Experimental investigation of subharmonic resonance in an axisymmetric jet

Abstract

A resonant subharmonic interaction between two axisymmetric travelling waves was induced in the shear layer of an axisymmetric jet by controlled sinusoidal perturbations with two frequencies separated by one octave. Wherever the two excited waves are non-dispersive and the fundamental is close to its linear neutral point the two waves may interact in a manner that enhances the amplification rate of the subharmonic wave train. The amplified subharmonic will exceed the fundamental's level to become the dominant instability component. The initial phase difference between the subharmonic and the fundamental plays an important role in the amplification of the subharmonic. For specific phase angles between the two excited waves a suppression of the subharmonic may be observed. The influence of other initial parameters such as amplitude ratio, overall forcing level, excitation frequency and flow conditions at the nozzle (i.e. the initial turbulence level and the initial momentum thickness) was also investigated. An increase in the combined forcing level reduces the effect of the initial phase difference on the amplification of the subharmonic. Stronger excitation moves the location at which the two waves are locked in space further upstream while the effect of the initial phase difference decreases. The energy transfer to the subharmonic wave has been analysed by estimating the production terms. The results clearly indicate that most of the energy for the resonant growth of the subharmonic comes directly from the mean flow. The fundamental wave acts as a catalyst, as long as the resonance conditions are satisfied, enhancing the rate of energy transfer from the mean flow to the subharmonic.