Publication Date:
2012-02-16
Description:
We study the linear stability of two-dimensional high-Reynolds-number flow in a rigid parallel-sided channel, of which part of one wall has been replaced by a flexible membrane under longitudinal tension T*. Far upstream the flow is parallel Poiseuille flow at Reynolds number Re; the width of the channel is a and the length of the membrane is λ a, where 1 Re1/7≲ λ Re. Steady flow was studied using interactive boundary-layer theory by Guneratne & Pedley (J. Fluid Mech., vol. 569, 2006, pp. 151-184) for various values of the pressure difference Pe across the membrane at its upstream end. Here unsteady interactive boundary-layer theory is used to investigate the stability of the trivial steady solution for Pe = 0. An unexpected finding is that the flow is always unstable, with a growth rate that increases with T*. In other words, the stability problem is ill-posed. However, when the pressure difference is held fixed (= 0) at the downstream end of the membrane, or a little further downstream, the problem is well-posed and all solutions are stable. The physical mechanisms underlying these findings are explored using a simple inviscid model; the crucial factor in the fluid dynamics is the vorticity gradient across the incoming Poiseuille flow. © 2011 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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