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Upper-branch instability of flow in pipes of large aspect ratio with three-dimensional nonlinear viscous critical layers

Citation

Bassom, AP and Gajjar, JSB, Upper-branch instability of flow in pipes of large aspect ratio with three-dimensional nonlinear viscous critical layers, IMA Journal of Applied Mathematics, 42, (2) pp. 119-145. ISSN 0272-4960 (1989) [Refereed Article]

DOI: doi:10.1093/imamat/42.2.119

Abstract

We consider the upper-branch neutral stability of flow in pipes of large aspect ratio, basically extending the work of F. T. Smith to the nonlinear regime. The inclusion of weak nonlinearity leads to an eigenproblem whose solution depends on the properties of three-dimensional nonlinear critical layers. Two special cases are considered. The first is for very small (≪O(R-1433)) amplitude perturbations, where R is a Reynolds number based on the height of the tube and which is assumed large. Then a fully analytical solution of the three-dimensional critical layers is possible, from which the linear results of Smith may be deduced. The second case studied is that of flow in a rectangular pipe, where a solution of the nonlinear critical layer problem can be obtained. Further analysis of neutral modes in this latter case suggests the possible existence, inter alia, of neutral modes for finite aspect ratio tubes. These modes depend on the scaled amplitude and have O(1) wavespeeds.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108056
Year Published:1989
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2016-04-05
Last Modified:2016-07-08
Downloads:0

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