Analytical methods for the development of Reynolds-stress closures in turbulence

Annual Review of Fluid Mechanics

Volumn 23, Issue 1, 1991, Pages 107-157

  Speziale, Charles G ^a  

^a NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

K model; Second order closures; Turbulence modeling; Two equation models

Indexed keywords

EID: 0001108144     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fl.23.010191.000543     Document Type: Article

References (121)

1. Avva, R. K., Kline, S. J., Fetziger, J. H. 1988. Computation of the turbulent flow over a backward-facing step using the zonal modeling approach. Rep. No. TF-33, Stanford Univ., Stanford, Calif.
2. Baldwin, B. S., Lomax, H. 1978. Thin layer approximation and algebraic model for separated turbulent flows. AIAA Pap. No. 78-257
3. Bardina, J., Ferziger, J. H., Reynolds, W. C. 1983. Improved turbulence models based on large-eddy simulation of homogeneous, incompressible turbulent flows. Rep. No. TF-19, Stanford Univ., Stanford, Calif.
4. Bardina, J., Ferziger, J. H., Rogallo, R. S. 1985. Effect of rotation on isotropic turbulence: computation and modeling. J. Fluid Mech. 154: 321-36
5. Bernard, P. S., Berger, B. S. 1982. A method for computing three-dimensional turbulent flows. SIAM J. Appl. Math. 42: 453-70
6. Bertoglio, J. P. 1982. Homogeneous turbulent field within a rotating frame. AIAA J. 20: 1175-81
7. Boussinesq, J. 1877. Théorie de l'écoulement tourbillant. Mém. Présentés par divers Savants Acad. Sci. Inst. Fr. 23: 46-50
8. Bradshaw, P., Ferriss, D. H., Atwell, N. P. 1967. Calculation of boundary layer development using the turbulent energy equation. J. Fluid Mech. 28: 593-616
9. Bradshaw, P., Cebeci, T., Whitelaw, J. H. 1981. Engineering Calculation Methods for Turbulent Flow. New York: Academic
10. Cebeci, T., Smith, A. M. O. 1968. A finite-difference solution of the incompressible turbulent boundary-layer equations by an eddy viscosity concept. Proc. AROSR-IFP-Stanford Conf. Comput. of Turbul. Boundary Layers, ed. S. J. Kline, M. V. Morkovin, G. Sovran, D. S. Cockrell, 1: 346-55. Stanford, Calif: Stanford Univ. Press
11. Cebeci, T., Smith, A. M. O. 1974. Analysis of Turbulent Boundary Layers. New York: Academic
12. Choi, K. S., Lumley, J. L. 1984. Return to isotropy of homogeneous turbulence revisited. In Turbulence and Chaotic Phenomena in Fluids, ed. T. Tatsumi, pp. 267-72. New York: North-Holland
13. Clark, T. L., Farley, R. D. 1984. Severe downslope windstorm calculations in two and three spatial dimensions using anelastic interactive grid nesting: a possible mechanism for gustiness. J. Atmos. Sci. 41: 329-50
14. Comte-Bellot, G., Corrsin, S. 1971. Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated, "isotropic" turbulence. J. Fluid Mech. 48: 273-337
15. Craft, T., Fu, S., Launder, B. E., Tselepidakis, D. P. 1989. Developments in modeling the turbulent second-moment pressure correlations. Rep. No. TFD/89/1, Mech. Eng. Dep., Univ. Manchester Inst. Sci. Technol. Engl.
16. Crow, S. C. 1968. Viscoelastic properties of fine-grained incompressible turbulence. J. Fluid Mech. 33: 1-20
17. Daly, B. J., Harlow, F. H. 1970. Transport equations in turbulence. Phys. Fluids 13: 2634-49
18. Deardorff, J. W. 1973. The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence. ASME J. Fluids Eng. 95: 429-38
19. Demuren, A., Rodi, W. 1984. Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140: 189-222
