One-dimensional turbulence: Model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows

Journal of Fluid Mechanics

Volumn 392, Issue , 1999, Pages 277-334

  Kerstein, Alan R ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BUOYANCY; MATHEMATICAL MODELS; MONTE CARLO METHODS; RANDOM PROCESSES; SHEAR FLOW;

BUOYANT STRATIFIED FLOWS; TURBULENT ADVECTION;

TURBULENCE;

EID: 0032655138     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099005376     Document Type: Article

References (79)

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. ANTONIA, R. A., TEITEL, M., KIM, J. & BROWNE, L. W. B. 1992 Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579-605.
3. AURELL, E., DORMY, E. & FRICK, P. 1997 Binary-tree models of high-Reynolds-number turbulence. Phys. Rev. E 56, 1692-1698.
4. BENZI, R., BIFERALE, L., TRIPICCIONE, R. & TROVATORE, E. 1997 (1+1)-dimensional turbulence. Phys. Fluids 9, 2355-2363.
5. BORUE, V. & ORSZAG, S. A. 1995 Self-similar decay of three-dimensional homogeneous turbulence with hyperviscosity. Phys. Rev. E 51, R856-R859.
6. BRUYN KOPS, S. M. DE & RILEY, J. J. 1998 Scalar transport characteristics of the linear-eddy model. Combust. Flame 112, 253-260.
7. CANUTO, V. M., DUBOVIKOV, M. S. & DIENSTFREY, A. 1997 A dynamical model for turbulence. IV. Buoyancy-driven flows. Phys. Fluids 9, 2118-2131.
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. CHASNOV, J. R. 1994 Similarity states of passive scalar transport in isotropic turbulence. Phys. Fluids 6, 1036-1051.
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. CHEKHLOV, A. & YAKHOT, V. 1995 Kolmogorov turbulence in a random-force-driven Burgers equation. Phys. Rev. E 51, R2739-R2742.
12. CHRISTODOULOU, G. C. 1986 Interfacial mixing in stratified flows. J. Hydraul. Res. 24, 77-92.
13. 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.
14. COLEMAN, G. N. & FERZIGER, J. H. 1996 Direct numerical simulation of a vigorously heated low Reynolds number convective boundary layer. Dyn. Atmos. Oceans 24, 85-94.
15. CONSTANTIN, P., LAX, P. D. & MAJDA, A. 1985 A simple one-dimensional model for the three-dimensional vorticity equation. Commun. Pure Appl. Maths. 38, 715-724.
16. DE GREGORIO, S. 1990 On a one-dimensional model for the three-dimensional vorticity equation. J. Statist. Phys. 59, 1251-1263.
17. DEARDORFF, J. W. 1970 Convective velocity and temperature scales for the unstable planetary boundary layer and for Rayleigh convection. J. Atmos. Sci. 27, 1211-1213.
18. 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.
19. DEARDORFF, J. W., WILLIS, G. E. & LILLY, D. K. 1969 Laboratory investigation of non-steady penetrative convection. J. Fluid Mech. 35, 7-31.
20. DEARDORFF, J. W., WILLIS, G. E. & STOCKTON, B. H. 1980 Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech. 100, 41-64.
21. EGGELS, J. G. M., UNGER, F., WEISS, M. H., WESTERWEEL, J., ADRIAN, R. J., FRIEDRICH, R. & NIEUWSTADT, F. T. M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175-209.
22. ELLISON, T. H. & TURNER, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423-448.
23. FERNANDO, H. J. S. 1991 Turbulent mixing in stratified fluids. Ann. Rev. Fluid Mech. 23, 455-493.
24. FITZJARRALD, D. E. 1976 An experimental study of turbulent convection in air. J. Fluid Mech. 73, 693-719.
25. GLOBE, S. & DROPKIN, D. 1959 Natural-convection heat transfer in liquids confined by two horizontal plates and heated from below. Trans. ASME: Heat Transfer 81, 24-28.
