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Spatial simulation of secondary instability in plane channel flow: comparison of K- and H-type disturbances

Published online by Cambridge University Press:  26 April 2006

E. M. Saiki ,
S. Biringen ,
G. Danabasoglu  and
C. L. Streett
E. M. Saiki
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, USA
S. Biringen
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, USA
G. Danabasoglu
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, USA Present address: National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA.
C. L. Streett
Affiliation:
Theoretical Aerodynamics Branch, Fluid Dynamics Division, NASA/Langley Research Center, Hampton, VA 23665, USA
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Abstract

This study involves a numerical simulation of spatially evolving secondary instability in plane channel flow. The computational algorithm integrates the time-dependent, three-dimensional, incompressible Navier–Stokes equations by a mixed finite-difference/spectral technique. In particular, we are interested in the differences between instabilities instigated by Klebanoff (K-) type and Herbert (H-) type inflow conditions, and in comparing the present spatial results with previous temporal models. It is found that for the present inflow conditions, H-type instability is biased towards one of the channel walls, while K-type instability evolves on both walls. For low initial perturbation amplitudes, H-type instability exhibits higher growth rates than K-type instability while higher initial amplitudes lead to comparable growth rates of both H-and K-type instability. In H-type instability, spectral analysis reveals the presence of the subharmonic two-dimensional mode which promotes the growth of the three-dimensional spanwise and fundamental modes through nonlinear interactions. An intermodal energy transfer study demonstrates that there is a net energy transfer from the three-dimensional modes to the two-dimensional mode. This analysis also indicates that the mean mode transfers net energy to the two-dimensional subharmonic mode and to the three-dimensional modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 253 , August 1993 , pp. 485 - 507
Copyright
© 1993 Cambridge University Press

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