Scaling in thermal convection: A unifying theory

Journal of Fluid Mechanics

Volumn 407, Issue , 2000, Pages 27-56

  Grossmann, Siegfried ^a   Lohse, Detlef ^b  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

CONVECTION; HEAT TRANSFER; NUSSELT NUMBER; REYNOLDS NUMBER; SCALING;

EID: 0033925498     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099007545     Document Type: Article

References (69)

1. ASHKENAZI, S. & STEINBERG, V. 1999 High Rayleigh number turbulent convection in a gas near the gas-liquid critical point. Phys. Rev. Lett. 83, 3641-3644.
2. BELMONTE, A., TILGNER, A. & LIBCHABER, A. 1993 Boundary layer length scales in thermal turbulence. Phys. Rev. Lett. 70, 4067-4070.
3. BELMONTE, A., TILGNER, A. & LIBCHABER, A. 1994 Temperature and velocity boundary layers in turbulent convection. Phys. Rev. E 50, 269-279.
4. BENZI, R., TOSCHI, F. & TRIPICCIONE, R. 1998 On the heat transfer in the Rayleigh-Bénard system. J. Statist. Phys. 93, 901-918.
5. BOBERG, L. & BROSA, U. 1988 Onset of turbulence in a pipe. Z. Naturforsch. 43a, 697-726.
6. BUSSE, F. H. 1978 The optimum theory of turbulence. Adv. Appl. Mech. 18, 77-121.
7. BUSSE, F. H. & CLEVER, R. M. 1981 An asymptotic model of two-dimensional convection in the limit of low Prandtl number. J. Fluid Mech. 102, 75-83.
8. CASTAING, B., GUNARATNE, G., HESLOT, F., KADANOFF, L., LIBCHABER, A., THOMAE, S., WU, X. Z., ZALESKI, S. & ZANETTI, G. 1989 Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J. Fluid Mech. 204, 1-30.
9. CHAN, S. K. 1971 Infinite Prandtl number turbulent convection. Stud. Appl. Maths 50, 13-49.
10. CHAVANNE, X., CHILLA, F., CASTAING, B., HEBRAL, B., CHABAUD, B. & CHAUSSY, J. 1997 Observation of the ultimate regime in Rayleigh-Bénard convection. Phys. Rev. Lett. 79, 3648-3651.
11. CHILLA, F., CILIBERTO, S., INNOCENTI, C. & PAMPALONI, E. 1993 Boundary layer and scaling properties in turbulent thermal convection. Il Nuovo Cimento D 15, 1229-1249.
12. CHING, E. S. C. 1997 Heat flux and shear rate in turbulent convection. Phys. Rev. E 55, 1189-1192.
13. CILIBERTO, S., CIONI, S. & LAROCHE, C. 1996 Large-scale flow properties of turbulent thermal convection. Phys. Rev. E 54, R5901-R5904.
14. CILIBERTO, S. & LAROCHE, C. 1999 Random roughness of boundary increases the turbulent convection scaling exponent. Phys. Rev. Lett. 82, 3998-4001.
15. CIONI, S., CILIBERTO, S. & SOMMERIA, J. 1995 Temperature structure functions in turbulent convection at low Prandtl number. Europhys. Lett. 32, 413-418.
16. CIONI, S., CILIBERTO, S. & SOMMERIA, J. 1997 Strongly turbulent Rayleigh-Bénard convection in mercury: comparison with results at moderate Prandtl number. J. Fluid Mech. 335, 111-140.
17. CLEVER, R. M. & BUSSE, F. H. 1981 Low Prandtl number convection in a layer heated from below. J. Fluid Mech. 102, 61-74.
18. CONSTANTIN, P. & DOERING, C. 1999 Infinite Prandtl number convection. J. Statist. Phys. 94, 159-172.
19. DAVIS, A. H. 1922a Natural convective cooling of wires. Phil. Mag. 43, 329-339.
