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Work-minimizing kinematics for small displacement of an infinitely long cylinder
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Mandre, Shreyas (2020) Work-minimizing kinematics for small displacement of an infinitely long cylinder. Journal of Fluid Mechanics, 893 . R4. doi:10.1017/jfm.2020.250 ISSN 0022-1120.
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Official URL: http://dx.doi.org/10.1017/jfm.2020.250
Abstract
We consider the time-dependent speed of an infinitely long cylinder that minimizes the net work done on the surrounding fluid to travel a given distance perpendicular to its axis in a fixed amount of time. The flow that develops is two-dimensional. An analytical solution is possible using calculus of variations for the case that the distance travelled and the viscous boundary layer thickness that develops are much smaller than the circle radius. If t represents the time since the commencement of motion and T the final time, then the optimum speed profile is Ct^{1/4}(T-t)^{1/4} , where C is determined by the distance travelled. The result also holds for rigid-body translations and rotation of cylinders formed by extrusion of smooth but otherwise arbitrary curves.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Kinematics, Fluid mechanics, Calculus of variations, Mathematical optimization | ||||||||
| Journal or Publication Title: | Journal of Fluid Mechanics | ||||||||
| Publisher: | Cambridge University Press | ||||||||
| ISSN: | 0022-1120 | ||||||||
| Official Date: | 25 June 2020 | ||||||||
| Dates: |
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| Volume: | 893 | ||||||||
| Article Number: | R4 | ||||||||
| DOI: | 10.1017/jfm.2020.250 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Journal of Fluid Mechanics http://dx.doi.org/10.1017/jfm.2020.250. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © The Author(s), 2020. Published by Cambridge University Press | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 6 May 2020 | ||||||||
| Date of first compliant Open Access: | 17 October 2020 |
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