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Influence of counter-rotating von Kármán flow on cylindrical Rayleigh-Bénard convection
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Bordja, Lyes, Tuckerman, Laurette S., Witkowski, Laurent Martin, Cruz Navarro, Maria, Barkley, Dwight and Bessaih, Rachid (2010) Influence of counter-rotating von Kármán flow on cylindrical Rayleigh-Bénard convection. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol.81 (No.3 Part 2). Article no. 036322. doi:10.1103/PhysRevE.81.036322
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Official URL: http://dx.doi.org/10.1103/PhysRevE.81.036322
Abstract
The axisymmetric flow in an aspect-ratio-one cylinder whose upper and lower bounding disks are maintained at different temperatures and rotate at equal and opposite velocities is investigated. In this combined Rayleigh-Benard/von Karman problem, the imposed temperature gradient is measured by the Rayleigh number Ra and the angular velocity by the Reynolds number Re. Although fluid motion is present as soon as Re not equal 0, a symmetry-breaking transition analogous to the onset of convection takes place at a finite Rayleigh number higher than that for Re = 0. For Re < 95, the transition is a pitchfork bifurcation to a pair of steady states, while for Re > 95, it is a Hopf bifurcation to a limit cycle. The steady states and limit cycle are connected via a pair of saddle-node infinite-period bifurcations except very near the Takens-Bogdanov codimension-two point, where the scenario includes global bifurcations. Detailed phase portraits and bifurcation diagrams are presented, as well as the evolution of the leading part of the spectrum, over the parameter ranges 0 <= Re <= 120 and 0 <= Ra <= 30 000.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QC Physics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) | ||||
| Publisher: | American Physical Society | ||||
| ISSN: | 1539-3755 | ||||
| Official Date: | March 2010 | ||||
| Dates: |
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| Volume: | Vol.81 | ||||
| Number: | No.3 Part 2 | ||||
| Number of Pages: | 16 | ||||
| Page Range: | Article no. 036322 | ||||
| DOI: | 10.1103/PhysRevE.81.036322 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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