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    Bifurcations and eddy genesis of Stokes flow within a sectorial cavity PART II: Co-moving lids
    (Elsevier Science Bv, 2016) Gurcan, Fuat; Bilgil, Halis; Sahin, A.
    This paper is a complementary study to earlier work (Gurcan, 2013), concerning eddy genesis and bifurcations in a sectorial driven cavity for Stokes flow, consisting of a pair of curved stationary side walls and two straight translating lids moving in the same radial direction with speeds U-1 and U-2. The flow is governed by two physical control parameters: the cavity aspect ratio A = r(2)/r(1) where r(1) and r(2) are the radii of the inner and outer curved side-walls, respectively and the ratio of the upper and lower lid speeds (S = U-1/U-2). In previous work (Gurcan, 2013), focus was on lids moving in the opposite direction or a single moving lid. By considering different A values for each S, the streamline patterns and their bifurcations are studied; occurrence of stagnation point bifurcations and transformation of the local flow topology are observed at critical values of A and S. The key results are shown in an (S, 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. Six different eddy genesis mechanisms are observed for S is an element of (0, 1] and A is an element of (1.45. 20). In each case the flow structures and eddy genesis mechanisms are illustrated in detail with figures and bifurcation diagrams. The study also serves as a benchmark problem for testing new numerical algorithms. (C) 2015 Elsevier Masson SAS. All rights reserved.