Sound production by vorticity fluctuations in a stagnation point flow

Abstract

A linear mechanism for the emergence of acoustic waves from aperiodic vorticity disturbances is presented for a simple stagnation point flow. The non-modal approach, which made possible the discovery of a similar mechanism in unbounded shear flows, is employed. The phenomenon is shown to be closely related to the non-normal nature of the linearized operator governing the evolution of small perturbations about the mean flow. The vorticity disturbance acts as an acoustic source by interacting with the mean velocity gradient and drives the acoustic waves in a non-resonant manner. The physical mechanism by which the acoustic and vortical components of the disturbance exchange energy with the mean flow is presented. The proposed mechanism is relevant for numerous applications involving mass addition or removal, such as aeroacoustic instabilities in a solid rocket motor. Similar phenomena are expected to occur in accelerated flows, like the flow in a nozzle. Numerical simulations using a high order, dispersion relation preserving scheme is used to demonstrate how a localized vorticity disturbance of small amplitude generates sound waves when strained by the gradients in the base flow. The simulations reveal that the vorticity disturbance acts as a quadrupole source of sound, whose origin is explained using physical arguments. Linear simulations using a spectral code verify the results of the nonlinear simulations performed at small amplitude.