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Nonlinear binary-mode interactions in a developing mixing layer

Published online by Cambridge University Press:  21 April 2006

D. E. Nikitopoulos  and
J. T. C. Liu
D. E. Nikitopoulos
Affiliation:
The Division of Engineering, Brown University, Providence, RI 02912, USA
J. T. C. Liu
Affiliation:
The Division of Engineering, Brown University, Providence, RI 02912, USA
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Abstract

In this paper we present the formulation and results of two-wave interactions in a spatially developing shear layer, directed at understanding and interpreting the physical mechanisms that underlie the results of quantitative observation. Our study confirms the existence of Kelly's mechanism that augments the growth of a subharmonic disturbance by extracting energy from its fundamental or vice versa. This mechanism is shown to be strongest in the region where the fundamental begins to return energy to the mean flow and the two wave modes are of comparable energy levels. It is found that the initial conditions and especially the initial phase angle between the two disturbances play a very significant role in the modal development and that of the shear layer itself. A doubling of the shear-layer thickness is shown to take place; the two successive plateaux in its growth are attributed to the peaking in the energy production rates of the fundamental and subharmonic fluctuations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 345 - 370
Copyright
© 1987 Cambridge University Press

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