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On the linear stability of Stokes layers

Citation

Blennerhassett, PJ and Bassom, AP, On the linear stability of Stokes layers, Philosophical Transactions of the Royal Society of London A, 366, (1876) pp. 2685-2697. ISSN 1364-503X (2008) [Refereed Article]

Copyright Statement

2015 The Author(s)

DOI: doi:10.1098/rsta.2008.0055

Abstract

Oscillatory flows occur naturally, with applications ranging across many disciplines from engineering to physiology. Transition to turbulence in such flows is a topic of practical interest and this article discusses some recent work that has furthered our understanding of the stability of a class of time-periodic fluid motions. Our study starts with an examination of the linear stability of a classical flat Stokes layer. Although experiments conducted over many years have demonstrated conclusively that this layer is unstable at a sufficiently large Reynolds number, it has only been relatively recently that rigorous theoretical confirmation of this behaviour has been obtained. The analysis and numerical calculations for the planar Stokes layer were subsequently extended to flows in channels and pipes and for the flow within a torsionally oscillating circular cylinder. We discuss why our predictions for the onset of instability in these geometries are in disappointingly poor agreement with experimental results. Finally, some suggestions for future experimental work are given and some areas for future theoretical analysis outlined.

Item Details

Item Type:Refereed Article
Keywords:linear stability, oscillatory flows, channel flows, cylinder flows, unsteady flows
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:105586
Year Published:2008
Web of Science® Times Cited:8
Deposited By:Mathematics and Physics
Deposited On:2016-01-08
Last Modified:2016-07-06
Downloads:0

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