Resonance in axisymmetric jet under controlled helical fundamental, and axisymmetric subharmonic forcing

An axisymmetric jet is forced with two helical fundamental waves of identic al frequency spinning in the opposite directions and an additional axisymme tric subharmonic wave, The subharmonic component rapidly grows downstream f rom resonant interaction with the fundamental, significantly depending on t he initial phase difference between the subharmonic and the fundamental. Th e variation of the subharmonic amplitude with the initial phase difference shows a cusplike shape. The amplification of the subharmonic results in a v ortex pairing of helical modes, Furthermore, the azimuthal variation of the amplification induces an asymmetric jet cross section. When the initial su bharmonic is imposed with an initial phase difference close to a critical v alue, the jet cross section evolves into a three-lobed shape. The robes are generated by vortex pairing. Therefore, the conclusion is made that the in itial phase difference between the fundamental and the subharmonic plays an important role in controlling the jet cross section.