Nonlinear mechanisms of sound generation in a perturbed parallel jet flow

Abstract

An initial value problem with relevance to jet noise is investigated. A plane parallel jet flow is subjected to a spatially localized initial disturbance and is then left to evolve according to the two-dimensional compressible Navier–Stokes equations. The hydrodynamic response is in the form of a convecting vortex packet. The Ffowcs Williams–Hawkings approach is formulated in the time domain and used to extrapolate from the simulated near field to the acoustic far field. The predominant downstream sound radiation comes from an early stage of nonlinear development of the vortex packet. Two simplified models to account for the radiation are introduced, based on nonlinear mode interactions on a prescribed base flow. The first uses two sets of linearized Euler equations, coupled via the inviscid Lilley–Goldstein acoustic analogy. This formulation separates the linear sound field from the sound field driven by nonlinear interactions; qualitative agreement of the latter with the Navier–Stokes computations demonstrates the importance of nonlinear interactions. The second model uses combinations of linear inviscid eigenmodes to drive the sound field, which allows extraction of the dominant mode interactions responsible for the observed radiation pattern. The results indicate that a difference-wavenumber nonlinear interaction mechanism dominates sound radiation from subsonic instability modes in shear flows.