Abstract
Linear and nonlinear evolution of disturbances in an axisymmetric, supersonic, low Reynolds number jet is studied using parabolized stability equations approach. Both axisymmetric and helical modes are considered and nonparallel effect is found to increase the disturbance growth rate, although there is very little effect on the wavenumber. Nonlinear interaction of the helical modes, which are the dominant instability modes of the jet, results in disturbance saturation, spectrum filling and large mean flow distortions. Similar to that for the supersonic boundary layer flow (Chang, C.-L., Malik, M.R., Oblique-mode breakdown and secondary instability in supersonic boundary layers. J. Fluid Mech. 273 (1994) 323–359), interaction of the helical modes induces streamwise vortices which cause significant mean flow distortion and growth of other harmonics. The computed evolution of disturbances is in reasonably good agreement with the experimental data of Morrison and McLaughlin (Morrison, G.L., McLaughlin, D.K., Instability process in low Reynolds number supersonic jets. AIAA J. 18(7) (1980) 793–800). The present marching scheme is able to compute evolution of supersonic disturbances without any numerical reflections and the induced far-field pressure disturbance is found to be almost in phase with the acoustic wave at ambient conditions.
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