20. DAVIS, A. H. 1922b Natural convective in cooling in fluids. Phil. Mag. 44, 920-940.
21. DOERING, C. & CONSTANTIN, P. 1996 Variational bounds on energy dissipation in incompressible flows: III.: Convection. Phys. Rev. E 53, 5957-5981.
22. DRAZIN, P. & REID, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
23. DU, Y. B. & TONG, P. 1998 Enhanced heat transport in turbulent convection over a rough surface. Phys. Rev. Lett. 81, 987-990.
24. ECKHARDT, B. & MERSMANN, A. 1999 Transition to turbulence in shear flow. Phys. Rev. E 60, 509-517.
25. FABER, T. E. 1995 Fluid Dynamics for Physicists. Cambridge University Press.
26. GARON, A. M. & GOLDSTEIN, R. J. 1973 Velocity and heat transfer measurements in thermal convection. Phys. Fluids 16, 1818-1825.
27. GERHARDT, T. & GROSSMANN, S. 1994 Chaos transition despite linear stability. Phys. Rev. E 50, 3705-3711.
28. GLAZIER, J. A., SEGAWA, T., NAERT, A. & SANO, M. 1999 Evidence against ultrahard thermal turbulence at very high Rayleigh numbers. Nature 398, 307-310.
29. GOLDSTEIN, R. J. & TOKUDA, S. 1980 Heat transfer by thermal convection at high Rayleigh numbers. Intl J. Heat Mass Transfer 23, 738-740.
30. GROSSMANN, S. 1995 Asymptotic dissipation rate in turbulence. Phys. Rev. E 51, 6275-6277.
31. GROSSMANN, S. 1999 The onset of shear flow turbulence. Rev. Mod. Phys., in press.
32. HESLOT, F., CASTAING, B. & LIBCHABER, A. 1987 Transition to turbulence in helium gas. Phys. Rev. A 36, 5870-5873.
33. HORANYI, S., KREBS, L. & MÜLLER, U. 1999 Turbulent Rayleigh-Bénard convection in low Prandtl number fluids. Intl J. Heat Mass Transfer 42, 3983-4003.
34. HOWARD, L. N. 1972 Bounds on flow quantities. Ann. Rev. Fluid. Mech. 4, 473-494.
35. KERR, R. 1996 Rayleigh number scaling in numerical convection. J. Fluid Mech. 310, 139-179.
36. KRAICHNAN, R. H. 1962 Turbulent thermal convection at arbrtrary Prandtl number. Phys. Fluids 5, 1374-1389.
37. KRISHNAMURTI, R. & HOWARD, L. N. 1981 Large scale flow generation in turbulent convection. Proc. Natl Acad. Sci. 78, 1981-1985.
38. LANDAU, L. D. & LIFSHITZ, E. M. 1987 Fluid Mechanics. Pergamon.
39. LATHROP, D. P., FINEBERG, J. & SWINNEY, H. S. 1992 Turbulent flow between concentric rotating cylinders at large Reynolds numbers. Phys. Rev. Lett. 68, 1515-1518.
40. LUI, S. L. & XIA, K. Q. 1998 Spatial structure of the thermal boundary layer in turbulent convection. Phys. Rev. E 57, 5494-5503.
41. MALKUS, M. V. R. 1954 The heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. A 225, 196-212.
42. PROCACCIA, I., CHING, E. S. C., CONSTANTIN, P., KADANOFF, L. P., LIBCHABER, A. & WU, X. Z. 1991 Transition to convective turbulence: The role of thermal plumes. Phys. Rev. A 44, 8091-8102.
43. QIU, X. L. & XIA, K.-Q. 1998 Viscous boundary layers at the sidewall of a convection cell. Phys. Rev. E 58, 486-491.
44. ROBERTS, G. O. 1979 Fast viscous Bénard convection. Geophys. Astrophys. Fluid Dyn. 12, 235-272.
45. ROSSBY, H. T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309-335.
