Nonlinear Instability of Free Shear Layers: Subharmonic Resonance and Three-Dimensional Vortex Dynamics

Abstract

The subharmonic resonance phenomenon in a free shear layer is studied experimentally and numerically. Excitation using both fundamental and subharmonic at an initial phase difference (ϕ_in shows stable pairing for a wide range of ϕ_in. However, for a narrow range of ϕ_in, either ‘shredding’ occurs or pairing is temporarily suppressed and occurs downstream without periodicity. Under detuned excitation, which is more representative of feedback-driven subharmonic growth, amplitude and phase modulations produce multiple sideband frequencies reflecting variations in the pairing location and occasional nonpairings. In direct numerical simulations (DNS) of a temporal shear layer, we uncover and analyze a new mechanism of transition, based on excitation of the ‘bulging’ instability by pairing of spanwise vortices (‘rolls’) with out-of-phase spanwise undulations. This 3D pairing generates strong internal core dynamics, consisting of core size oscillation driven by oscillating cells of spanwise flow within the rolls. Core dynamics amplify due to instability, can grow alongside streamwise vortices (‘ribs’), and eventually initiate mixing transition at a lower initial 3D disturbance level than that required for transition by ribroll interaction alone. We emphasize that the limitations of traditional perturbation analysis in understanding of the nonlinear and 3D aspects of instability and transition need to be overcome by new approaches such as vortex dynamics and topology.

This research is supported by ONR grant N00014-89-J-1361 and AFOSR grant F496620-92-J-0200.