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Non-parallel linear stability analysis of the vertical boundary layer in a differentially heated cavity

Published online by Cambridge University Press:  10 December 1997

A. M. H. BROOKER ,
J. C. PATTERSON  and
S. W. ARMFIELD
A. M. H. BROOKER
Affiliation:
Centre for Water Research, The University of Western Australia, Nedlands 6907, Australia Present address: Technische Thermodynamik, Technische Universität Chemnitz-Zwickau, D09107 Chemnitz, Germany.
J. C. PATTERSON
Affiliation:
Centre for Water Research, The University of Western Australia, Nedlands 6907, Australia Present address: Department of Civil and Systems Engineering, James Cook University, Townsville 4811, Australia.
S. W. ARMFIELD
Affiliation:
Department of Mechanical and Mechatronic Engineering, Sydney University, Sydney 2006, Australia
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Abstract

A non-parallel linear stability analysis which utilizes the assumptions made in the parabolized stability equations is applied to the buoyancy-driven flow in a differentially heated cavity. Numerical integration of the complete Navier–Stokes and energy equations is used to validate the non-parallel theory by introducing an oscillatory heat input at the upstream end of the boundary layer. In this way the stability properties are obtained by analysing the evolution of the resulting disturbances. The solutions show that the spatial growth rate and wavenumber are highly dependent on the transverse location and the disturbance flow quantity under consideration. The local solution to the parabolized stability equations accurately predicts the wave properties observed in the direct simulation whereas conventional parallel stability analysis overpredicts the spatial amplification and the wavenumber.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 352 , 10 December 1997 , pp. 265 - 281
Copyright
© 1997 Cambridge University Press

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