Govindarajan, Rama ; Narasimha, R. (2001) Estimating amplitude ratios in boundary layer stability theory: a comparison between two approaches Journal of Fluid Mechanics, 439 . pp. 403-412. ISSN 0022-1120
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Official URL: http://journals.cambridge.org/abstract_S0022112001...
Related URL: http://dx.doi.org/10.1017/S0022112001004864
Abstract
We first demonstrate that, if the contributions of higher-order mean flow are ignored, the parabolized stability equations (Bertolotti et al. 1992) and the 'full' non-parallel equation of Govindarajan & Narasimha (1995, hereafter GN95) are both equivalent to order R-1 in the local Reynolds number R to Gaster's (1974) equation for the stability of spatially developing boundary layers. It is therefore of some concern that a detailed comparison between Gaster (1974) and GN95 reveals a small difference in the computed amplitude ratios. Although this difference is not significant in practical terms in Blasius flow, it is traced here to the approximation, in Gaster's method, of neglecting the change in eigenfunction shape due to flow non-parallelism. This approximation is not justified in the critical and the wall layers, where the neglected term is respectively O(R-2/3) and O(R-1) compared to the largest term. The excellent agreement of GN95 with exact numerical simulations, on the other hand, suggests that the effect of change in eigenfunction is accurately taken into account in that paper.
Item Type: | Article |
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Source: | Copyright of this article belongs to Cambridge University Press. |
ID Code: | 24630 |
Deposited On: | 29 Nov 2010 10:13 |
Last Modified: | 17 May 2016 08:17 |
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