A computational study of Rayleigh-Benard convection. Part 1. Rayleigh-number scaling

Journal of Fluid Mechanics

Volumn 222, Issue , 1991, Pages 231-250

  Deane, Anil E ^b   Sirovich, Lawrence ^b  

^a PRINCETON UNIVERSITY   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW OF FLUIDS - ANALYSIS; MATHEMATICAL TECHNIQUES - EIGENVALUES AND EIGENFUNCTIONS; PROBABILITY; STATISTICAL METHODS;

RAYLEIGH NUMBER; RAYLEIGH-BENARD CONVECTION;

HEAT TRANSFER;

EID: 0025995195     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112091001088     Document Type: Article

References (55)

1. ASH, R. B. & GARDNER, M. F. 1975 Topics in Stochastic Processes. Academic.
2. AUBRY, N., HOLMES, P., LUMLEY, J. L. & STONE, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115.
3. BALACHANDAR, S., MAXEY, M. R. & SIROVICH, L. 1989 Numerical simulation of high Rayleigh number convection. J. Sci. Comput. 4, 219.
4. BENETTIN, G., GALQANI, L., GIORGILLI, A. & STRELCYN, J.-M. 1980 Lyapunov characteristic exponents for smooth dynamical systems and Hamiltonian systems: A method for computing all of them. Pts. 1 and 2. Meccanica 15, 9–30.
5. BUSSE, F. H. 1985 In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub). Springer.
6. CASTAING, B., GUNARATNE, G., HESLOT, F., KADANOFF, L., LIBSCHABER, A., THOMAE, S., WU, X.-Z., ZALESKI, S. & ZANETTI, G. 1989 Scaling of hard thermal turbulence in Rayleigh-Benard convection. J. Fluid Mech. 204, 1.
7. CATTON, I. 1966 Natural convection in horizontal liquid layers. Phys. Fluids 19, 252.
8. CHANDRASEKHAR, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
9. CONSTANTIN, P., FOIAŞ, C., MANLEY, O. P. & TEMAM, R. 1985 Determining modes and fractal dimension of turbulent flows. J. Fluid Mech. 150, 427.
10. DRAZIN, P. G. & REID, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
11. FEIGENBAUM, M. J. 1978 Quantitative universality for a class of nonlinear transformations. J. Statist. Phys. 19, 25.
12. FENSTERMACHER, P. R., SWINNEY, H. L. & GOLLUB, J. P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94, 103.
13. FOIAŞ, C., MANLEY, O. & TEMAM, R. 1987 Nonlin. Anal. Theory, Meth. Applies. 11, 939–967.
14. GARON, A. M. & GOLDSTEIN, R. J. 1973 Velocity and heat transfer measurements in thermal convection. Phys. Fluids 16, 1818–1825.
15. GILBERT, N. & KLEISER, L. 1987 Low-resolution simulations of transitional and turbulent channel flow. In Proc. Intl Conf. on Fluid Mechanics. Peking University Press, Beijing, China.
16. GLAUSER, M. N., LIEB, S. J. & GEORGE, N. K. 1987 Coherent structure in the axisymmetric jet mixing layer. In Turbulent Shear Flows 5 (ed. F. Durst et al.). Springer.
17. GRENANDER, U. & SZEGO, G. 1958 Toeplitz Forms and Their Application. University of California Press, Berkeley.
18. HERRING, J. H. & WYNGAARD, J. 1987 Convection with a simple chemically reactive passive scalar. 10.39-10.43 In Turbulent Shear Flows 5 (ed. F. Dust), p. 328. Springer.
19. KAPLAN, J. & YORKE, J. 1979 Chaotic behavior in multi-dimensional difference equations. In Functional Differential Equations and the Approximation of Fixed Points (ed. H. O. Peitgen & H. O. Walther). In Lecture Notes in Mathematics, vol. 730, p. 228. Springer.
20. KEEFE, L. & MOIN, P. 1987 Bull. Am. Phys. Soc. II 32, 2026.
21. LANDAU, L. D. 1944 Dokl. Akad. Nauk. SSSR 44, 339.
22. LORENZ, E. N. 1959 Prospects for statistical weather forecasting. Final Rep., Statistical Forecasting Project, MIT.
23. LORENZ, E. N. 1963 Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130.
24. LORENZ, E. N. 1980 Noisy periodicity and reverse bifurcation. In Nonlinear Dynamics (ed. R. H. G. Helleman). NY Acad. Sci.
