From stationary to complex time-dependent flows at moderate Rayleigh numbers in two-dimensional annular thermal convection

Physics of Fluids

Volumn 15, Issue 5, 2003, Pages 1314-1326

  Net, Marta ^a   Alonso, Arantxa ^a   Sánchez, Juan ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

NAVIER STOKES EQUATIONS; PRANDTL NUMBER; STABILITY; STEADY FLOW;

RAYLEIGH NUMBERS;

HEAT CONVECTION;

BOUSSINESQ EQUATION; CONVECTION; HEAT TRANSFER; NAVIER-STOKES EQUATIONS; PRANDTL NUMBER; RAYLEIGH NUMBER; TWO-DIMENSIONAL FLOW;

EID: 0037930671     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1565335     Document Type: Article

References (36)

1. F.H. Busse and C.R. Carrigan. "Convection induced by centrifugal buoyancy," J. Fluid Mech. 62, 579 (1974).
2. M.A. Azouni, E.W. Bolton, and F.H. Busse, "Convection driven by centrifugal buoyancy in a rotating annulus," Geophys. Astrophys. Fluid Dyn. 34, 301 (1986).
3. F.H. Busse and A.C. Or, "Convection in a rotating cylindrical annulus: Thermal Rossby waves," J. Fluid Mech. 166, 173 (1986).
4. A.C. Or and F.H. Busse, "Convection in a rotating cylindrical annulus. Part 2, Transitions to asymmetric and vacillating flow," J. Fluid Mech. 174, 313 (1987).
5. R.-Q. Lin, F.H. Busse, and M. Ghil, "Transition to two-dimensional turbulent convection in a rapidly-rotating annulus," Geophys. Astrophys. Fluid Dyn. 45, 131 (1989).
6. R.-Q. Lin, "Double column instabilities in the barotropic annulus," Geophys. Astrophys. Fluid Dyn. 54, 161 (1990).
7. A.C. Or, "Chaotic transitions of convection rolls in a rapidly rotating annulus," J. Fluid Mech. 261, 1 (1994).
8. N.H. Brummell and J.E. Hart, "High Rayleigh number Β-convection," Geophys. Astrophys. Fluid Dyn. 68, 85 (1993).
9. D. Pino, I. Mercader, and M. Net, "Thermal and inertial modes of convection in a rapidly rotating annulus," Phys. Rev. E 61, 1507 (2000).
10. D. Pino, M. Net, J. Sánchez, and I. Mercader, "Thermal Rossby waves in a rotating annulus," Phys. Rev. E 63, 056312 (2001).
11. H. F. Goldstein, E. Knobloch, I. Mercader, and M. Net, "Convection in a rotating cylinder. Part I. Linear theory for moderate Prandtl numbers," J. Fluid Mech. 248, 583 (1993).
12. A. Alonso, M. Net, and E. Knobloch, "On the transition to columnar convection," Phys. Fluids 7, 935 (1995).
13. K. Zhang and G.T. Greed, "Convection in rotating annulus: An asymptotic theory and numerical solutions," Phys. Fluids 10, 2396 (1998).
14. A. Alonso, M. Net, I. Mercader, and E. Knobloch, "Onset of convection in a rotating annulus with radial gravity and heating," Fluid Dyn. Res. 24, 133 (1999).
15. G.T. Greed and K. Zhang, "Two- and three-dimensional linear convection in a rotating annulus," Geophys. Astrophys. Fluid Dyn. 82, 23 (1996).
16. S.M. Cox, "Mode interactions in Rayleigh-Bénard convection," Physica D 95, 50 (1996).
17. G. Manogg and P. Metzener, "Strong resonance in two-dimensional non-Boussinesq convection," Phys. Fluids 6, 2944 (1994).
18. J. Mizushima and K. Fujimura, "Higher harmonic resonance of two-dimensional disturbances in Rayleigh-Bénard convection," J. Fluid Mech. 234, 651 (1992).
19. M. Golubitsky and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory (Springer, New York, 1985), Vol. I.
20. E. Knobloch, "Symmetry and instability in rotating hydrodynamic and magnetohydrodynamic flows," Phys. Fluids 8, 1446 (1996).
21. E.S. Landsberg and E. Knobloch, "Direction-reversing travelling waves," Phys. Lett. A 159, 17 (1991).
22. Z.A. Daya, V.B. Deyirmenjian, S.W. Morris, and J.R. de Bruyn, "Annular electroconvection with shear," Phys. Rev. Lett. 80, 964 (1998).
23. Z.A. Daya, V.B. Deyirmenjian, and S.W. Morris, "Bifurcation in annular electroconvection with imposed shear," Phys. Rev. E 64, 036212 (2001).
24. A. Alonso, M. Net, and J. Sánchez, "Spatially resonant interactions in annular convection," Proceedings of the Conference on Bifurcations Symmetry and Patterns (Birkhäuser, Boston, in press ).
25. A. Alonso, J. Sánchez, and M. Net, "Transition to temporal chaos in an O (2)-symmetric convective system for low Prandtl numbers," Prog. Theor. Phys. Suppl. 139, 315 (2000).
26. Y.A. Kuznetsov, Elements of Applied Bifurcation Theory (Springer, New York, 1998).
27. M. Golubitsky, I. Stewart and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory (Springer, New York, 1985), Vol. 2.
28. J.P. Gollub and H.L. Swinney, "Onset of turbulence in a rotating fluid," Phys. Rev. Lett. 35, 927 (1975).
29. G. Dangelmayr, "Steady-state mode interactions in the presence of O(2)-symmetry," Dyn. Stab. Syst. 1, 159 (1986).
30. M.R.E. Proctor and C.A. Jones, "The interaction of two spatially resonant patterns in thermal convection," J. Fluid Mech. 188, 301 (1988).
31. 4He," J. Phys. (France) Lett. 41, L-515 (1980).
32. J.P. Gollub and S.V. Benson, "Many routes to turbulent convection," J. Fluid Mech. 100, 449 (1980).
33. J.M. Lopez and F. Marques, "Dynamics of three-tori in a periodically forced Navier-Stokes flow," Phys. Rev. Lett. 85, 972 (2000).
34. D. Armbruster, B. Nicolaenko, N. Smaoui, and P. Chossat, "Symmetries and dynamics for 2-D Navier-Stokes flow," Physica D 95, 81 (1996).
35. J.M. Massaguer, I. Mercader, and M. Net, "Nonlinear dynamics of vertical vorticity in low-Prandtl-number thermal convection," J. Fluid Mech. 214, 579 (1990).
36. J.E. Hart, G.A. Glatzmaier, and J. Toomre, "Space-laboratory and numerical simulations of thermal convection in a rotating hemispherical shell with radial gravity," J. Fluid Mech. 173, 519 (1986).