@inproceedings{9224e6e3a74441ef92a6dd532ee5b1b4,
title = "The development (and suppression) of very short-scale in mixed forced-free convection boundary",
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 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.",
author = "Duck, {P. W.} and Denier, {J. P.} and J. Li",
year = "2006",
doi = "10.1007/978-1-4020-4150-1-30",
language = "English",
isbn = "9781402041495",
volume = "129",
series = "Solid Mechanics and its Applications",
publisher = "Springer, Springer Nature",
pages = "313--323",
editor = "G Meier and {Sreenivasan }, K and H Heinemann",
booktitle = "IUTAM Symposium on One Hundred Years of Boundary Layer Research: Proceedings of the IUTAM Symposium Held at DLR-Gottingen, Germany, August 12-14, 2004",
address = "United States",
}