25. LUMLEY, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (ed. A. M. Yaglom & V. I. Tatarski), pp. 166–178. Moskow: Nauka.
26. LUMLEY, J. L. 1970 Stochastic Tools in Turbulence. Academic.
27. LUMLEY, J. L. 1981 Coherent structures in turbulence. In Transition and Turbulence (ed. R. E. Meyer), pp. 215–242. Academic.
28. MALKUS, W. V. R. 1954a Discrete transitions in turbulent convection. Proc. R. Soc. Lond. 225, 185.
29. MALKUS, W. V. R. 1954b The heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. 225, 198.
30. MALKUS, W. V. R. & VERONIS, G. 1958 Finite amplitude cellular convection. J. Fluid Mech. 4, 225.
31. MALRAISON, D., ATTEN, P., BERGE, P. & DUBOIS, M. 1983 Dimension d'attracteurs etranges: une determination experimentale en regime chaotique de deux systems convectifs. CR Acad. Sci. Paris C297, 209.
32. MASSAGUER, J. M. & MERCADER, I. 1988 Instability of swirl in low-Prandtl-number thermal convection. J. Fluid Mech. 189, 367.
33. MOIN, P. 1984 Probing turbulence via large eddy simulation. AIAA Paper-84-0174.
34. MOIN, P. & MOSER, R. D. 1989 Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech. 200, 471.
35. MONIN, A. S. & YAGLOM, A. M. 1975 Statistical Fluid Mechanics Vol.2. MIT Press.
36. PILLOW, A. F. 1952 The free convection cell in two dimensions. Rep. Aero. Res. Lab. Melbourne A79.
37. PREISENDORFER, R. W. 1988 Principal component analysis in meteorology and oceanography. In Meteorology and Oceanography. Elsevier.
38. RUELLE, D. & TAKENS, F. 1971 On the nature of turbulence. Commun. Math. Phys. 20, 167.
39. SHIMADA, I. & NAGASHIMA, T. 1979 A numerical approach to the ergodic problem of dissipative dynamical systems. Prog. Theor. Phys. 61, 1605.
40. SIROVICH, L. 1987 a Turbulence and the dynamics of coherent structures, Pt. I: Coherent Structures. Q. Appl. Maths XLV, 561.
41. SIROVICH, L. 1987b Turbulence and the dynamics of coherent structures, Pt. II. Symmetries and transformations. Q. Appl. Maths XLV, 573.
42. SIROVICH, L., BALACHANDAR, S. & MAXEY, M. R. 1989a Simulations of turbulent thermal convection. Phys. Fluids A 1, 1911–1914.
43. SIROVICH, L. & DEANE, A. E. 1991 A computational study of Rayleigh-Bénard convection. Part 2. Dimension considerations. J. Fluid Mech. 222, 251 (referred to herein as II).
44. SIROVICH, L., MAXEY, M. & TARMAN, H. 1989b Analysis of turbulent thermal convection. In Sixth Symposium on Turbulent Shear Flow, Toulouse, France, p. 68. Springer.
45. SIROVICH, L. & RODRIGUEZ, J. D. 1987 Coherent structures and chaos: A model problem. Phys. Lett A 120, 211–214.
46. SPIEGEL, E. A. 1962 On the Malkus Theory of Turbulence, p. 181. Centre National de la Researche Scientifique, Paris.
47. TARMAN, H. 1989 Analysis of turbulent thermal convection. Ph.D. thesis, Brown University.
48. TARMAN, H. & SIROVICH, L. 1990 Low dimensional dynamics for the turbulent convection problem (to appear).
49. THEODORSEN, T. 1952 Mechanism of turbulence. In Proc. 2nd Midwestern Conf. on Fluid Mech., Ohio State Univ., Columbus, Ohio.
50. THRELFALL, D. C. 1975 Free convection in low-temperature gaseous helium. J. Fluid Mech. 67, 17.
51. TOOMRE, J., GOUGH, D. O. & SPIEGEL, E. A. 1977 Numerical solutions of single-mode convection equations. J. Fluid Mech. 79, 1.
52. TOOMRE, J., GOUGH, D. O. & SPIEGEL, E. A. 1982 Time-dependent solutions of multimode convection equations. J. Fluid Mech. 125, 99.
53. TOWNSEND, A. A. 1956 The Structure of Turbulent Shear flow. Cambridge University Press.
54. TURNER, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
55. WOLF, A., SWIFT, J. B., SWINNEY, H. L. & VASTANO, J. A. 1985 Determining Lyapunov exponents from a time series. Physica 16D, 285.