Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/129890
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Type: | Journal article |
Title: | Local stable and unstable manifolds and their control in nonautonomous finite-time flows |
Author: | Balasuriya, S. |
Citation: | Journal of Nonlinear Science, 2016; 26(4):895-927 |
Publisher: | Springer |
Issue Date: | 2016 |
ISSN: | 0938-8974 1432-1467 |
Statement of Responsibility: | Sanjeeva Balasuriya |
Abstract: | It is well known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each instance in time is the focus of this article. Within a nearly autonomous setting, it is shown that these time-varying directions can be characterised through the accumulated effect of velocity shear. Connections to Oseledets spaces and projection operators in exponential dichotomies are established. Availability of data for both infinite- and finite-time intervals is considered. With microfluidic flow control in mind, a methodology for manipulating these directions in any prescribed time-varying fashion by applying a local velocity shear is developed. The results are verified for both smoothly and discontinuously time-varying directions using finite-time Lyapunov exponent fields, and excellent agreement is obtained. |
Keywords: | Local manifolds; Nonautonomous flows; Controling flow barriers; Oseledets spaces; Hyperbolic trajectories |
Description: | Published online: 21 March 2016 |
Rights: | © Springer Science+Business Media New York 2016 |
DOI: | 10.1007/s00332-016-9293-x |
Grant ID: | http://purl.org/au-research/grants/arc/FT130100484 |
Published version: | http://dx.doi.org/10.1007/s00332-016-9293-x |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
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hdl_129890.pdf | Accepted version | 1.04 MB | Adobe PDF | View/Open |
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