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Nonlinear effects in the farfield of a directive sound source. (English) Zbl 0577.76064

Summary: Nonlinear propagation of a periodic sound beam in a dissipative fluid is considered using Fourier series expansion and numerical methods to solve the governing equation of motion in the parabolic approximation. The nearfield was considered in a previous paper [S. I. Aanonsen, T. Barkve, the second and the third author, J. Acoust. Soc. Am. 75, 749- 768 (1984; Zbl 0548.76061)]. The analysis is now extended to the farfield. Numerical and asymptotic results are derived and used to explain the development of the fundamental and harmonic components from the nearfield into the farfield. A discussion is also given of some earlier models for the farfield of directional waves. Emphasis is put on the importance of imposing the proper matching conditions between the nearfield solution and the spherical solution in the farfield in order to obtain a good approximation. Propagation and saturation curves are calculated, as well as beam patterns for various harmonic components. The results are compared with available experimental observations. Nonlinear effects, although generated in the nearfield, are found to be propagated to ranges many tens of Rayleigh distances if the absorption is weak.

MSC:

76G25 General aerodynamics and subsonic flows
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0548.76061
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