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Spectral broadening and flow randomization in free shear layers

Published online by Cambridge University Press:  06 July 2012

Xuesong Wu  and
Feng Tian
Xuesong Wu*
Affiliation:
Department of Mechanics, Tianjin University, Tianjin 300072, PR China Department of Mathematics, Imperial College London 180 Queen’s Gate, London SW7 2AZ, UK
Feng Tian
Affiliation:
Department of Mechanics, Tianjin University, Tianjin 300072, PR China
*
†Email address for correspondence: [email protected]
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Abstract

It has been observed experimentally that when a free shear layer is perturbed by a disturbance consisting of two waves with frequencies and , components with the combination frequencies ( and being integers) develop to a significant level thereby causing flow randomization. This spectral broadening process is investigated theoretically for the case where the frequency difference is small, so that the perturbation can be treated as a modulated wavetrain. A nonlinear evolution system governing the spectral dynamics is derived by using the non-equilibrium nonlinear critical layer approach. The formulation provides an appropriate mathematical description of the physical concepts of sideband instability and amplitude–phase modulation, which were suggested by experimentalists. Numerical solutions of the nonlinear evolution system indicate that the present theory captures measurements and observations rather well.

JFM classification

Instability: Nonlinear instability Instability: Parametric instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 706 , 10 September 2012 , pp. 431 - 469
Copyright
Copyright © Cambridge University Press 2012

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