Beyond what Distance are Finite-Amplitude Effects Unimportant?

Abstract

Summarized in this paper are the results of a numerical investigation of the effects of inhomogeneity, ordinary attenuation and dispersion, and nonlinear distortion on the propagation of finite-amplitude transients in a lossy stratified ocean. The results are obtained using a weak-shock propagation algorithm based on the equations of nonlinear geometrical acoustics (Cotaras, 1985). Reflections and caustics are avoided by careful selection of ray paths. Two explosion waveforms are considered: a weak shock with an exponentially decaying tail (hereinafter referred to as Pulse I) and a more realistic waveform that includes the first bubble pulse (hereinafter referred to as Pulse II). Numerical propagation of Pulse I along a 58.1 km path starting at a depth of 300 m (hereinafter referred to as the shallow source path) leads to the following conclusions. (1) The effect of inhomogeneity on nonlinear distortion is small. (2) Dispersion plays an important role in determining the arrival time of the pulse. (3) Neither nonlinear distortion nor ordinary attenuation (and dispersion) are paramount; both need to be included. The propagation of Pulse II is along a 23 km path starting from a depth of 4300 m (hereinafter referred to as the deep source path). For this pulse we consider two charge weights, 0.818 kg and 22.7 kg TNT, for each of which the energy spectrum of the received signal is calculated. The “true” energy spectrum, obtained by including finite-amplitude effects over the entire path, is compared with spectra obtained by neglecting finite-amplitude effects (1) entirely, (2) after the first 150 m, and (3) after the first 1100 m. Finite-amplitude effects are found to be of small consequence in the case of the 0.818 kg TNT explosion for frequencies below 6 kHz at distances beyond 1100 m. For the 22.7 kg explosion the corresponding quantities are 4 kHz and 1100 m.