Nowadays, a better understanding of the effects induced by a mean flow on acoustic scattering is required, in order to develop efficient techniques to reduce the noise produced by the planes, in the neighborhood of the airports. However, there exist no satisfactory way to solve the Linearized Euler Equations in harmonic regime and in unbounded domains. We develop an original approach, which consists in solving a linearized equation, set on the perturbation of displacement, the so-called Galbrun's equation. First we derive an augmented formulation of the problem, which allows to work in the $H^1$ framework. This formulation includes a term which is non-local in space, linked to the convection of vortices along the stream lines. Then we show that it is possible to combine this idea with Perfectly Matched Layers, leading to a Fredholm formulation of the problem, which can be solved by finite elements. Some numerical illustrations will be presented on the case of acoustic radiation in a 2D waveguide in the presence of a parallel shear flow.