Modeling supersonic jet screech part 2: Acoustic radiation from the shock-vortex interaction

An analytical model is developed for the sound field generated by a jet shear-layer instability wave passing through a shock cell of an imperfectly expanded supersonic jet. The jet shear layer is modeled by a vortex sheet. The amplitude ∈ of the shear-layer instability wave and the turning angle α across the shocks within the jet region are both assumed to be small quantities. A sound field arises at O(∈α) in the expansion, driven by a volume source in the jet region and a surface source concentrated on the vortex sheet. The strength of the volume source decays exponentially with distance inside the jet, and is concentrated in the vicinity of the points where the shock waves reflect off the jet boundary. Thus, attention is concentrated on a single shock reflection point, and a closed form solution for the O(α∈) field is obtained using Fourier transform techniques. Characteristics of both the far and near sound fields are examined. The amplitude of the near field sound just outside the jet is found to decay rapidly with upstream distance.