Scattering of sound by a lifting boundary

Sound-wave scattering by a lifting surface is analyzed using an essentially two-dimensional model for the lifting surface which consists of a cylinder of arbitrary cross section placed in a steady stream and irradiated by sound waves from a harmonic line source parallel to the generators of the cylinder. A solution to the governing partial differential equations for the case of a small main-stream Mach number is obtained by solving two subsidiary problems that involve the scattering and circulation associated with the specific cross section assumed. An explicit solution giving the far field is determined for a circular cylinder, the scattered field at low frequencies is found for arbitrary cross sections, and the circulatory contribution with noncircular cross sections is examined. Explicit calculations for an elliptic cylinder show that peaking takes place on a principal axis if the source is on that axis regardless of whether circulation is present unless the ellipse degenerates to a flat plate. In the degenerate case, it is found that peaking always occurs in a direction perpendicular to the flat plate regardless of circulation or source location