Rayleigh number scaling in numerical convection

Journal of Fluid Mechanics

Volumn 310, Issue , 1996, Pages 139-179

  Kerr, Robert M ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; BOUNDARY LAYERS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PRANDTL NUMBER; TEMPERATURE DISTRIBUTION; TURBULENCE;

HARD TURBULENCE; NUMERICAL CONVECTION; RAYLEIGH NUMBER;

HEAT CONVECTION;

CONVECTION; NAVIER-STOKES EQUATIONS; RAYLEIGH NUMBER; SCALE EFFECTS;

EID: 0030088288     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096001760     Document Type: Article

References (59)

1. ADRIAN, R. J., FERREIRA, R. T. D. S. & BOBERG, T. 1986 Turbulent thermal convection in wide horizontal fluid layers. Exps. Fluids 4, 121-141.
2. BALACHANDAR, S. & SIROVICH, L. 1991 Probability distribution functions in turbulent convection. Phys. Fluids A 3, 919-927.
3. BATCHELOR, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids Suppl II 12, 233-239.
4. BOLGIANO, R. 1959 Turbulent spectra in a stably stratified atmosphere. J. Geophys. Res. 64, 2226-2229.
5. BUSSE, F. H. & WHITEHEAD, J. A. 1974 Oscillatory and collective instabilities in large Prandtl number convection. J. Fluid Mech. 66, 67-79.
6. 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.
7. CHAMPAGNE, F. H., FRIEHE, C. A., LARUE, J. C. & WYNGAARD, J. C. 1977 Flux measurements, flux estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land. J. Atmos. Sci. 34, 515-530.
8. CHANDRASEKAR, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
9. CHU, T. Y. & GOLDSTEIN, R. J. 1973 Turbulent convection in a horizontal layer of water. J. Fluid Mech. 60, 141-159.
10. CURRY, J. C., HERRING, J. R., LONCARIC, J. & ORSZAG, S. A. 1984 Order and disorder in two- and three-dimensional Bénard convection. J. Fluid Mech. 147, 1-38.
11. DEARDORFF, J. W. 1970 Convective velocity and temperature scales for the unstable planetary boundary layer and for Rayleigh-Bénard convection. J. Atmos. Sci. 27, 1211-1213.
12. DEARDORFF, J. W. & WILLIS, G. E. 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28, 675-704.
13. DEARDORFF, J. W. & WILLIS, G. E. 1985 Further results from a laboratory model of the convective planetary boundary layer. Boundary-Layer Met. 32, 205-236.
14. DELUCA, E. E., WERNE, J., ROSNER, R. & CATTANEO, F. 1990 Numerical simulations of soft and hard turbulence: preliminary results for two-dimensional convection. Phys. Rev. Lett. 64, 2370-2373.
15. DOMARADZKI, J. A. & METCALFE, R. W. 1988 Direct numerical simulations of the effects of shear on turbulent Rayleigh-Bénard convection. J. Fluid Mech. 193, 499-531.
16. EIDSON, T. M., HUSSAINI, M. Y. & ZANG, T. A. 1986 Simulation of the turbulent Rayleigh-Bénard problem using a spectral/finite difference technique. ICASE Rep. 86-6. Also in Direct and Large Eddy Simulation of Turbulence (ed. U. Schumann & R. Friedrich), pp. 188-209. Vieweg, 1986.
17. EIDSON, T. M., HUSSAINI, M. Y. & ZANG, T. A. 1986 Simulation of the turbulent Rayleigh-Bénard problem using a spectral/finite difference technique. ICASE Rep. 86-6. Also in Direct and Large Eddy Simulation of Turbulence (ed. U. Schumann & R. Friedrich), pp. 188-209. Vieweg, 1986.
18. FIEDLER, B. H. & KHAIROUTDINOV, M. 1994 Cell broadening in three-dimensional thermal convection between poorly conducting boundaries: large eddy simulations. Beitr. Phys. Atmos. 67, 235-241.
19. GRÖTZBACH, G. 1982 Direct numerical simulation of laminar and turbulent Bénard convection. J. Fluid Mech. 119, 27-53.
20. GRÖTZBACH, G. 1983 Spatial resolution requirement for direct numerical simulation of Rayleigh-Bénard convection. J. Comput. Phys. 49, 241-264.
21. HERRING, J. R., 1966 Some analytic results in the theory of thermal convection. J. Atmos. Sci. 23, 672-677.
22. HERRING, J. R. & KERR, R. M. 1982 Comparison of direct numerical simulations with predictions of two-point closures for isotropic turbulence convecting a passive scalar. J. Fluid Mech. 118, 205-219.
23. HESLOT, F., CASTAING, B. & LIBCHABER, A. 1987 Transition to turbulence in helium gas. Phys. Rev. A 36, 5870-5873.
24. KAIMAL, J. C., WYNGAARD, J. C., HAUGEN, D. A., COTÉ, O., IZUMI, Y., CAUGHEY, S. J. & READINGS, C. J. 1976 Turbulence structure in the convective boundary layer. J. Atmos. Sci. 33, 2152-2169.
