On estimating aerodynamic sound from flow fields represented by discrete vortices

Abstract

The sound radiated by a nearly incompressible inviscid free flow, and approximated by an incompressible one, may be expressed in terms of the vorticity movement. If the field is represented by a set of point (line) vortices, their motion and hence the sound field can be determined, precisely. The sound field is dependent upon the second derivative of the flow field, and hence the effects of the fine structure of the flow are emphasized. Thus while a real flow may be reasonably well portrayed by a distribution of point vortices, the sound field may have some dependence on the details of the distribution. This is illustrated in the extreme case of an unstable shear layer represented by a single line of vortices, where the dependence of the impulsive sound on the vortex spacing wan not at first emphasized (A. Powell, Proc. Noise-Con 75). While this is an extreme case, it serves to draw attention to this feature which may be less overt in more complex situations.