Stability Characteristics of a Periodically Unsteady Mixing Layer
Hajj, Muhammad R.
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In nature, in many technological applications and in some laboratory experiments, the basic state of shear flows can be time-varying. The effects of such variations on the stability characteristics of these flows are not well understood. In previous work, Miksad et al. [J. Fluid Mech. 123, 1 (1982)] and Hajj et al. [J. Fluid Mech. 256, 385 (1992)], it has been shown that low-frequency components, generated by nonlinear difference interactions, play an important role in the redistribution of energy among spectral components. In particular, phase modulation was found to be the most effective mechanism in energy transfer to the sidebands of unstable modes. In this work, the effects of small-amplitude low-frequency mean how unsteadiness on the stability of a plane mixing layer are determined. By extending earlier analytical arguments, it is shown that periodicity in the mean flow causes modulations of the most unstable modes. The analysis is then verified experimentally by comparing levels of amplitude and phase modulations in mixing layers with steady and unsteady basic flows. The results show that small-amplitude low-frequency unsteadiness results in enhanced modulations of the fundamental mode. These modulations cause variations in the growth rates of the unstable modes and energy redistribution among them. (C) 1997 American Institute of Physics.