25. KERR, R. M. 1985 Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31-58.
26. KERR, R. M. 1991 Velocity, scalar and transfer spectra in numerical turbulence. J. Fluid Mech. 211, 309-332.
27. KERR, R. M. HERRING, J. R. & BRANDENBURG, A. 1995 Large-scale structure in Rayleigh-Bénard convection with impenetrable side-walls. Chaos, Solitons and Fractals 5, 2047-2053.
28. KIM, J., MOIN, P. & MOSER, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133-166.
29. KRAICHNAN, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417-1423.
30. KRISHNAMURTI, R. 1995 Low frequency oscillations in turbulence convection: laboratory experiments. Fluid Dyn. Res. (in press).
31. KRISHNAMURTI, R. & HOWARD, L. N. 1981 Large-scale flow generation in turbulent convection. Proc. Nat. Acad. Sci. 78, 1981-1985.
32. LENSCHOW, D. H., WYNGAARD, J. C. & PENNELL, W. T. 1980 Mean-field and second-moment budgets in a baroclinic, convective boundary layer. J. Atmos. Sci. 37, 1313-1326.
33. MASON, P. J. 1989 Large eddy simulation of a convective atmospheric boundary layer. J. Atmos. Sci. 46, 1492-1516.
34. MCLAUGHLIN, J. B. & ORSZAG, S. A. 1982 Transition from periodic to chaotic thermal convection. J. Fluid Mech. 122, 123-142.
35. MÉTAIS, O. & LESIEUR, M. 1992 Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239, 157-194.
36. MOENG, C. H. & ROTUNNO, R. 1990 Vertical-velocity skewness in the buoyancy-driven boundary layer. J. Atmos. Sci. 47, 1149-1162.
37. MOENG, C. H. & WYNGAARD, J. C. 1988 Spectral analysis of large-eddy simulations of the convective boundary layer. J. Atmos. Sci. 45, 3573-3587.
38. MOSER, R. D., MOIN, P. & LEONARD, A. 1983 A spectral numerical method for the Navier-Stokes equations with application to Taylor-Couette now. J. Comput. Phys. 52, 524-544.
39. PRANDTL, L. 1932 Meteorologische Anwendungen der Strömungslehre. Beitr. Phys. Atmos. 19, 188-202.
40. PRIESTLEY, C. H. B. 1954 Convection from a large horizontal surface. Austral. J. Phys. 7, 176-201.
41. SANO, M., WU, X. Z., & LIBCHABER, A. 1989 Turbulence in helium-gas free convection. Phys. Rev. A 40, 6421-6430.
42. SCHMIDT, H. & SCHUMANN, U. 1989 Conherent structure of the convective boundary layer derived from large-eddy simulations. J. Fluid Mech. 200, 511-562.
43. SHE, Z. S. 1989 On the scaling laws of thermal turbulent convection. Phys. Fluids A 1, 911-913.
44. SHRAIMAN, B. I. & SIGGIA, E. D. 1990 Heat transport in high-Rayleigh-number convection. Phys. Rev. A 42, 3650-3653.
45. SIROVICH, L., BALACHANDAR, S. & MAXEY, M. R. 1989 Simulations of turbulent thermal convection. Phys. Fluids A 1, 1911-1914.
46. θ = 1410. J. Fluid Mech. 187, 61-98.
47. SPALART, P. R., MOSER, R. D. & ROGERS, M. M. 1991 Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297-324.
48. SREENIVASAN, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165-182.
49. THUAL, O. 1992 Zero Prandtl number convection J. Fluid Mech. 240, 229-258.
50. TONG, P. & SHEN, Y. 1992 Relative velocity fluctuations in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 69, 2066-2069.
51. VINCENT, A. & MENEGUZZI, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1-20.
52. WERNE, J. 1993 Structure of hard-turbulent convection in two dimensions: Numerical evidence. Phys. Rev. E 48, 1020-1035.
53. WERNE, J., DELUCA, E. E., ROSNER, R. & CATTANEO, F. 1991 Development of hard-turbulent convection in two dimensions: Numerical evidence. Phys. Rev. Lett. 67, 3519-3522.
54. WILLIS, G. E. & DEARDORFF, J. W. 1974 A laboratory model of diffusion into the convective planetary boundary layer. Q. J. R. Met. Soc. 102, 421-445.
55. Wu, X.-Z., KADANOFF, L., LIBCHABER, A. & SANO, M. 1990 Frequency power spectrum of temperature fluctuations in free convection. Phys. Rev Lett. 64, 2140-2143.
56. Wu, X.-Z. & LIBCHABER, A. 1992 Scaling relations in thermal turbulence: The aspect-ratio dependence. Phys. Rev. A 45, 842-845.
57. WYNGAARD, J. C. & WEIL, J. C. 1991 Transport asymmetry in skewed turbulence. Phys. Fluids A 3, 155-162.
58. YAKHOT, V. 1992 The 4/5-Kolmogorov law for statistically stationary turbulence. Application to high Rayleigh number Bénard convection. Phys. Rev. Lett. 69, 769-771.
59. ZOCCHI, G., MOSES, E. & LIBCHABER, A. 1990 Coherent structures in turbulent convection, an experimental study. Physica 166A, 387-407.