corner
corner
APS » Journals » Phys. Rev. E » Volume 81 » Issue 3
< Previous Article | Next Article >

Phys. Rev. E 81, 036322 (2010) [16 pages]

Influence of counter-rotating von Kármán flow on cylindrical Rayleigh-Bénard convection

Download: PDF (2,565 kB) Buy this article Export: BibTeX or EndNote (RIS)

Lyes Bordja1, Laurette S. Tuckerman2,*, Laurent Martin Witkowski3, María Cruz Navarro4, Dwight Barkley5, and Rachid Bessaih6
1Faculté Sciences de l’Ingénieur, Département de Génie Mécanique, Université de Jijel, BP 98, Ouled Aissa, Jijel-18000, Algeria
2PMMH-ESPCI, CNRS (UMR 7636), Univ. Paris 6 & 7, 10 rue Vauquelin, 75231 Paris, France
3LIMSI–CNRS (UPR 3251) and UPMC Paris 6, 4 Place Jussieu, 75005, Paris, France
4Departamento de Matemáticas, Facultad de CC. Químicas, Universidad de Castilla La Mancha, Camilo José Cela s/n, 13071 Ciudad Real, Spain
5Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
6LEAP, Département de Génie Mécanique, Université Mentouri de Constantine, Route d’Aïn El Bey, 25000 Constantine, Algeria

See Also: Erratum

Received 9 October 2009; published 26 March 2010

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-Bénard/von Kármán 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≠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.

© 2010 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.81.036322
DOI:
10.1103/PhysRevE.81.036322
PACS:
47.20.Ky, 47.20.Bp, 47.10.Fg, 47.32.Ef

*www.pmmh.espci.fr/~laurette; laurette@pmmh.espci.fr

See Also

See Also: M. C. Navarro, L. Martin Witkowski, L. S. Tuckerman, and P. Le Quéré, Building a reduced model for nonlinear dynamics in Rayleigh-Bénard convection with counter-rotating disks, Phys. Rev. E 81, 036323 (2010).

Erratum: Lyes Bordja, Laurette S. Tuckerman, Laurent Martin Witkowski, María Cruz Navarro, Dwight Barkley, and Rachid Bessaih, Erratum: Influence of counter-rotating von Kármán flow on cylindrical Rayleigh-Bénard convection [Phys. Rev. E 81, 036322 (2010)], Phys. Rev. E 81, 069903 (2010).

 
< Previous Article | Next Article >