The development (and suppression) of very short-scale in mixed forced-free convection boundary

P. W. Duck, J. P. Denier, J. Li

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution


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 to break self-similarity), then standard numerical schemes exhibit a breakdown at a finite distance downstream. This breakdown is shown to be related to very short-scale disturbance modes, which manifest themselves by means of 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 quasielliptic manner, in particular by prescribing suitable downstream (in addition to upstream) boundary conditions.

Original languageEnglish
Title of host publicationIUTAM Symposium on One Hundred Years of Boundary Layer Research: Proceedings of the IUTAM Symposium Held at DLR-Gottingen, Germany, August 12-14, 2004
EditorsG Meier, K Sreenivasan , H Heinemann
Place of PublicationDordrecht, Netherlands
PublisherSpringer, Springer Nature
Number of pages11
ISBN (Print)9781402041495
Publication statusPublished - 2006
Externally publishedYes

Publication series

NameSolid Mechanics and its Applications
ISSN (Print)09250042

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