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Stability of the flow in a slowly diverging rectangular duct

Published online by Cambridge University Press:  11 May 2006

IOANNIS GALIONIS  and
PHILIP HALL
IOANNIS GALIONIS
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ, UK
PHILIP HALL
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ, UK
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Abstract

The spatial instability problem in a slowly diverging rectangular duct is investigated. The mean flow for the present problem is three-dimensional and has been obtained asymptotically using lubrication theory. Using a WKBJ expansion for the disturbance quantities, the zeroth- and first-order equations are derived. The zeroth-order problem corresponds to a locally parallel flow approximation and the first-order problem yields the non-parallel-flow correction to the eigenvalues obtained from the former through the use of a solvability condition. The solution of these equations is discussed and the results used to determine the effect of the variation in duct geometry on the neutral curves.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 555 , 25 May 2006 , pp. 43 - 58
Copyright
© 2006 Cambridge University Press

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