Effect of a Shear Layer on Plane Waves of Sound in a Fluid

Abstract

Available theory indicates that plane waves of sound are reflected and refracted at an interface of relative motion (a velocity discontinuity) between two regions of fluid. If the relative velocity is sufficiently great, three types of reflection occur, ordinary, total, and amplified, depending on the incident wave angle. In the amplification regime, theory predicts resonances. Here the velocity discontinuity replaced by a transition layer of finite thickness separating the two fluid regions. This layer is approximated by two equal velocity discontinuities (Model I) and by a linear velocity profile shear layer (Model II). For one example in the regime of ordinary reflection, the effects of thickness are negligible for thicknesses up to 1/10 of the incident wavelength. For the chosen examples in amplified reflection, extreme reductions in transmission and reflection coefficients occur for a thickness as little as 1/50 of a wavelength. The two models approach (at unequal rates) total reflection and zero transmission at larger thicknesses. These effects are produced by layers of fluid traveling at or near the apparent wave speed parallel to the shear layer. Such layers tend to “insulate” the two fluid regions from each other.