26. GOLDSTEIN, R. J., CHAING, H. D. & SEE, D. L. 1990 High-Rayleigh-number convection in a horizontal enclosure. J. Fluid Mech. 213, 111-126.
27. GOLDSTEIN, R. J. & TOKUDA, S. 1980 Heat transfer by thermal convection at high Rayleigh numbers. Intl. J. Heat Mass Transfer 23, 738-740.
28. GROSSMANN, S. & L'vov, V. S. 1993 Crossover of spectral scaling in thermal turbulence. Phys. Rev. E 47, 4161-4168.
29. HANJALIĆ, K., KENJEREŠ, S. & DURST, F. 1996 Natural convection in partitioned two-dimensional enclosures at higher Rayleigh numbers. Intl. J. Heat Mass Transfer 39, 1407-1427.
30. HANJALIĆ, K. & VASIĆ, S. 1993 Computation of turbulent natural convection in rectangular enclosures with an algebraic flux model. Intl. J. Heat Mass Transfer 36, 3603-3624.
31. HINZE, J. O. 1975 Turbulence. McGraw-Hill.
32. HOLZER, M. & PUMIR, A. 1993 Simple models of non-Gaussian statistics for a turbulently advected passive scalar. Phys. Rev. E 47, 202-219.
33. KAIMAL, J. C. & FINNIGAN, J. J. 1994 Atmospheric Boundary Layer Flows. Oxford University Press.
34. KATO, H. & PHILLIPS, O. M. 1969 On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 643-655.
35. KAYS, W. M. & CRAWFORD, M. E. 1980 Convective Heat and Mass Transfer. McGraw-Hill.
36. KERR, R. M. 1996 Rayleigh number scaling in numerical convection. J. Fluid Mech. 310, 139-179.
37. KERSTEIN, A. R. 1991 Linear-eddy modelling of turbulent transport. Part 6. Microstructure of diffusive scalar mixing fields. J. Fluid Mech. 231, 361-394.
38. KERSTEIN, A. R. 1992 Linear-eddy modelling of turbulent transport. Part 7. Finite-rate chemistry and multi-stream mixing. J. Fluid Mech. 240, 289-313.
39. KERSTEIN, A. R., CREMER, M. A. & MCMURTRY, P. A. 1995 Scaling properties of differential molecular diffusion effects in turbulence. Phys. Fluids 7, 1999-2007.
40. KERSTEIN, A. R. & MCMURTRY, P. A. 1994a Mean-field theories of random advection. Phys. Rev. E 49, 474-482.
41. KERSTEIN, A. R. & MCMURTRY, P. A. 1994a Low-wave-number statistics of randomly advected passive scalars. Phys. Rev. E 50, 2057-2063.
42. KRAICHNAN, R. H. 1962 Turbulent thermal convection at arbitrary Prandtl number. J. Fluid Mech. 5, 1374-1389.
43. LAUNDER, B. E., REECE, G. J. & RODI, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537-566.
44. LESIEUR, M. 1990 Turbulence in Fluids. Kluwer.
45. LIGHTHILL, M. J. 1970 Fourier Analysis and Generalized Functions. Cambridge University Press.
46. LUMLEY, J. L., ZEMAN, O. & SIESS, J. 1978 The influence of buoyancy on turbulent transport. J. Fluid Mech. 84, 581-597.
47. L'VOV, V. S. 1991 Spectra of velocity and temperature fluctuations with constant entropy flux of fully developed free-convective turbulence. Phys. Rev. Lett. 67, 687-690.
48. MANSOUR, N. N., KIM, J. & MOIN, P. 1988 Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15-44.
49. MELLOR, G. L. & YAMADA, T. 1982 Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys. 20, 851-875.
50. MENON, S. & CALHOON, W. H., JR. 1996 Subgrid mixing and molecular transport modeling in a reacting shear layer. 26th Symp. (Intl.) on Combustion, pp. 59-66. The Combustion Institute.
51. MONIN, A. S. & YAGLOM, A. M. 1971 Statistical Fluid Mechanics, vol. 1. MIT Press.
52. MONIN, A. S. & YAGLOM, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT Press.
