Numerical study of sound of underwater explosions in deep water and shallow water

A numerical model has been developed for sound generated by underwater explosions. For propagation up to a distance of typically 300 m, a finite-element method (FEM) model is used. For propagation to larger ranges, up to typically 10 km, a parabolic equation (PE) model is used. The FEM model takes into account the explosive material in the water layer. The calculated waveform contains the direct shock wave and surface and sediment reflections. Nonlinear-acoustics effects are taken into account by FEM, but are neglected by PE. FEM also accounts for cavitation near the surface. For a deep-water scenario with 100 kg trinitrotoluene (TNT), model results are compared with the empirical Weston relationships and with the Kirkwood-Bethe theory. The comparison focuses on nonlinear propagation effects. For a shallow-water scenario with 263 kg TNT, model results are compared with experimental data for the North Sea. Good agreement is obtained for the broadband sound exposure level, while for the spectrum, deviations occur at high frequency, as a result of numerical dissipation. The model results are also compared with results calculated with the mode-stripping formula for shallow water, which yields a difference of about 10 dB.