A one-way wave equation is presented with the following properties. (1) For low angles and small sound-speed variations, it reduces to the standard parabolic approximation. (2) It allows a split-step solution. (3) The rays associated with this equation are exactly the rays of the Helmholtz equation in a range-independent environment. It is in the last sense an optimal one-way wave equation. Results of the split-step solution of this equation are presented and compared to normal-mode calculations and results of another modification of the standard parabolic equation, which was given by Thomson and Chapman [D. J. Thomson and N. R. Chapman, J. Acoust. Soc. Am. 74, 1848–1854 (1983)].
We present a computer-implemented algorithm for underwater acoustic propagation based upon a theoretical formulation which simultaneously incorporates probabilistic random volume scattering and deterministic refraction and diffraction. The model, called the Combined Effects Model, adds the vertical scattering caused by the random inhomogeneities in the ocean to the multipath features produced by the mean sound-speed structure. The analysis is based on the two-point coherence function which describes the acoustic field in terms of position and the direction of energy flux, and as such is directly related to the field as seen by an acoustic array. Basic to the theoretical formulation is a locally quadratic approximation on the index of refraction. Although multipath interference effects (which are apparent when the coherence function is calculated directly from a propagation algorithm) are lost with this assumption, estimates for the output of a vertical array are not significantly affected. The incorporation of random volume scatter with realistic background sound-speed structure results in the distribution of arriving energy being smoothed over vertical arrival angles. This effect depends on the magnitude of the strength of the fluctuating field. The multipath structure can still exist for over 100 km, for signals below a few hundred Hz, in the presence of a typical scattering field or can deteriorate in the first few kilometers in the presence of strong scatter.
Source level spectra for 14 large merchant ships have been measured with hydrophones at about 400 m from the ships' tracks. The measured broadband levels tend to be fairly constant from 20 or 30 Hz down to 4 or 5 Hz, instead of decreasing. A possible cause of these high measured low-frequency levels is flow-induced noise radiated from the turbulent boundary layer on the ship's hull [E. A. Vecchio and C. A. Wiley, J. Acoust. Soc. Am. 53, 596–601(1975)]. This paper presents results of calculating the radiated flow-induced noise, as received at the experimental ranges. The smooth-plate expressions for boundary layer thickness and source spectral density have been modified to conform to typical hull roughness. The computed levels, above 5 Hz, are generally less than 10 dB from the measured received levels, suggesting that flow-induced noise is an important component of merchant ship radiated noise from about 5 to 20 Hz.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.