On vortical flow and sound generation

The generation of an acoustic field by an unsteady viscous vortical flow is investigated analytically, with a focus on the case where the reference scale length of the flow is much smaller than that of the acoustic field. The expansion schemes, governing equations, and far-field behavior are described; the effect of pressure and density fluctuations on the next-order far-field solution is explored; and the method of matched asymptotics is applied to construct the leading-order solution of the induced acoustic field. Particular attention is given to the sound generated by turbulence and by slender vortex filaments.