The tailored Greens function for a forward facing step

摘要

This paper describes the theoretical development of a tailored Greens function for a step based on an application of the Weiner Hopf technique. The results are applied to a boundary layer flow over forward and backward facing steps using the approach developed by P.E. Doak. It is concluded that the sound radiation is a consequence of scattering mechanism that can be modeled from solutions for scattering by parallel semi-infinite plates. At very low frequencies the far-field sound has the characteristics of a streamwise dipole and the sound from turbulent flow in the vicinity of the step scales with the sixth power of the flow velocity. At higher frequencies the directionality is almost omnidirectional and the radiated sound scales as U5. Interference effects become important at high frequencies and the spectrum exhibits a dip at certain angles to the flow. The directionality and spectral characteristics are similar to those measured experimentally.