Midplane-symmetry breaking in the flow between two counter-rotating disks |
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Authors: | Richard E Hewitt Andrew L Hazel |
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Affiliation: | (1) School of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK |
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Abstract: | This paper considers the axisymmetric steady flow driven by exact counter rotation of two co-axial disks of finite radius.
At the edges of the rotating disks one of three conditions is (typically) imposed: (i) zero velocity, corresponding to a stationary,
impermeable, cylindrical shroud (ii) zero normal velocity and zero tangential fluid traction, corresponding to a (confined)
free surface and (iii) an edge constraint that is consistent with a similarity solution of von Kármán form. The similarity
solution is valid in an infinite geometry and possesses a pitchfork bifurcation that breaks the midplane symmetry at a critical
Reynolds number. In this paper, similar bifurcations of the global (finite-domain) flow are sought and comparisons are made
between the resulting bifurcation structure and that found for the similarity solution. The aim is to assess the validity
of the nonlinear similarity solutions in finite domains and to explore the sensitivity of the solution structure to edge conditions
that are implicitly neglected when assuming a self-similar flow. It is found that, whilst the symmetric similarity solution
can be quantitatively useful for a range of boundary conditions, the bifurcated structure of the finite-domain flow is rather
different for each boundary condition and bears little resemblance to the self-similar flow. |
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Keywords: | Rotating disk Bifurcation Similarity solution |
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