A plane wave approximation to sound transmission in parallel sheared mean flow

In a number of fluid machinery applications, a simplified plane wave analysis of the problem of sound transmission in a sheared mean flow is often sufficient for engineering purposes. Although there exists an extensive literature on 3-D solution of this problem, a simplified non-isentropic plane wave formulation is not seen. A quasi 1-D theory is presented in this paper in a general form encompassing non-uniform ducts, compressible and axially non-uniform flows. An analytical solution of these equations is presented for uniform ducts carrying an incompressible mean flow and the wave field is shown to consist of superposed forward and backward acoustic waves and a hydrodynamic wave, which occur in general as coupled waves. The propagation constants and the corresponding modal matrix that determines the degree of the coupling are analyzed with reference to applications to some standard mean flow profile shapes and compared with previous results.