The interaction between sound and circulatory fluid motion as a problem in matched expansions

A circular cylinder is at rest in a compressible fluid witha given circulation K'. At time t=0 the cylinder is made tomove with low Mach number along a straight line perpendicularto its axis. A modified matching argument is used to describethe sound field induced by the lifting body. The velocity potentialin the sound field can be represented, to leading order, interms of a moving line dipole aligned along the direction ofmotion together with a transverse dipole sheet that extendsfrom the starting location of the centre of the cylinder toits current location. The next-order term is that of a movingline source. The line dipole accounts for the motion of thecylinder. The dipole sheet represents the sound field due tothe circulatory motion. If the circulation is constant, thenso is the strength of the dipole sheet and the time dependencearises from the changing length of the layer. In a more realisticcase, where vorticity is shed to form a wake behind the movingbody, there is a corresponding change in the circulation andin the strength of the evolving dipole sheet.