be invoked unless fully warranted by the data, especially in the near-field.…”

“…However, linear analytical models still serve as adequate approximations for the interpretation of seismic signals in the farfield of the long-wavelength approximation (e.g. Lamb, Callen & Sullivan 1992;Glenn 1993). This means that, on the strength of the logic of 'Ockham's razor', non-linearity must not be invoked unless fully warranted by the data, especially in the near-field.…”

The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

“…This section constructs the solutions to the Riemann problem (1) and (2). Notice that Lemmas 2.1-2.3, we can analyze the solutions by means of the projections of the elementary wave curves on the ( , u)-plane.…”

“…The study of fluid mixing solid particles is an important topic in the field of mathematics and physics, such as in explosive volcanic eruptions, interstellar masses, and underground explosions. [1][2][3] Dusty gas is a mixture of solid particles with a gas, where the particles occupy a small volume fraction. 4 The strong shock wave propagation in an ideal dusty gas which is a mixture of solid particles with an ideal polytropic gas was discussed by Pai, Menon, and Fan.…”

Shock-Formation Down a Non-Uniform Tube in Two Phase Flow

“…In such cases due to the existence of solid particles in the gas, properties of mixture differ significantly from those of gas alone. Such types of studies have numerous applications in underground explosion (Lamb, Collen, & Sullivan, 1992;Nagayama, 1993).…”