20. Donaldson, C. duP. 1972. Calculation of turbulent shear flows for atmospheric and vortex motions. AIAA J. 10: 4-12
21. Donaldson, C. duP., Rosenbaum, H. 1968. Calculation of the turbulent shear flows through closure of the Reynolds equations by invariant modeling. Rep. No. 127, Aeronaut. Res. Assoc. Princeton, Princeton, N.J.
22. Donaldson, C. duP., Sandri, G. 1981. On the inclusion of information on eddy structure in second-order closure model of turbulent flow. AGARD Rep. No. CP-308
23. Fu, S., Launder, B. E., Tselepidakis, D. P. 1987. Accommodating the effects of high strain rates in modelling the pressure-strain correlation. Rep. No. TFD/87/5, Mech. Eng. Dep., Univ. Manchester Inst. Sci. Technol., Engl.
24. Gatski, T. B., Savill, A. M. 1989. An analysis of curvature effects for the control of wall-bounded shear flows. AIAA Pap. No. 89-1014
25. Gessner, F. B., Po, J. K. 1976. A Reynolds stress model for turbulent corner flow - Part II: comparisons between theory and experiment. ASME J. Fluids Eng. 98: 269-77
26. Gibson, M. M., Launder, B. E. 1978. Ground effects on pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86: 491-511
27. Gibson, M. M., Rodi, W. 1981. A Reynolds stress closure model of turbulence applied to the calculation of a highly curved mixing layer. J. Fluid Mech. 103: 161-82
28. Gibson, M. M., Younis, B. A. 1986. Calculation of swirling jets with a Reynolds stress closure. Phys. Fluids 29: 38-48
29. Hanjalić, K., Launder, B. E. 1972. A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52: 609-38
30. Hanjalić, K., Launder, B. E. 1976. Contribution towards a Reynolds stress closure for low Reynolds number turbulence. J. Fluid Mech. 74: 593-610
31. Hanjalić, K., Launder, B. E. 1980. Sensitizing the dissipation equation to irrotational strains. ASME J. Fluids Eng. 102: 34-40
32. Haworth, D. C., Pope, S. B. 1986. A generalized Langevin model for turbulent flows. Phys. Fluids 29: 387-405
33. Hinze, J. O. 1975. Turbulence. New York: McGraw-Hill. 2nd ed.
34. Hussain, A. K. M. F. 1983. Coherent structures: reality and myth. Phys. Fluids 26: 2816-50
35. Hussaini, M. Y., Speziale, C. G., Zang, T. A. 1990. Discussion of the potential and limitations of direct and large-eddy simulations. Proc. Whither Turbul. Workshop, Ithaca, N.Y. Lect. Notes Phys., ed. J. L. Lumley, pp. 354-68. Berlin: Springer-Verlag
36. Johnson, D. A., King, L. S. 1984. A new turbulence closure model for boundary layer flows with strong adverse pressure gradients and separation. AIAA Pap. No. 84-0175
37. Johnston, J. P., Halleen, R. M., Lezius, D. K. 1972. Effects of a spanwise rotation on the structure of two-dimensional fully-developed turbulent channel flow. J. Fluid Mech. 56: 533-57
38. Kim, J. 1983. The effect of rotation on turbulence structure. NASA TM-84379
39. Kim, J., Kline, S. J., Johnston, J. P. 1980. Investigation of a reattaching turbulent shear layer: flow over a backward-facing step. ASME J. Fluids Eng. 102: 302-8
40. Kline, S. J., Cantwell, B. J., Lilley, G. M., eds. 1981. Proceedings of the 1980-81 AFOSR-HTTM-Stanford Conference on Complex Turbulent Flows. Stanford, Calif: Stanford Univ. Press
41. Kolmogorov, A. N. 1942. The equations of turbulent motion in an incompressible fluid. Izv. Acad. Sci. USSR, Phys. 6: 56-58
42. Kraichnan, R. H. 1964. Direct interaction approximation for shear and thermally driven turbulence. Phys. Fluids 7: 1048-62
43. Lai, Y. G., So, R. M. C. 1990. On near wall turbulent flow modeling. J. Fluid Mech. In press
