On invariant manifolds attached to oscillating boundaries in Stokes flows

Consider a steady Stokes flow bounded by a flat wall to which a separatrix, not tangent to the wall, is attached at point S. If the wall is made to slowly oscillate periodically with small amplitude in a longitudinal direction, then the Poincare map associated with this perturbed flow has a fixed point on the wall near S with an invariant manifold. This result also holds for flows bounded by a cylindrical wall and flows in which the small periodic perturbation is not due to the oscillation of the wall. This result is applied to several flow geometries in the literature

Title	On invariant manifolds attached to oscillating boundaries in Stokes flows
Creator	Hackborn, W. W.
Creator	Yuster, Thomas
Publisher	Chaos
Academic Department	Mathematics
Division	Natural Sciences
Organization	Lafayette College
Date Issued	December 1997
Date Available	2013-03-04T20:17:32Z
Type	Article
Language	English
Bibliographic Citation	Yuster, T. and W. W. Hackborn (1997 Dec.) "On invariant manifolds attached to oscillating boundaries in Stokes flows." Chaos 7 (4): 769-776.
Standard Identifier	Handle 10385/1153
Standard Identifier	DOI 10.1063/1.166274
Permalink	http://hdl.handle.net/10385/1153
Rights Statement	In Copyright
Rights Holders	American Institute of Physics