Re-entrant hexagons in non-Boussinesq convection

Journal of Fluid Mechanics

Volumn 548, Issue , 2006, Pages 341-360

  Madruga, Santiago ^a   Riecke, Hermann ^a   Pesch, Werner ^b  

^a Northwestern University   (United States)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; HEAT CONVECTION; KINEMATICS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; STABILITY; THERMAL CONDUCTIVITY; VISCOSITY;

BOUSSINESQ HEXAGONAL CONVECTION; KINEMATIC VISCOSITY; RAYLEIGH NUMBERS; STABILITY ANALYSIS;

FLUID DYNAMICS;

BOUSSINESQ EQUATION; CONVECTION; NAVIER-STOKES EQUATIONS;

EID: 32044444826     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005007640     Document Type: Article

References (42)

1. Ahlers, G. 2005 Experiments with Rayleigh-Bénard convection. In Dynamics of Spatio-temporal Cellular Structures - Henri Bénard Centenary Review (ed. I. Mutabazi, J. E. Wesfreid & E. Guyon). Springer.
2. Assenheimer, M. & Steinberg, V. 1996 Observation of coexisting upflow and downflow hexagons in Boussinesq Rayleigh-Bénard convection. Phys. Rev. Lett. 76, 756-759.
3. Bodenschatz, E., deBruyn, J. R., Ahlers, G. & Cannell, D. 1991 Transitions between patterns in thermal convection. Phys. Rev. Lett. 67, 3078.
4. Bodenschatz, E., Pesch, W. & Ahlers, G. 2000 Recent developments in Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 32, 709-778.
5. Bragard, J. & Velarde, M. G. 1998 Bénard-Marangoni convection: planforms and related theoretical predictions. J. Fluid Mech. 368, 165-194.
6. Busse, F. H. 1967 The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30, 625-649.
7. Busse, F. H. 1989 Fundamentals of thermal convection. In Mantle Convection: Plate Tectonics and Global Dynamics (ed. W. Peltier), p. 23. Gordon and Breach.
8. Busse, F. H. & Clever, R. M. 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319-335.
9. Busse, F. H. & Clever, R. M. 1999 New patterns in Rayleigh-Bénard convection. In Des Phenomenes Critiques au Chaos (ed. P. Manneville), pp. 79-92. Saclay: DRECAM/SPEC CEA.
10. Busse, F. H., Clever, R. M. & Grote, E. 1999 Weakly nonlinear and fully nonlinear pattern formation in isotropic convection layers. Chaos Solitons Fractals 10, 753-760.
11. Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
12. Clever, R. M. & Busse, F. H. 1996 Hexagonal convection cells under conditions of vertical symmetry. Phys. Rev. E 53, R2037-R2040.
13. Cross, M. & Hohenberg, P. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851-1112.
14. Davis, S. H. & Segel, L. A. 1968 Effects of surface curvature and property variation on cellular convection. Phys. Fluids 11, 470-476.
15. Decker, W., Pesch, W. & Weber, A. 1994 Spiral defect chaos in Rayleigh-Bénard convection. Phys. Rev. Lett. 73, 648-651.
16. Dubois, M., Bergé, P. & Wesfreid, J. 1978 Non-Boussinesq convective structure in water near 4-degrees-C. J. Physique 39, 1253-1257.
17. Echebarria, B. & Pérez-García, C. 1998 Phase instabilities in hexagonal patterns. Europhys. Lett. 43, 35-40.
18. Echebarria, B. & Riecke, H. 2000 Defect chaos of oscillating hexagons in rotating convection. Phys. Rev. Lett. 84, 4838-4841.
19. Friedrichs, R. & Engel, A. 2001 Pattern and wave number selection in magnetic fluids. Phys. Rev. E 64, 021406.
20. Gough, D. O. 1969 The anelastic approximation in thermal convection. J. Atmos. Sci. 26, 448-456.
21. Hoyle, R. 1995 Nonlinear phase diffusion equations for the long-wave instabilities of hexagons. Appl. Math. Lett. 8(3), 81-85.
22. Lauzeral, J., Metens, S. & Walgraef, D. 1993 On the phase dynamics of hexagonal patterns. Europhys. Lett. 24, 707-712.
23. Madruga, S. & Pérez-García, C. 2004 Hexagonal patterns in a model for rotating convection. Int. J. Bifurcation Chaos 14, 107-117.
24. Nuz, A. E., Nepomnyashchy, A. A. & Pismen, L. M. 1998 Stability of non-equilateral hexagonal patterns governed by generalized amplitude equations. Physica A 249, 179-183.
25. Oh, J., Ortiz de Zárate, J., Sengers, J. V. & Ahlers, G. 2004 Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection. Phys. Rev. E 69, 021106.
26. Palm, E. 1960 On the tendency towards hexagonal cells in steady convection. J. Fluid Mech. 8, 183-192.
27. Palm, E., Ellingsen, T. & Gjevik, B. 1967 On occurrence of cellular motion in Bénard convection. J. Fluid Mech. 30, 651-661.
28. Pampaloni, E., Pérez-García, C., Albavetti, L. & Ciliberto, S. 1992 Transition from hexagons to rolls in convection in fluids under non-Boussinesq conditions. J. Fluid Mech. 234, 393-416.
29. Pesch, W. 1996 Complex spatio-temporal convection patterns. Chaos 6. 348-357.
30. Plaut, E. & Pesch, W. 1999 Extended weakly nonlinear theory of planar nematic convection. Phys. Rev. E 59, 1747-1769.
31. Richter, F. M. 1978 Experiments on the stability of convection rolls in fluids whose viscosity depends on temperature. J. Fluid Mech. 89, 553-560.
32. Roy, A. & Steinberg, V. 2002 ReEntrant hexagons in non-Boussinesq Rayleigh-Bénard convection: Effect of compressibility. Phys. Rev. Lett. 88, 244503.
33. Segel, L. A. 1965 Non-linear interaction of finite number of disturbances to a layer of fluid heated from below. J. Fluid Mech. 21, 359-384.
34. Segel, L. A. & Stuart, J. T. 1962 On the question of the preferred mode in cellular thermal convection. J. Fluid Mech. 13, 289-306.
35. Semwogerere, D. & Schatz, M. F. 2002 Evolution of hexagonal patterns from controlled initial conditions in a Bénard convection experiment. Phys. Rev. Lett. 88, 054501.
36. Semwogerere, D. & Schatz, M. F. 2004 Secondary instabilities of hexagonal patterns in a Bénard-Marangoni convection experiment. Phys. Rev. Lett. 93, 124502.
37. Somerscales, E. F. & Dougherty, T. S. 1970 Observed flow patterns at initiation of convection in a horizontal liquid layer heated from below. J. Fluid Mech. 42, 755-768.
38. Soward, A. M. 1985 Bifurcation and stability of finite amplitude convection in a rotating layer. Physica D 14, 227-241.
39. Swift, J. W. 1984 Convection in a rotating fluid layer. In Contemporary Mathematics, Vol. 28, p. 435. American Mathematical Society.
40. Walden, R. W. & Ahlers, G. 1981 Non-Boussinesq and penetrative convection in a cylindrical cell. J. Fluid Mech. 109, 89-114.
41. Young, Y.-N. & Riecke, H. 2002 Mean flow in hexagonal convection: stability and nonlinear dynamics. Physica D 163, 166-183.
42. Young, Y.-N., Riecke, H. & Pesch, W. 2003 Whirling hexagons and defect chaos in hexagonal non-Boussinesq convection. New J. Phys. 5, 135.