Rayleigh-Bénard convection in the presence of spatial temperature modulations

Journal of Fluid Mechanics

Volumn 673, Issue , 2011, Pages 318-348

  Freund, G ^a   Pesch, W ^a   Zimmermann, W ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

B nard convection; nonlinear instability; pattern formation

Indexed keywords

MODULATION;

ASYMPTOTIC EXPANSION; AVERAGE TEMPERATURE GRADIENTS; BOUSSINESQ EQUATIONS; CRITICAL RAYLEIGH NUMBER; NONLINEAR INSTABILITY; PATTERN FORMATION; SWIFT-HOHENBERG EQUATIONS; TEMPERATURE MODULATION;

NATURAL CONVECTION;

AMPLITUDE; BIFURCATION; BOUSSINESQ EQUATION; CONVECTION; EXPERIMENTAL STUDY; FLUID DYNAMICS; NONLINEARITY; RAYLEIGH NUMBER; STABILITY ANALYSIS; TEMPERATURE GRADIENT; VECTOR; WAVE EQUATION;

EID: 79956001917     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010006270     Document Type: Article

References (39)

1. Bodenschatz, E., Pesch, W. & Ahlers, G. 2000 Recent developments in Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 32, 709-778.
2. Buka, A., Dressel, B., Kramer, L. & Pesch, W. 2004 Direct transition to electroconvection in a homeotropic nematic liquid crystal. Chaos 14, 793-802. (Pubitemid 39443311)
3. Busse, F. H. & Clever, R. M. 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319-335. (Pubitemid 9448702)
4. Busse, F. H. & Whitehead, J. A. 1971 Instabilities of convection rolls in a high Prandtl number fluid. J. Fluid Mech. 47, 305-320.
5. Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.
6. Chiam, K. H., Paul, M. R., Cross, M. C. & Greenside, H. S. 2003 Mean flow and spiral defect chaos in Rayleigh-Bénard convection. Phys. Rev. E 67, 056206.
7. Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625-645.
8. Coullet, P. 1986 Commensurate-incommensurate transition in nonequilibrium systems. Phys. Rev. Lett. 56, 724-727.
9. Coullet, P. & Huerre, P. 1986 Resonance and phase solitons in spatially forced thermal convection. Physica D 23, 27-44.
10. Cross, M. C. 1980 Derivation of the amplitude equation at the Rayleigh-Bénard instability. Phys. Fluids 23, 1727-1731.
11. Cross, M. C. & Greenside, H. 2009 Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge University Press.
12. Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851-1112.
13. Decker, W. & Pesch, W. 1994 Order parameter and amplitude equations for the Rayleigh-Bénard convection. J. Phys. II 4, 419-438.
14. Hall, P. & Walton, I. C. 1978 The smooth transition to a convective regime in a two-dimensional box. Proc. R. Soc. Lond. A 358, 199-221. (Pubitemid 8578904)
15. Henriot, M., Burguete, J. & Ribotta, R. 2003 Entrainment of a spatially extended nonlinear structure under selective forcing. Phys. Rev. Lett. 91, 104501.
16. Kelly, R. E. 1993 Thermal convection in fluid layers with nonuniform thickness or surface temperature. In IUTAM Symp. on Nonlinear Instability of Nonparallel Flows (ed. S. P. Lin, W. R. C. Phillips & D. T. Valentine), pp. 1-12.
17. Springer. Kelly, R. E. & Pal, D. 1976 Thermal convection induced between non-uniformly heated horizontal surfaces. In Proc. 1976 Heat Transfer and Fluid Mechanics Institute (ed. A. A. McKillop, J. W. Baughn & H. A. Dwyer), pp. 1-17. Stanford University Press.
18. Kelly, R. E. & Pal, D. 1978 Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation. J. Fluid Mech. 86, 433-456. (Pubitemid 8608523)
19. Lowe, M. & Gollub, J. P. 1985a Pattern selection near the onset of convection: the Eckhaus instability. Phys. Rev. Lett. 55, 2575-2578.
20. Lowe, M. & Gollub, J. P. 1985b Solitons and the commensurate- incommensurate transition in a convecting nematic fluid. Phys. Rev. A 31, 3893-3897.
21. Manneville, P. & Piquemal, J. M. 1983 Zigzag instability and axisymmetric rolls in Rayleigh-Bénard convection: the effects of curvature. Phys. Rev. A 28, 1774-1790.
22. Manor, R., Hagberg, A. & Meron, E. 2008 Wavenumber locking in spatially forced pattern-forming systems. Europhys. Lett. 83, 10005.
23. Manor, R., Hagberg, A. & Meron, E. 2009 Wavenumber locking and pattern formation in spatially forced systems. New J. Phys. 11, 063016.
24. McCoy, J. 2008 Pattern formation due to spatially periodic forcing. PhD thesis, Cornell University.
25. McCoy, J. H., Brunner, W., Pesch, W. & Bodenschatz, E. 2008 Self-organization of topological defects due to applied constraints. Phys. Rev. Lett. 101, 254102.
26. Obé, M. & Khayat, R. E. 2010 Spatially modulated thermal convection. Intl J. Numer. Meth. Heat Fluid Flow 20, 17-36.
27. Pal, D. & Kelly, R. E. 1979 Three-dimensional thermal convection produced by two-dimensional thermal forcing. In Proc. Joint ASME/AIChE 18th Natl Heat Transfer Conf., San Diego, California, 1979, pp. 1-8. ASME 79-HT-109.
28. Pesch, W. 1996 Complex spatiotemporal convection patterns. Chaos 6, 348-357.
29. Plaut, E. & Pesch, W. 1999 Extended weakly nonlinear theory of planar nematic convection. Phys. Rev. E 59, 1747-1769. (Pubitemid 129586244)
30. Schlüter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 23, 129-144.
31. Schmitz, R. & Zimmermann, W. 1996 Spatially periodic modulated Rayleigh-Bénard convection. Phys. Rev. E 53, 5993-6011. (Pubitemid 126584166)
32. Seiden, G., Weiss, S. & Bodenschatz, E. 2009 Superlattice patterns in forced thermal convection. Chaos 19, 041102.
33. Seiden, G., Weiss, S., McCoy, J. H., Pesch, W. & Bodenschatz, E. 2008 Pattern forming system in the presence of different symmetry-breaking mechanisms. Phys. Rev. Lett. 101, 214503.
34. Semwogerere, D. & Schatz, M. F. 2002 Evolution of hexagonal patterns from controlled initial conditions in a Bénard-Marangoni convection experiment. Phys. Rev. Lett. 88, 054501.
35. Trainoff, S. P. & Cannell, D. S. 2002 Physical optics treatment of the shadowgraph. Phys. Fluids 14, 1340-1363. (Pubitemid 34439817)
36. Vozovoi, L. P. & Nepomnyashchy, A. A. 1974 Convection in a horizontal layer in the presence of spatial modulation of temperature at the boundaries. Gidrodinamika 7, 105-117 (published by the Governmental Pedagogical Institute of the University of Perm, Russia).
37. Weiss, S. 2009 On forcing in thermal convection experiments. PhD thesis, Universiẗat Göttingen.
38. Xi, H. W., Gunton, J. D. & Vinals, J. 1993 Spiral defect chaos in a model of Rayleigh-Bénard convection. Phys. Rev. Lett. 71 (13), 2030-2033.
39. Zimmermann, W., Ogawa, A., Kai, S., Kawasaki, K. & Kawakatsu, T. 1993 Wavelength competition in convective systems. Europhys. Lett. 24, 217-222.