Abstract
It is generally accepted that one of the main sources of acoustic radiation from a supersonic jet is due to spatial instability wave packets propagating downstream within the jet. This approach has enabled us to explain and predict the principal features of sound radiated by a supersonic jet with a circular nozzle. The aim of this present work is to generalize such an approach to jets with a circular nozzle deformed into a weakly corrugated (s-lobed) shape. This leads to the presence of two additional parameters, the lobe number (an integer) characterizing the corrugation wavelength and the corrugation amplitude. Their presence can be shown to lead to a resonant coupling between different instability waves which, in turn, can both intensify and suppress the aerodynamic noise. The assumption of a small corrugation amplitude allows us to consider the problem analytically using disturbance theory methods. The structure of the eigen-oscillations is determined at leading orders, where it is shown that differing azimuthal harmonics are coupled over a wide range of frequencies. The result of such couplings on the radiated sound is significant, even for a small corrugation amplitude. The above suggests that the effect of mode coupling, due to nozzle corrugation, could be used as a tool for noise control in supersonic jets.
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