Acoustic wave propagation in a sheared fluid contained in a duct

Abstract

In assessing the propagation of an acoustic wave in a sheared fluid, first, the derivation of the linearized wave-equation for two-dimensional viscous flow is presented. Interactions with the acoustic wave of the mean flow, the shear and the viscosity of the fluid through shear have been included. This is followed by a numerical solution to the inviscid case, using a constant gradient and a turbulent velocity profile, for the first three symmetric modes. The “plane” mode is compared with results obtained by Pridmore-Brown using an analytical approach; there is good agreement for the case with constant gradient profile. Methods of solution are also presented for the problems of acoustic wave propagation in a flowing medium, both with and without shear, contained in ducts with finite wall admittance.