Why Do Vortices Generate Sound?

Abstract

Emphasizing physical pictures with a minimum of analysis, an introductory account is presented as to how vortices generate sound. Based on the observation that a vortex ring induces the same hydrodynamic (incompressible) flow as does a dipole sheet of the same shape, simple physical arguments for sound generation by vorticity are presented, first in terms of moving vortex rings of fixed strength and then of fixed rings of variable strength. These lead to the formal results of the theory of vortex sound, with the source expressed in terms of the vortex force ρ(u ∧ ζ) and of the form introduced by Möhring in terms of the vortex moment (y ∧ ζ′), (ρ is the constant fluid density, u the flow velocity, ζ = ∇ ∧ u the vorticity and y is the flow coordinate). The simple “Contiguous Method” of finding the contiguous acoustic field surrounding an acoustically compact hydrodynamic (incompressible) field is also discussed. Some very simple vortex flows illustrate the various ideas. These are all for acoustically compact, low Mach number flows of an inviscid fluid, except that a simple argument for the effect of viscous dissipation is given and its relevance to the “dilatation” of a vortex is mentioned.