ON THE ANISOTROPY OF THE LINEAR MECHANISM OF AERODYNAMIC SOUND GENERATION BY VORTICAL PERTURBATIONS IN SHEAR FLOWS

Abstract

We investigate the basics of the linear generation of acoustic waves by vortex modes in homentropic compressible flows with constant shear of velocity, U0 = (Ay,0,0). The mathematical and physical aspects of the generation are grasped by analyzing the dynamics of single, up-shear tilted pure vortex spatial Fourier harmonics (SFHs). The key to comprehending the wave generation process is the possibility of splitting the perturbation field of the considered SFH into its vortex and wave parts at the moment of abrupt wave emergence. Essentially, the linear wave generation mechanism by vortex SFHs in three dimensions (3-D) is similar as in two dimensions (2-D), whereas latter dominates the generation process. The anisotropy of this linear mechanism is also active in 3-D and, thus, confirms the conclusion drawn by Hau et al. (2015) that the anisotropic linear generation mechanism is missed by any formulation of an acoustic analogy as introduced by Lighthill (1952, 1954) due to their topological incompatibility.