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

journal contribution
posted on 2023-05-18, 17:35 authored by Blennerhassett, PJ, Andrew BassomAndrew Bassom
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.


Publication title

Journal of Fluid Mechanics








School of Natural Sciences


Cambridge Univ Press

Place of publication

40 West 20Th St, New York, USA, Ny, 10011-4211

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Copyright © 2006 Cambridge University Press

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