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The Linear Stability of High-frequency Oscillatory Flow in a Channel


Blennerhassett, PJ and Bassom, AP, The Linear Stability of High-frequency Oscillatory Flow in a Channel, Journal of Fluid Mechanics, 556 pp. 1-25. ISSN 0022-1120 (2006) [Refereed Article]

Copyright Statement

Copyright 2006 Cambridge University Press

DOI: doi:10.1017/S0022112006009141


The linear stability of the Stokes layers generated between a pair of synchronously oscillating parallel plates is investigated. The disturbance equations were studied using Floquet theory and pseudospectral numerical methods used to solve the resulting system. Neutral curves for an extensive range of plate separations were obtained and when the plate separation is large compared to the Stokes layer thickness the linear stability properties of the Stokes layer in a semi-infinite fluid were recovered. A detailed analysis of the damping rates of disturbances to the basic flow provides a plausible explanation of why several previous studies of the problem have failed to detect any linear instability of the flow.To compare more faithfully with experimental work the techniques used for the channel problem were modified to allow the determination of neutral curves for axisymmetric disturbances to purely oscillatory flow in a circular pipe. Critical Reynolds numbers for the pipe flow tended to be smaller than their counterparts for the channel case but the smallest critical value was still almost twice the experimentally reported result.

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
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107131
Year Published:2006
Web of Science® Times Cited:42
Deposited By:Mathematics and Physics
Deposited On:2016-03-04
Last Modified:2016-07-08

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