Subharmonic growth by parametric resonance

Abstract

An experimental investigation is conducted in order to quantify the nonlinear and parametric resonance mechanisms that are associated with the subharmonic growth in the transition to turbulence in plane mixing layers. Higher-order digital statistical analysis techniques are used to investigate the nonlinear and parametric mechanisms responsible for the energy transfer to the subharmonic. The results show that the dominant interaction is a parametric resonance mechanism between the fundamental and the subharmonic modes which leads to a pronounced growth of the subharmonic. Measurements also indicate that the fundamental, besides interacting with the subharmonic, is also engaged in redistributing its energy to the other Fourier components of the flow via nonlinear three-wave interactions. Local wavenumber measurements verify that frequency—wavenumber resonance matching conditions exist between the fundamental and subharmonic in the region where the subharmonic gains its energy by parametric resonance. The results are in general agreement with theoretical models by Kelly (1967), and Monkewitz (1988) on subharmonic growth.