Bifurcations and eddy genesis of Stokes flow within a sectorial cavity

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dc.contributor.authorGürcan, Fuat
dc.contributor.authorBilgil, Halis
dc.date.accessioned13.07.201910:50:10
dc.date.accessioned2019-07-29T19:29:02Z
dc.date.available13.07.201910:50:10
dc.date.available2019-07-29T19:29:02Z
dc.date.issued2013
dc.departmentFen-Edebiyat Fakültesi
dc.description.abstractThis work analyzes the Stokes flow generated in a sectorial driven cavity formed by a pair of curved stationary side walls capped by straight translating lids. The flow is governed by two physical control parameters: the cavity aspect ratio, A = r(2)/r(1) (where r1 and r2 are the radii of the inner and outer curved side walls, respectively) and the ratio (S = U-1/U-2) of the upper to the lower lid speed. A boundary value problem is formulated, which is solved analytically for the streamfunction, psi, expressed as an infinite series of Papkovich-Faddle eigenfunctions. The streamfunction solution is then expanded about any stagnation point to reveal changes in the local flow structure as A and S are varied. At critical values of A and S, stagnation point bifurcations arise and the local flow topology is transformed. For S is an element of [-1, 0) and A is an element of [1.6, 6.5), the various flow transformations are tracked as A is decreased and hence the means is identified by which new eddies appear and become fully developed. The key results are shown in an (5, A) control space diagram which exhibits an intricate structure due to the intersection and confluence of eight bifurcation curves representing flow bifurcations at degenerate critical points. There are eight points where two critical curves intersect and the flow bifurcations are described. It is shown that, for S not equal 0, the number of eddies increases from 1 to 3 via several key flow transformations, which become more complicated as vertical bar S vertical bar is reduced. For S = 0, as A is decreased slowly, the number of eddies also increases, in this case, from 1 to 2 via the development of corner eddies.
dc.identifier.doi10.1016/j.euromechflu.2012.11.002
dc.identifier.endpage51en_US
dc.identifier.issn0997-7546
dc.identifier.scopusqualityQ1
dc.identifier.startpage42en_US
dc.identifier.urihttps://doi.org/10.1016/j.euromechflu.2012.11.002
dc.identifier.urihttps://hdl.handle.net/20.500.12451/6119
dc.identifier.volume39en_US
dc.identifier.wosWOS:000316514100004
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherGauthier-Villars/Editions Elsevier
dc.relation.ispartofEuropean Journal of Mechanics - B/Fluids
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectStokes Flow
dc.subjectEddy
dc.subjectFluid Mechanics
dc.subjectFlow Structure
dc.subjectBifurcation
dc.subjectStagnation Point
dc.titleBifurcations and eddy genesis of Stokes flow within a sectorial cavity
dc.typeArticle

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