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Mathematical Problems in Engineering
Volume 2013, Article ID 681246, 8 pages
http://dx.doi.org/10.1155/2013/681246
Research Article

A Spectral Solenoidal-Galerkin Method for Rotating Thermal Convection between Rigid Plates

1Mechanical Engineering Department, Akdeniz University, Antalya 07058, Turkey
2Mathematics Department, Osmaniye Korkut Ata University, Osmaniye 80000, Turkey
3Engineering Sciences Department, Middle East Technical University, Ankara 06531, Turkey

Received 18 January 2013; Accepted 21 February 2013

Academic Editor: Safa Bozkurt Coskun

Copyright © 2013 Cihan Yıldırım et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Krishnamurti, “On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow,” Journal of Fluid Mechanics, vol. 42, no. 02, pp. 295–307, 1970. View at Google Scholar
  2. J. B. McLaughlin and S. A. Orszag, “Transition from periodic to chaotic thermal convection,” Journal of Fluid Mechanics, vol. 122, pp. 123–142, 1982. View at Google Scholar · View at Scopus
  3. J. P. Gollub and S. V. Benson, “Many routes to turbulent convection,” Journal of Fluid Mechanics, vol. 100, no. 3, pp. 449–470, 1980. View at Google Scholar · View at Scopus
  4. O. Mikolasek, B. Barlet, E. Chia, V. Pouomogne, and E. T. M. Tomedi, “Développement de la petite pisciculture marchande au Cameroun: la recherche-action en partenariat,” Cahiers Agricultures, vol. 18, no. 2-3, pp. 157–163, 2009. View at Google Scholar · View at Scopus
  5. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford, UK, 1961. View at Zentralblatt MATH · View at MathSciNet
  6. R. M. Clever and F. H. Busse, “Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis,” Journal of Fluid Mechanics, vol. 94, no. 4, pp. 609–627, 1979. View at Google Scholar · View at Scopus
  7. G. Veronis, “Motions at subcritical values of the Rayleigh number in a rotating fluid,” Journal of Fluid Mechanics, vol. 24, pp. 545–554, 1966. View at Publisher · View at Google Scholar · View at MathSciNet
  8. G. Veronis, “Cellular convection with finite amplitude in a rotating fluid,” Journal of Fluid Mechanics, vol. 5, pp. 401–435, 1959. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. Veronis, “Large-amplitude bénard convection in a rotating fluid,” Journal of Fluid Mechanics, vol. 31, no. 01, pp. 113–139, 1968. View at Google Scholar
  10. G. Küppers and D. Lortz, “Transition from laminar convection to thermal turbulence in a rotating fluid layer,” Journal of Fluid Mechanics, vol. 35, no. 3, pp. 609–620, 1969. View at Google Scholar · View at Scopus
  11. G. Küppers, “The stability of steady finite amplitude convection in a rotating fluid layer,” Physics Letters A, vol. 32, no. 1, pp. 7–8, 1970. View at Google Scholar · View at Scopus
  12. R. M. Clever and F. H. Busse, “Convection in a low Prandtl number fluid layer rotating about a vertical axis,” European Journal of Mechanics B, vol. 19, no. 2, pp. 213–227, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. Kurt, F. H. Busse, and W. Pesch, “Hydromagnetic convection in a rotating annulus with an azimuthal magnetic field,” Theoretical and Computational Fluid Dynamics, vol. 18, no. 2–4, pp. 251–263, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. E. Kurt, W. Pesch, and F. H. Busse, “Pattern formation in the rotating cylindrical annulus with an azimuthal magnetic field at low Prandtl numbers,” Journal of Vibration and Control, vol. 13, no. 9-10, pp. 1321–1330, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. T. Rossby, “A study of Bénard convection with and without rotation,” Journal of Fluid Mechanics, vol. 36, no. 02, pp. 309–335, 1969. View at Google Scholar
  16. R. C. J. Somerville and F. B. Lipps, “A Numerical study in three space dimensions of Benard convection in a rotating fluid,” Journal of Atmospheric Sciences, vol. 30, pp. 590–596, 1973. View at Google Scholar
  17. E. Knobloch and T. Clune, “Pattern selection in rotating convection with experimental boundary conditions,” Physical Review E, vol. 47, no. 4, pp. 2536–2550, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  18. S. A. Orzag and L. C. Kells, “Transition to turbulence in plane poiseuille and plane couette flow,” Journal of Fluid Mechanics, vol. 96, no. 1, pp. 159–205, 1980. View at Google Scholar · View at Scopus
  19. L. Kleiser and U. Schumann, “Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows,” in Proceedings of the 3rd Conference on Numerical Methods in Fluid Mechanics, E. H. Hirschel, Ed., pp. 165–173, 1980.
  20. R. D. Moser, P. Moin, and A. Leonard, “A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow,” Journal of Computational Physics, vol. 52, no. 3, pp. 524–544, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. R. Kessler, “Nonlinear transition in three-dimensional convection,” Journal of Fluid Mechanics, vol. 174, pp. 357–379, 1987. View at Google Scholar · View at Scopus
  22. A. Y. Gelfgat, “Different modes of rayleigh-bénard instability in twoand three-dimensional rectangular enclosures,” Journal of Computational Physics, vol. 156, pp. 300–324, 1999. View at Google Scholar
  23. D. Puigjaner, J. Herrero, F. Giralt, and C. Simó, “Stability analysis of the flow in a cubical cavity heated from below,” Physics of Fluids, vol. 16, no. 10, pp. 3639–3655, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Á. Meseguer and L. N. Trefethen, “Linearized pipe flow to Reynolds number 107,” Journal of Computational Physics, vol. 186, no. 1, pp. 178–197, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. J. A. C. Weideman and S. C. Reddy, “A MATLAB differentiation matrix suite,” Association for Computing Machinery, vol. 26, no. 4, pp. 465–519, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  26. J. P. Boyd, Chebyshev and Fourier Spectral Methods, Dover, Mineola, NY, USA, 2001. View at MathSciNet
  27. J. D. Scheel, Rotating Rayleigh-Benard convection [Ph.D. thesis], California Institute of Technology, 2007.