Hostname: page-component-7c8c6479df-hgkh8 Total loading time: 0 Render date: 2024-03-29T01:56:20.975Z Has data issue: false hasContentIssue false

On the growth (and suppression) of very short-scale disturbances in mixed forced–free convection boundary layers

Published online by Cambridge University Press:  25 February 2005

JAMES P. DENIER
Affiliation:
School of Mathematical Sciences, The University of Adelaide, South Australia, 5005, Australia
PETER W. DUCK
Affiliation:
Department of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
JIAN LI
Affiliation:
School of Mathematical Sciences, The University of Adelaide, South Australia, 5005, Australia

Abstract

The two-dimensional boundary-layer flow over a cooled/heated flat plate is investigated. A cooled plate (with a free-stream flow and wall temperature distribution which admit similarity solutions) is shown to support non-modal disturbances, which grow algebraically with distance downstream from the leading edge of the plate. In a number of flow regimes, these modes have diminishingly small wavelength, which may be studied in detail using asymptotic analysis.

Corresponding non-self-similar solutions are also investigated. It is found that there are important regimes in which if the temperature of the plate varies (in such a way as to break self-similarity), then standard numerical schemes exhibit a breakdown at a finite distance downstream. This breakdown is analysed, and shown to be related to very short-scale disturbance modes, which manifest themselves in the spontaneous formation of an essential singularity at a finite downstream location. We show how these difficulties can be overcome by treating the problem in a quasi-elliptic manner, in particular by prescribing suitable downstream (in addition to upstream) boundary conditions.

Type
Papers
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)