On sound emission by acoustic sources in a shear flow

The Green's function for the plane unidirectional shear flow is obtained without restriction to either the high or low frequencies, that is in an exact form that applies also to local wavelengths comparable to the lengthscale of variation of the shear velocity of the mean flow. The method is a version of the variation of constants, and applies to any velocity profile for which the free wave solution of the unforced wave equation is available. The hyperbolic tangent shear velocity profile is taken as an example, and its eigenfunctions are used in the exact, closed expression for the sound field due to a monopole source in the shear flow. The acoustic pressure due to a point monopole source is plotted as a function of the coordinate transverse to the shear layer for several source positions in the shear flow and several values of the shear layer thickness, free stream Mach number and angle of incidence.