44. Launder, B. E. 1990. Phenomenological modeling: present and future. Proc. Whither Turbul. Workshop, Ithaca, N.Y. Lect Notes Phys., ed. J. L. Lumley, pp. 439-85. Berlin: Springer-Verlag
45. Launder, B. E., Reece, G. J., Rodi, W. 1975. Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68: 537-66
46. Launder, B. E., Shima, N. 1989. Second-moment closure for the near-wall sublayer: development and application. AIAA J. 27: 1319-23
47. Launder, B. E., Spalding, D. B. 1974. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 3: 269-89
48. Launder, B. E., Tselepidakis, D. P., Younis, B. A. 1987. A second-moment closure study of rotating channel flow. J. Fluid Mech. 183: 63-75
49. Launder, B. E., Ying, W. M. 1972. Secondary flows in ducts of square cross-section. J. Fluid Mech. 54: 289-95
50. Lesieur, M. 1987. Turbulence in Fluids. Boston: Martinus Nijhoff
51. Lumley, J. L. 1970. Toward a turbulent constitutive equation. J. Fluid Mech. 41: 413-34
52. Lumley, J. L. 1978. Computational modeling of turbulent flows. Adv. Appl. Mech. 18: 123-76
53. Lumley, J. L. 1983. Turbulence modeling. ASME J. Appl. Mech. 50: 1097-1103
54. Lumley, J. L., Khajeh-Nouri, B. 1974. Computational modeling of turbulent transport. Adv. Geophys. 18A: 169-92
55. Mansour, N. N., Kirn, J., Moin, P. 1988. Reynolds stress and dissipation rate budgets in turbulent channel flow. J. Fluid Mech. 194: 15-44
56. Mansour, N. N., Shih, T. H. 1989. Advancements in turbulence modeling. In Forum on Turbulent Flows - 1989, ed. W. W. Bower, M. J. Morris, FED-76: 129-41. New York: ASME
57. Mellor, G. L., Herring, H. J. 1973. A survey of mean turbulent field closure models. AIAA J. 11: 590-99
58. Mellor, G. L., Yamada, T. 1974. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31: 1791-1806
59. Moin, P., Kim, J. 1982. Numerical investigation of turbulent channel flow. J. Fluid Mech. 118: 341-77
60. Nisizima, S., Yoshizawa, A. 1987. Turbulent channel and Couette flows using an anisotropic K-ε model. AIAA J. 25: 414-20
61. Norris, L. H., Reynolds, W. C. 1975. Turbulent channel flow with a moving wavy boundary. Rep. No. FM-10, Stanford Univ., Stanford, Calif.
62. Orszag, S. A. 1970. Analytical theories of turbulence. J. Fluid Mech. 41: 363-86
63. Patel, V. C., Rodi, W., Scheuerer, G. 1985. Turbulence models for near-wall and low Reynolds number flows: a review. AIAA J. 23: 1308-19
64. Piomelli, U., Ferziger, J. H., Moin, P. 1987. Models for large eddy simulations of turbulent channel flows including transpiration. Rep. No. TF-32, Stanford Univ., Stanford, Calif.
65. Pope, S. B. 1975. A more general effective viscosity hypothesis. J. Fluid Mech. 72: 331-40
66. Pope, S. B. 1978. An explanation of the turbulent round jet/plane jet anomaly. AIAA J. 16: 279-81
67. Pope, S. B. 1985. Pdf methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11: 119-92
68. Prandtl, L. 1925. Über die ausgebildete Turbulenz. ZAMM 5: 136-39
69. Prandtl, L. 1945. Über ein neues Formel-system für die ausgebildete Turbulenz. Nachr. Akad. Wiss. Göltingen, Math.-Phys. Kl. 1945: 6-19
70. Reynolds, O. 1895. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. R. Soc. London Ser. A 186: 123-64
71. Reynolds, W. C. 1976. Computation of turbulent flows. Annu. Rev. Fluid Mech. 8: 183-208
72. Reynolds, W. C. 1987. Fundamentals of turbulence for turbulence modeling and simulation. In Lecture Notes for Von Kármán Institute. AGARD Lect. Ser. No. 86, pp. 1-66. New York: NATO
