Abstract
Intense cylindrical sources are widely used in underwater acoustics and medical ultrasound; however, nonlinear-diffraction phenomena in acoustic fields of this geometry are not studied yet as well as the fields produced by unfocused and weakly focused circular piston sources. The present work is based on a special analytical method that has been developed recently [M. F. Hamilton, V. A. Khokhlova, and O. V. Rudenko, J. Acoust. Soc. Am. 101, 1298–1308 (1997)] to model nonlinear and diffraction effects near the axis of an acoustic beam radiated by apodized circular source. This method combines the advantages of the parabolic approximation with nonlinear geometrical acoustics, and it permits an exact solution of the nonlinear problem. The approach is extended to acoustic waves radiated by a finite-length cylinder. A system of nonlinear coupled equations describing waveform distortion in the paraxial region of the beam is derived from the modified KZ equation. Analytical solutions are obtained in the time and frequency domains for an initially sinusoidal wave radiated by the cylinder with Gaussian shading of the amplitude along the axis. Nonlinear waveform distortion, shock formation distance, harmonic propagation curves, directivity pattern, and effect of steering are investigated for various parameters of the source. [Work supported by ONR, RFBR, and CRDF.]
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