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

  • JAMES P. DENIER (a1), PETER W. DUCK (a2) and JIAN LI (a1)

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.

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

  • JAMES P. DENIER (a1), PETER W. DUCK (a2) and JIAN LI (a1)

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