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Global linear stability analysis of weakly non-parallel shear flows

Published online by Cambridge University Press:  26 April 2006

Peter A. Monkewitz,
Patrick Huerre and
Jean-Marc Chomaz
Peter A. Monkewitz
Affiliation:
Department of Mechanical, Aerospace & Nuclear Engineering, University of California, Los Angeles, CA 90024-1597, USA
Patrick Huerre
Affiliation:
Laboratoire d'Hydrodynamique (LADHYX), Ecole Polytechnique, 91128 Palaiseau Cédex, France
Jean-Marc Chomaz
Affiliation:
Laboratoire d'Hydrodynamique (LADHYX), Ecole Polytechnique, 91128 Palaiseau Cédex, France
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Abstract

The global linear stability of incompressible, two-dimensional shear flows is investigated under the assumptions that far-field pressure feedback between distant points in the flow field is negligible and that the basic flow is only weakly non-parallel, i.e. that its streamwise development is slow on the scale of a typical instability wavelength. This implies the general study of the temporal evolution of global modes, which are time-harmonic solutions of the linear disturbance equations, subject to homogeneous boundary conditions in all space directions. Flow domains of both doubly infinite and semi-infinite streamwise extent are considered and complete solutions are obtained within the framework of asymptotically matched WKBJ approximations. In both cases the global eigenfrequency is given, to leading order in the WKBJ parameter, by the absolute frequency ω0(Xt) at the dominant turning point Xt of the WKBJ approximation, while its quantization is provided by the connection of solutions across Xt. Within the context of the present analysis, global modes can therefore only become time-amplified or self-excited if the basic flow contains a region of absolute instability.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 251 , June 1993, pp. 1 - 20
Copyright
© 1993 Cambridge University Press

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