73. Reynolds, W. C. 1989. Effects of rotation on homogeneous turbulence. Proc. Australas. Fluid Mech. Conf., 10th, pp. 1-6. Melbourne: Univ. Melbourne
74. Reynolds, W. C. 1990. The potential and limitations of direct and large-eddy simulations. Proc. Whither Turbul. Workshop, Ithaca, N.Y. Lect. Notes Phys., ed. J. L. Lumley, pp. 313-42. Berlin: Springer-Verlag
75. Rivlin, R. S. 1957. The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids. Q. Appl. Math. 15:212-15
76. Rodi, W. 1976. A new algebraic relation for calculating the Reynolds stresses. ZAMM 56: T219-21
77. Rodi, W. 1980. Turbulence Models and Their Application in Hydraulics. Delft, Neth: Int. Assoc. Hydraul. Res.
78. Rogallo, R. S., Moin, P. 1984. Numerical simulation of turbulent flows. Annu. Rev. Fluid Mech. 16:99-137
79. Rotta, J. C. 1951. Statistische Theorie nichthomogener Turbulenz. Z. Phys. 129: 547-72
80. Rotta, J. C. 1972. Recent attempts to develop a generally applicable calculation method for turbulent shear flow layers. AGARD CP-93
81. Rubinstein, R., Barton, J. M. 1990. Nonlinear Reynolds stress models and the renormalization group. Phys. Fluids A 2: 1472-76
82. Saffman, P. G. 1977. Results of a two-equation model for turbulent flows and development of a relaxation stress model for application to straining and rotating flows. Proc. Proj. SQUID Workshop Turbul. in Intern. Flows, ed. S. Murthy, pp. 191-231. New York: Hemisphere
83. Sarkar, S., Erlebacher, G., Hussaini, M. Y., Kreiss, H. O. 1989. The analysis and modeling of dilatational terms in compressible turbulence. Rep. No. 89-79, ICASE, NASA Langley Res. Cent., Hampton, Va.
84. Sarkar, S., Speziale, C. G. 1990. A simple nonlinear model for the return to isotropy in turbulence. Phys. Fluids A 2: 84-93
85. Schlichting, H. 1968. Boundary Layer Theory. New York: McGraw-Hill
86. Schumann, U. 1977. Readability of Reynolds stress turbulence models. Phys. Fluids 20: 721-25
87. Shih, T.-H., Lumley, J. L. 1985. Modeling of pressure correlation terms in Reynolds stress and scalar flux equations. Rep. No. FDA-85-3, Cornell Univ., Ithaca, N.Y.
88. Shih, T.-H., Mansour, N. N. 1990. Second-order modeling of low Reynolds number turbulence near walls. Submitted for publication
89. Smagorinsky, J. 1963. General circulation experiments with the primitive equations. Mon. Weather Rev. 91: 99-165
90. Smith, G. F. 1971. On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int. J. Enq. Sci. 9: 899-916
91. Smolarkiewicz, P. K., Clark, T. L. 1985. Numerical simulation of a three-dimensional field of cumulus clouds. Part I. Model description, comparison with observations and sensitivity studies. J. Atmos. Sci. 42: 502-22
92. Speziale, C. G. 1981. Some interesting properties of two-dimensional turbulence. Phys. Fluids 24: 1425-27
93. Speziale, C. G. 1983. Closure models for rotating two-dimensional turbulence. Geophys. Astrophys. Fluid Dyn. 23: 69-84
94. Speziale, C. G. 1985. Modeling the pressure gradient-velocity correlation of turbulence. Phys. Fluids 28: 69-71
95. Speziale, C. G. 1987a. Second-order closure models for rotating turbulent flows. Q. Appl. Math. 45: 721-33
96. Speziale, C. G. 1987b. On nonlinear K-l and K-ε models of turbulence. J. Fluid Mech. 178:459-75
97. Speziale, C. G. 1989. Turbulence modeling in non-inertial frames of reference. Theor. Comput. Fluid Dyn. 1: 3-19
98. Speziale, C. G. 1990. Discussion of turbulence modeling: present and future. Proc. Whither Turbul. Workshop, Ithaca, N.Y. Lect. Notes Phys., ed. J. L. Lumley, pp. 490-512. Berlin: Springer-Verlag
