On the generalization to swirling flows of Lighthill’s eighth-power law: Part I: Waves in axisymmetric sheared and swirling isentropic flows

Abstract

The Lighthill–Proudman theory of sound generation by turbulence, inhomogeneities, and dissipation in a medium at rest is extended to an axisymmetric mean flow with (i) arbitrary unidirectional shear velocity profile and (ii) arbitrary angular velocity of rotation, both depending only on the radius and also (iii) isentropic conditions. The forced acoustic-vortical wave equation is obtained in space-time and in frequency-wavenumber domain retaining the radial dependence. The wave operator describes the propagation of coupled acoustic-vortical waves including the special cases of potential vortex and rigid-body swirl. The forcing term specifies the compressive, shear, and swirl wave sources that model the generation of acoustic-vortical waves (part II).