Effect of viscosity on acoustic diffraction by a circular disk

Abstract

A complete solution is obtained for the diffraction of a time-harmonic acoustic plane wave by a circular disk in a viscous fluid. Arbitrary disk radius size and arbitrary angle of incidence are considered. The linearized equations of viscous flow and the no-slip condition on the rigid disk are used to derive sets of dual integral equations for the fluid velocity and pressure. The dual integral equations are solved by analytic reduction to sets of linear algebraic equations. An asymptotic approximation for the far-field scattered pressure is given, and this approximation is compared to results of previous inviscid acoustic analyses. It is shown that our results for the force on the disk and the far-field scattered pressure are consistent with the prediction of the theory of aerodynamic sound. Numerical results are presented for the fluid velocity field in the case of tangential incidence. The velocity field near the disk is shown to contain vortices that are swept along the disk with the passage of the incident plane wave.