99. Speziale, C. G., Gatski, T. B., Mac Giolla Mhuiris, N. 1989. A critical comparison of turbulence models for homogeneous shear flows in a rotating frame. Proc. Symp. Turbul. Shear Flows, 7th, 2: 27.3.1-27.3.6. Stanford, Calif: Stanford University Press
100. Speziale, C. G., Mac Giolla Mhuiris, N. 1989a. On the prediction of equilibrium states in homogeneous turbulence. J. Fluid Mech. 209: 591-615
101. Speziale, C. G., Mac Giolla Mhuiris, N. 1989b. Scaling laws for homogeneous turbulent shear flows in a rotating frame. Phys. Fluids A 1:294-301
102. Speziale, C. G., Mansour, N. N., Rogallo, R. S. 1987. The decay of isotropic turbulence in a rapidly rotating frame. Proc. Summer Program Cent. for Turbul. Res., ed. P. Moin, W. C. Reynolds, J. Kim, pp. 205-11. Stanford, Calif: Stanford Univ. Press
103. Speziale, C. G., Ngo, T. 1988. Numerical solution of turbulent flow past a backward-facing step using a nonlinear K-ε model. Int. J. Eng. Sci. 26: 1099-1112
104. Speziale, C. G., Sarkar, S., Gatski, T. B. 1990. Modeling the pressure-strain correlation of turbulence - an invariant dynamical systems approach. Rep. No. 90-5, ICASE, NASA Langley Res. Cent., Hampton, Va.
105. Swinney, H. L., Gollub, J. P., eds. 1981. Hydrodynamic Instabilities and the Transition to Turbulence. New York: Springer-Verlag
106. Tavoularis, S., Corrsin, S. 1981. Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part I. J. Fluid Mech. 104: 311 47
107. Taylor, G. I. 1915. Eddy motion in the atmosphere. Philos. Trans. R. Soc. London Ser. A 1215: 1-26
108. Tennekes, H., Lumley, J. L. 1972. A First Course in Turbulence. Cambridge, Mass: MIT Press. 300 pp.
109. von Kármán, T. 1930. Mechanische ähnlichkeit und Turbulenz. Proc. Int. Congr. Appl. Mech., 3rd, Stockholm, Pt. 1, pp. 85-105
110. von Kármán, T. 1948. Progress in the statistical theory of turbulence. Proc. Natl. Acad. Sci. USA 34: 530-39
111. Weinstock, J. 1981. Theory of the pressure-strain rate correlation for Reynolds stress turbulence closures. Part 1. J. Fluid Mech. 105: 369-96
112. Wigeland, R. A., Nagib, H. M. 1978. Grid-generated turbulence with and without rotation about the streamwise direction. Rep. No. R78-1, Ill. Inst. Technol., Chicago
113. Wilcox, D. C. 1988. Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26: 1299-1310
114. Wilcox, D. C., Traci, R. M. 1976. A complete model of turbulence. AIAA Pap. No. 76-351
115. Wolfshtein, M. 1970. On the length scale of turbulence equation. Isr. J. Technol. 8: 87-99
116. Yakhot, V., Orszag, S. A. 1986. Renormalization group analysis of turbulence. I. Basic theory. J. Sci. Comput. 1: 3-51
117. Yoshizawa, A. 1984. Statistical analysis of the deviation of the Reynolds stress from its eddy viscosity representation. Phys. Fluids 27: 1377-87
118. Yoshizawa, A. 1987. Statistical modeling of a transport equation for the kinetic energy dissipation rate. Phys. Fluids 30: 628-31
119. Zeman, O. 1990. Dilatation dissipation: the concept and application in modeling compressible mixing layers. Phys. Fluids A 2: 178-88
120. Zeman, O., Lumley, J. L. 1976. Modeling buoyancy-driven mixed layers. J. Atmos. Sci. 33: 1974-88
121. Zeman, O., Lumley, J. L. 1979. Buoyancy effects in entraining turbulent boundary layers: a second-order closure study. In Turbulent Shear Flows I, ed. F. Durst, B. E. Launder, F. W. Schmidt, J. H. Whitelaw, pp. 295-302. Berlin: Springer-Verlag