Linear and non linear development of instabilities in shear layers

New aeroacoustic noise prediction methods rely on the computation of linearized Euler equations (LEE) associated with source terms. The process may be described as follows: aerodynamic mean fields are deduced from the time-averaged Navier-Stokes equations associated with a closure scheme ensured for example by a k-6 turbulence modelling; the source terms resulting from turbulent fluctuation effects are calculated separately; these terms are finally incorporated into the linearized propagation equations providing the acoustic field. While the LEE are known to bear convective modes, the difficulty associated with the growth of this mode in an inflexional shear flow profile has not been adressed explicitely. This issue is considered in this article. It is first shown that a small flow perturbation, solution of the Rayleigh equation, when used as input to the LEE, will grow exponentially. In order to avoid this unwanted behaviour, a new semilinearized wave operator including non linear terms is built. This ensures stability and in this way acoustic flow interactions may be correctly described. The SLEE set features finite amplitude perturbations.