Denier, J.Duck, P.Li, J.2006-12-042006-12-042005Journal of Fluid Mechanics, 2005; 526:147-1700022-11201469-7645http://hdl.handle.net/2440/17835The 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.enCopyright © 2005 Cambridge University PressJournal article002005022310.1017/S00221120040027820002280820000062-s2.0-1594439389955207