Propagation of nonlinear acoustic waves induced by a vibrating cylinder. I. The two-dimensional case

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Abstract
This study details the first successful uniformly valid expansion for a multidimensional nonlinear wave in a system described by curvilinear coordinates. The problem of interest is the steady‐state wave motion induced within an inviscid compressible fluid by an infinite circular cylinder executing a harmonic planar vibration in its nth circumferential mode. The solution is achieved by employing a regular perturbation series to obtain an outer expansion for the velocity potential. Then outer expansions for the pressure and the velocity components are derived by the method of renormalization. Finally, uniformly valid expansions for the response are determined by matching the outer solutions with the results of a linearized analysis, which represent the inner solutions. Examples considering the effect of the nondimensional parameters are treated by presenting pressure and velocity profiles, as well as nodal and antinodal lines of radial velocity. The range of validity for farfield approximations is discussed.

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