ALL-FREQUENCY NORMAL-MODE SOLUTION OF THE 3-DIMENSIONAL ACOUSTIC SCATTERING FROM A VERTICAL CYLINDER IN A PLANE-HORIZONTAL WAVE-GUIDE

The three-dimensional acoustic scattering from a vertical, impenetrabl e cylinder in a waveguide is studied. The analytical solution of the p roblem, for a Dirichlet or a Neumann boundary condition on the scatter er, has been derived recently by Athanassoulis and Prospathopoulos [J. Acoust. Sec. Am. 100, 206-218 (1996)] in the form of a double-infinit e normal-mode series, representing the total acoustic field. In order to extend the applicability of this solution to higher frequencies, th e total field is decomposed into the incident and the scattered parts. A series expansion for the scattered field is obtained, and the criti cal parameter controlling its azimuthal convergence is shown to be the nondimensional wave number ka based on the radius a of the cylinder. The general term of the series starts to decay exponentially immediate ly after the azimuthal index has exceeded the critical value ka, a fac t justifying the introduction of the concept of azimuthal-evanescent m odes. By exploiting the above decomposition, the direct numerical summ ation of the normal-mode series becomes feasible up to ka approximate to 1000. For calculations at even higher frequencies (ka --> infinity) , asymptotic expressions are derived by using appropriate integral rep resentations of Bessel and Hankel functions, in conjunction with the m ethod of stationary phase. The asymptotic analysis shows that the scat tered field is obtained as a superposition of 2-D point sources lying on the boundary of the vertical cylinder, with appropriate amplitudes and phases. Excellent agreement between asymptotic and direct summatio n numerical results has been demonstrated, at moderate frequencies, wh ere both representations are expected to be valid. (C) 1997 Acoustical Society of America.