The Mathematical Institute, University of Oxford, Eprints Archive

Local and global instabilities of flow in a flexible-walled channel

Stewart, Peter S and Waters, Sarah L and Jensen, Oliver E (2009) Local and global instabilities of flow in a flexible-walled channel. European Journal of Mechanics B/Fluids .

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Abstract

We consider laminar high-Reynolds-number flow through a long finite-length planar channel, where a segment of one wall is replaced by a massless membrane held under longitudinal tension. The flow is driven by a fixed pressure difference across the channel and is described using an integral form of the unsteady boundary-layer equations. The basic flow state, for which the channel has uniform width, exhibits static and oscillatory global instabilities, having distinct modal forms. In contrast, the corresponding local problem (neglecting boundary conditions associated with the rigid parts of the system) is found to be convectively, but not absolutely, unstable to small-amplitude disturbances in the absence of wall damping. We show how amplification of the primary global oscillatory instability can arise entirely from wave reflections with the rigid parts of the system, involving interacting travelling wave flutter and static-divergence modes that are convectively stable; alteration of the mean flow by oscillations makes the onset of this primary instability subcritical. We also show how distinct mechanisms of energy transfer differentiate the primary global mode from other modes of oscillatory instability.

Item Type:Article
Subjects:D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:907
Deposited By:Ruth Preston
Deposited On:25 Mar 2010 14:54
Last Modified:25 Mar 2010 14:54

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