Propagation of Sound Pulses with Shocks in Fluids: Analytical and Numerical Calculations

Explosions in fluids generate sound pulses with shocks. In this article, we analyze the effect of the initial waveform on the nonlinear propagation of the sound pulses. We focus on peak pressure, pulse duration, waveform, and sound exposure integrated over the waveform. We use an analytical method based on weak-shock theory and the equal-area rule. For an N wave and an exponential wave, the analytical solutions for peak pressure and pulse duration agree with solutions reported in the literature. For a Friedlander wave, we present a solution that illustrates how analytical solutions for other, more complex, waveforms can be derived. We also describe an efficient numerical method for nonlinear propagation of sound pulses with shocks. Numerical results are in good agreement with analytical results. We use the numerical method to calculate the effect of dissipation. The analytical and numerical solutions are developed for plane, cylindrical, and spherical sound pulses. For sound pulses generated by explosions in water and in air, we compare analytical and numerical results with experimental data and empirical relations from the literature.