Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle
File(s)20170134.full.pdf (535.53 KB) FinalPaper.pdf (337.17 KB)
Published version
Accepted version
Author(s)
Crowdy, DG
Brzezicki, S
Type
Journal Article
Abstract
An analytical method to find the flow generated by
the basic singularities of Stokes flow in a wedge of
arbitrary angle is presented. Specifically, we solve a
biharmonic equation for the streamfunction of the
flow generated by a point stresslet singularity and
satisfying no-slip boundary conditions on the two
walls of the wedge. The method, which is readily
adapted to any other singularity type, takes full
account of any transcendental singularities arising
at the corner of the wedge. The approach is also
applicable to problems of plane strain/stress of an
elastic solid where the biharmonic equation also
governs the Airy stress function.
the basic singularities of Stokes flow in a wedge of
arbitrary angle is presented. Specifically, we solve a
biharmonic equation for the streamfunction of the
flow generated by a point stresslet singularity and
satisfying no-slip boundary conditions on the two
walls of the wedge. The method, which is readily
adapted to any other singularity type, takes full
account of any transcendental singularities arising
at the corner of the wedge. The approach is also
applicable to problems of plane strain/stress of an
elastic solid where the biharmonic equation also
governs the Airy stress function.
Date Issued
2017-06-07
Date Acceptance
2017-03-13
Citation
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 2017, 473
ISSN
0080-4630
Publisher
Royal Society, The
Journal / Book Title
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Volume
473
Copyright Statement
© 2017 The Authors.
Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
The Royal Society
Grant Number
EP/K041134/1
EP/K019430/1
WM120037
Publication Status
Published
Article Number
20170134