Experiments on the role of amplitude and phase modulations during transition to turbulence

Abstract

The transition of a laminar two-dimensional wake is studied experimentally to establish the role of amplitude and phase modulations in the spectral-broadening and energy-redistribution process. Multiple instability modes fo and fi are triggered by acoustic excitation. The spectrum of the fluctuating velocity field formed by the growing and interacting instabilities shows the development of a complicated side- band structure reminiscent of amplitude- and phase-modulated waves. Digital com- plex demodulation techniques are used to obtain quantitative measurements of local instantaneous amplitude and phase modulations. Measurements of the modulation time traces, their modulation indices, the lag between phase and amplitude modula- tions, and the power spectra of the modulations are presented. Our results show that both phase and amplitude modulation play a role in the transition process. The dominant modulation frequency of both amplitude and phase is that of the difference mode fv = f₁−f₀ produced by the interaction of the two excited instabilities. Phase modulation becomes progressively more important as transition proceeds down- stream, and seems to play the dominant role in the spectral-broadening and energy- redistribution process. Measurements of the bicoherency spectrum indicate that sideband structures, and accompanying modulations, are produced by nonlinear interactions between the low-frequency difference mode and higher-frequency in- stability modes. Some limited measurements indicate that finite-amplitude induced nonlinear dispersion effects ω(k, a²) may provide a physical mechanism by which amplitude modulations generated by nonlinear interactions can induce simultaneous phase modulations.