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Chaotic diffusion in steady wavy vortex flow - Dependence on wave state and correlation with Eulerian symmetry measures
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King, G. P., Rudman, Murray and Rowlands, G. (George) (2008) Chaotic diffusion in steady wavy vortex flow - Dependence on wave state and correlation with Eulerian symmetry measures. Fluid Dynamics Research, Vol.40 (No.1). pp. 45-67. doi:10.1016/j.fluiddyn.2007.04.003
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Official URL: http://dx.doi.org/10.1016/j.fluiddyn.2007.04.003
Abstract
The dimensionless effective axial diffusion coefficient, D-z calculated from particle trajectories in steady wavy vortex flow in a narrow gap Taylor-Couette system, has been determined as a function of Reynolds number (R = Re/Re-c), axial wavelength (lambda(z)), and the number of azimuthal waves (m). Two regimes of Reynolds number were found: (i) when R < 3.5, D-z has a complex and sometimes multi-modal dependence on Reynolds number; (ii) when R > 3.5, D-z decreases monotonically.
Eulerian quantities measuring the departure from rotational symmetry, phi(0), and flexion-free flow, phi(v), were calculated. The space-averaged quantities (phi) over bar (0) and (phi) over bar (v) were found to have, unlike D-z a simple unimodal dependence on R. In the low R regime the correlation between D-z and phi(0)phi(v) was complicated and was attributed to variations in the spatial distribution of the wavy disturbance occurring in this range of R. In the large R regime, however, the correlation simplified to D-z alpha (phi) over bar (0) (phi) over bar (v) for all wave states, and this was attributed to the growth of an integrable vortex core and the concentration of the wavy disturbance into narrow regions near the outflow and inflow jets.
A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the 'escape basins' (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low R regime after the breakup of all KAM tori, the outflow basin (gamma(O)) is larger than the inflow basin (gamma(I)), and both gamma(O) and gamma(I) are (approximately) independent of R. In the large R regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a sliaht increase. This implies that the growth of the integrable core occurs at the expense of the outflow escape basin. Finally, it is shown that the variation of the weighted escape rates (gamma(O)r(O,) gamma(I)r(I)) with Reynolds number was in excellent qualitative agreement with the variation of (((phi) over bar (0))(O), ((phi) over bar (0))(I)). (C) 2007 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics T Technology > TJ Mechanical engineering and machinery |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Physics |
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| Library of Congress Subject Headings (LCSH): | Taylor vortices, Vortex-motion, Fluid dynamics, Chaotic behavior in systems, Diffusion | ||||
| Journal or Publication Title: | Fluid Dynamics Research | ||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||
| ISSN: | 0169-5983 | ||||
| Official Date: | January 2008 | ||||
| Dates: |
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| Volume: | Vol.40 | ||||
| Number: | No.1 | ||||
| Number of Pages: | 23 | ||||
| Page Range: | pp. 45-67 | ||||
| DOI: | 10.1016/j.fluiddyn.2007.04.003 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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