46. SCHMIEGEL, A. & ECKHARDT, B. 1997 Fractal stability border in plane Couette flow. Phys. Rev. Lett. 79, 5250-5253.
47. SCHMIEGEL, A. & ECKHARDT, B. 1999 Dynamics of perturbations in plane Couette flow. Preprint, Marburg.
48. SHEN, Y., TONG, P. & XIA, K. Q. 1996 Turbulent convection over rough surfaces. Phys. Rev. Lett. 76, 908-911.
49. SHRAIMAN, B. I. & SIGGIA, E. D. 1990 Heat transport in high-Rayleigh number convection. Phys. Rev. A 42, 3650-3653.
50. SIGGIA, E. D. 1994 High Rayleigh number convection. Ann. Rev. Fluid Mech. 26, 137-168.
51. SOLOMON, T. H. & GOLLUB, J. P. 1990 Sheared boundary layers in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 64, 2382-2385.
52. SPIEGEL, E. A. 1971 Convection in stars. Ann. Rev. Astron. Astrophys. 9, 323-352.
53. TAKESHITA, T., SEGAWA, T., GLAZIER, J. A. & SANO, M. 1996 Thermal turbulence in mercury. Phys. Rev. Lett. 76, 1465-1468.
54. TANAKA, H. & MIYATA, H. 1980 Turbulent natural convection in a horizontal water layer heated from below. Intl J. Heat Mass Transfer 23, 1273-1281.
55. THRELFALL, D. C. 1975 Free convection in low temperature gaseous helium. J. Fluid Mech. 67, 17-28.
56. TILGNER, A., BELMONTE, A. & LIBCHABER, A. 1993 Temperature and velocity profiles of turbulence convection in water. Phys. Rev. E 47, R2253-R2256.
57. TREFETHEN, L., TREFETHEN, A., REDDY, S. & DRISCOL, T. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578-584.
58. VILLERMAUX, E. 1995 Memory-induced low frequency oscillations in closed convection boxes. Phys. Rev. Lett. 75, 4618-4621.
59. WALEFFE, F. 1995 Transition in shear flows: Nonlinear normality versus non-normal linearity. Phys. Fluids 7, 3060-3066.
60. WERNE, J. 1993 Structure of hard-turbulent convection in two-dimensions: Numerical evidence. Phys. Rev. E 48, 1020-1035.
61. WU, X. Z. 1991 Along a road to developed turbulence: Free thermal convection in low temperature He gas. PhD thesis, University of Chicago.
62. WU, X. Z. & LIBCHABER, A. 1991 Non-Boussinesq effects in free thermal convection. Phys. Rev. A 43, 2833-2839.
63. WU, X. Z. & LIBCHABER, A. 1992 Scaling relations in thermal turbulence: The aspect ratio dependence. Phys. Rev. A 45, 842-845.
64. XIA, K.-Q. & LUI, S.-L. 1997 Turbulent thermal convection with an obstructed sidewall. Phys. Rev. Lett. 79, 5006-5009.
65. XIN, Y. B. & XIA, K. Q. 1997 Boundary layer length scales in convective turbulence. Phys. Rev. E 56, 3010-3015.
66. XIN, Y. B., XIA, K. Q. & TONG, P. 1996 Measured velocity boundary layers in turbulent convection. Phys. Rev. Lett. 77, 1266-1269.
67. YAKHOT, V. 1992 4/5 Kolmogorov law for statistically staionary turbulence: application to high Rayleigh number Bénard convection. Phys. Rev. Lett. 69, 769-771.
68. ZALESKI, S. 1998 The 2/7 law in turbulent thermal convection. In Geophysical and Astrophysical Convection (ed. P. Fox & R. Kerr). Gordon and Breach.
69. ZOCCHI, G., MOSES, E. & LIBCHABER, A. 1990 Coherent structures in turbulent convection: an experimental study. Physica A 166, 387-407.