A method for acoustic scattering by slender bodies. I. Theory and verification

This paper presents a new approach for calculating sound scattering by slender scatterers. The method is based on the assumption that the sound scattering function can be approximated by superimposing the scattered waves from a series of small adjacent cylindrical elements, with each of these elements scattering sound as though it were part of an infinite straight cylinder of the same radius. Using the Kirchhoff integral theorem, the bistatic scattering function is derived rigorously within the accuracy of the assumption. To validate the approach, the solution is applied to sound scattering by fluid prolate spheroids, for which the exact solution is known. Numerical comparison with the exact solution reveals that the new approach is very versatile; it can predict scattering patterns remarkably comparable to that obtained by the exact solution for a wide range of incident angles. For incidence within approximately ±20° of the broadside direction, the scattering patterns predicted by the new method coincide uniformly with the exact results. Agreement in the absolute scattering amplitude slowly deteriorates as the incidence is tilted away from the broadside aspect. However, the method consistently produces scattering patterns highly correlated to the results from the exact solution; this is potentially useful for target identification based on pattern recognition techniques. The results also show that the new method works better on the whole as the elongation of the target increases. Furthermore, calculation of cross-correlation coefficients indicates that the present method works slightly better for rigid bodies than for weak fluid bodies. The low-frequency scattering by gas-filled spheroids is also considered. It is shown that near resonance the scattering is almost isotropic, in agreement with the prediction of previous simple analytic solution.