Weakly nonlinear waves generated by vibration of a spherical body
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概要
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The nonlinear propagation of directional spherical waves generated in an unbounded inviscid ideal gas by vibratory motions with small but finite amplitude and moderate frequency of a spherical body is considered. Starting with a regular perturbation expansion for a velocity potential in the near field, a higher-order problem is investigated in the far field up to the shock formation distance. It is thereby shown that, in the far field concerned, a well-known simple far-field equation remains valid for the radial velocity u* including higher-order corrections up to O(εN/r) (N<–1/ε lnε ), where r is a nondimensional radial coordinate and ε(≪1) is the expansion parameter of the expansion. A boundary condition appropriate to the equation, which ensures the matching of a far-field solution with a near-field solution, can be determined from the near-field solution obtained by the regular perturbation procedure. As an application of the theory, the third-order problem is solved for weakly nonlinear acoustic waves radiated by a pulsating sphere. It is further shown that, for weakly nonlinear cylindrical waves with moderate frequency, a similar far-field equation becomes invalid at the third approximation in the far field up to the shock formation distance.
- American Institute of Physics (The Acoustical Society of America)の論文
American Institute of Physics (The Acoustical Society of America) | 論文
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