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Secondary instability of a temporally growing mixing layer

Published online by Cambridge University Press:  21 April 2006

Ralph W. Metcalfe ,
Steven A. Orszag ,
Marc E. Brachet ,
Suresh Menon  and
James J. Riley
Ralph W. Metcalfe
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77004, USA
Steven A. Orszag
Affiliation:
Applied & Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
Marc E. Brachet
Affiliation:
CNRS, Observatoire de Nice, 06-Nice, France
Suresh Menon
Affiliation:
Flow Research Company, 21414-68th Avenue South, Kent, WA 98032, USA
James J. Riley
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
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Abstract

The three-dimensional stability of two-dimensional vortical states of planar mixing layers is studied by direct numerical integration of the Navier-Stokes equations. Small-scale instabilities are shown to exist for spanwise scales at which classical linear modes are stable. These modes grow on convective timescales, extract their energy from the mean flow and exist at moderately low Reynolds numbers. Their growth rates are comparable with the most rapidly growing inviscid instability and with the growth rates of two-dimensional subharmonic (pairing) modes. At high amplitudes, they can evolve into pairs of counter-rotating, streamwise vortices, connecting the primary spanwise vortices, which are very similar to the structures observed in laboratory experiments. The three-dimensional modes do not appear to saturate in quasi-steady states as do the purely two-dimensional fundamental and subharmonic modes in the absence of pairing. The subsequent evolution of the flow depends on the relative amplitudes of the pairing modes. Persistent pairings can inhibit three-dimensional instability and, hence, keep the flow predominantly two-dimensional. Conversely, suppression of the pairing process can drive the three-dimensional modes to more chaotic, turbulent-like states. An analysis of high-resolution simulations of fully turbulent mixing layers confirms the existence of rib-like structures and that their coherence depends strongly on the presence of the two-dimensional pairing modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 184 , November 1987 , pp. 207 - 243
Copyright
© 1987 Cambridge University Press

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