Nonlinear interactions as precursors to mode jumps in resonant acoustics

This paper examines instability mode switching in various supersonic jet configurations that involve resonant acoustics. Resonant acoustics includes situations where flow instabilities are enhanced by feedback. The pressure spectra in such situations are rich in multiple modes, and mode switching can occur rather unpredictably. Our experiments reveal that mode switching and the number of nonlinear interactions are interconnected and this number increases just prior to a mode switch. We quantified nonlinear interactions by counting the number of such interactions occurring over a threshold level in the nonlinear cross-bicoherence spectrum and confirmed that nonlinear interactions are precursors to mode jumps. Further, this result was found to be independent of the threshold level. Moreover, if more than one instability mode coexisted, the decay of one and the persistence of the other caused a similar increase in nonlinearities. On the other hand, if there was no mode switch, the nonlinearities remained at comparable limits over the entire operating range. The latter part of the work focused on why difference interactions significantly outnumbered sum interactions in the spectra of shock-containing resonant flows. Using linear stability calculations it is shown that most of the difference interactions that occurred had a positive spatial growth rate and were, hence, unstable. In contrast, a majority of the sum interactions lay outside the amplified region which indicated that they tend to decay spatially. © 2005 American Institute of Physics.