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Fundamental–subharmonic interaction: effect of phase relation

Published online by Cambridge University Press:  26 April 2006

M. R. Hajj ,
R. W. Miksad  and
E. J. Powers
M. R. Hajj
Affiliation:
Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219, USA
R. W. Miksad
Affiliation:
College of Engineering, The University of Texas at Austin, Austin, TX 78712, USA
E. J. Powers
Affiliation:
College of Engineering, The University of Texas at Austin, Austin, TX 78712, USA
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Abstract

The effect of the phase relation (i.e. phase difference and coupling) between the fundamental and subharmonic modes on the transition to turbulence of a mixing layer is investigated. Experiments are conducted to study the development of the subharmonic and fundamental modes under different phase-controlled excitations. Higher-order spectral moments are used to measure phase differences, levels of phase coupling, and energy transfer rates between the two modes at different downstream locations. Local measurements of the wavenumber–frequency spectra are used to examine the phase-speed matching conditions required for efficient energy transfer. The results show that when the phase coupling between the fundamental and the subharmonic is high, maximum subharmonic growth is found to occur at a critical phase difference close to zero. The subharmonic growth is found to result from a resonant parametric interaction between the fundamental and the subharmonic in which phase-speed matching conditions are satisfied. In contrast, when the phase coupling level is low, the phase difference is irregular and varying, the efficiency of parametric interactions is low, phase-speed matching conditions are not met and subharmonic growth is suppressed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 403 - 426
Copyright
© 1993 Cambridge University Press

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