53. PROCACCIA, I. & ZEITAK, R. 1989 Scaling exponents in nonisotropic convective turbulence. Phys. Rev. Lett. 62, 2128-2131.
54. REY, C., SCHON, J. P. & MATHIEU, J. 1979 Buoyancy effects in a wind tunnel simulation of the atmospheric boundary layer. Phys. Fluids 22, 1020-1028.
55. SCHLICHTING, H. 1979 Boundary-Layer Theory. McGraw-Hill.
56. SIGGIA, E. D. 1994 High Rayleigh number convection. Ann. Rev. Fluid Mech. 26, 137-168.
57. SIROVICH, L., SMITH, L. & YAKHOT, V. 1994 Energy spectrum of homogeneous turbulence in far dissipation range. Phys. Rev. Lett. 72, 344-347.
58. SNYDER, D. L. 1975 Random Point Processes. Wiley.
59. SO, R. M. C., LAI, Y. G., ZHANG, H. S. & HWANG, B. C. 1991 Second-order near-wall turbulence closures: a review. AIAA J. 29, 1819-1835.
60. SPARROW, E. M., HUSAR, R. B. & GOLDSTEIN, R. J. 1970 Observations and other characteristics of thermals. J. Fluid Mech. 41, 793-800.
61. SREENIVASAN, K. R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778-2784.
62. SREENIVASAN, K. R. 1996 The passive scalar spectrum and the Obukhov-Corrsin constant. Phys. Fluids 8, 189-196.
63. STULL, R. B. 1984 Transilient turbulence theory. Part 1 : The concept of eddy-mixing across finite distance. J. Atmos. Sci. 41, 3351-3367.
64. STULL, R. B. 1988 An Introduction to Boundary Layer Meteorology. Kluwer.
65. STULL, R. B. & DRIEDONKS, A. G. M. 1987 Applications of the transilient turbulence parameterization to atmospheric boundary-layer simulations. Boundary-Layer Met. 40, 209-239.
66. TANAKA, H. & MIYATA, H. 1980 Turbulent natural convection in a horizontal water layer heated from below. Intl. J. Heat Mass Transfer 23, 1273-1281.
67. TAYLOR, G. I. 1932 The transport of vorticity and heat through fluids in turbulent motion. Proc. R. Soc. Lond. A 135, 685-706.
68. TENNEKES, H. 1976 Fourier-transform ambiguity in turbulence dynamics. J. Atmos. Sci. 33, 1660-1663.
69. TONG, P. & SHEN, Y. 1992 Relative velocity fluctuations in turbulent Rayleigh-Bénard Convection. Phys. Rev. Lett. 69, 2066-2069.
70. TOWNSEND, A. A. 1964 Natural convection in water over an ice surface. Q. J. R. Met. Soc. 90, 248-259.
71. TSARENKO, V. M. 1989 Model calculations of the Monin-Obukhov similarity functions. Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 23, 1041-1048 (87-93 in English transl. of the journal).
72. TURNER, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
73. TURNER, J. S. 1991 Convection and mixing in the oceans and the Earth. Phys. Fluids A 3, 1218-1232.
74. VAINSHTEIN, S. I., SREENIVASAN, K. R., PIERREHUMBERT, R. T., KASHYAP, V. & JUNEJA, A. 1994 Scaling exponents for turbulence and other random processes and their relationships with multifractal structure. Phys. Rev. E 50, 1823-1835.
75. WEI, T. & WILLMARTH, W. W. 1989 Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57-95.
76. WU, X.-Z., KADANOFF, L., LIBCHABER, A. & SANO, M. 1990 Frequency power spectrum of fluctuations in free convection. Phys. Rev. Lett. 64, 2140-2143.
77. YAGLOM, A. M. 1994 Fluctuation spectra and variances in convective turbulent boundary layers: A reevaluation of old models. Phys. Fluids 6, 962-972.
78. YOON, K. & WARHAFT, Z. 1990 The evolution of grid-generated turbulence under conditions of stable thermal stratification. J. Fluid Mech. 215, 601-638.
79. ZHANG, Q. & STULL, R. 1992 Alternative nonlocal description of boundary-layer evolution. J. Atmos. Sci. 49, 2267-2281.