1932

Abstract

This review highlights major developments and milestones during the early days of numerical simulation of turbulent flows and its use to increase our understanding of turbulence phenomena. The period covered starts with the first simulations of decaying homogeneous isotropic turbulence in 1971–1972 and ends about 25 years later. Some earlier history of the progress in weather prediction is included if relevant. Only direct simulation, in which all scales of turbulence are accounted for explicitly, and large-eddy simulation, in which the effect of the smaller scales is modeled, are discussed. The method by which all scales are modeled, Reynolds-averaged Navier–Stokes, is not covered.

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2024-01-19
2024-12-14
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Literature Cited

  1. Adrian RJ. 2007. Hairpin vortex organization in wall turbulence. Phys. Fluids 19:40413014
    [Google Scholar]
  2. Antonia RA, Zhu Y, Kim J. 1993. On the measurement of lateral velocity derivatives in turbulent flows. Exp. Fluids 15:6569
    [Google Scholar]
  3. Arakawa A. 1966. Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. J. Comput. Phys. 1:11943
    [Google Scholar]
  4. Batchelor GK. 1967. The Theory of Homogeneous Turbulence Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  5. Benzi R 2011. Lewis Fry Richardson. A Voyage Through Turbulence PA Davidson, Y Kaneda, K Moffatt, KR Sreenivasan 187208. Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  6. Blaisdell GA, Mansour NN, Reynolds WC. 1991. Numerical simulation of compressible homogeneous turbulence Rep. TF-50 Dep. Mech. Eng., Stanford Univ. Stanford, CA:
    [Google Scholar]
  7. Blaisdell GA, Mansour NN, Reynolds WC. 1993. Compressibility effects on the growth and the structure of homogeneous turbulent shear flow. J. Fluid Mech. 256:44385
    [Google Scholar]
  8. Buell JC. 1990. Direct simulations of compressible wall-bounded turbulence. Annual Research Briefs 199034756. Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  9. Case KM, Dyson FJ, Frieman EA, Grosch CE, Perkins FW. 1973. Numerical simulation of turbulence Stanford Res. Inst. Rep. AD-774-161 Stanford, CA:
    [Google Scholar]
  10. Champagne FH, Harris VG, Corrsin S. 1970. Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41:81139
    [Google Scholar]
  11. Chapman D. 1979. Computational aerodynamics development and outlook. AIAA J. 17:121293313
    [Google Scholar]
  12. Charney JG, Fjörtoft R, von Neumann J. 1950. Numerical integration of the barotropic vorticity equation. Tellus 2:23754
    [Google Scholar]
  13. Choi H, Moin P, Kim J. 1993a. Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255:50339
    [Google Scholar]
  14. Choi H, Moin P, Kim J. 1994. Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262:75110
    [Google Scholar]
  15. Choi H, Temam R, Moin P, Kim J. 1993b. Feedback control for unsteady flow and its application to the stochastic Burgers equation. J. Fluid Mech. 253:50943
    [Google Scholar]
  16. Clark RA, Ferziger JH, Reynolds WC. 1979. Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91:116
    [Google Scholar]
  17. Coleman GN, Kim J, Moser RD. 1995. A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305:15983
    [Google Scholar]
  18. 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. 48:2273337
    [Google Scholar]
  19. Cooley JW, Tukey JW. 1965. An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19:297301
    [Google Scholar]
  20. Corrsin S. 1961. Turbulent flow. Am. Sci. 49:30025
    [Google Scholar]
  21. Dang K, Morchoisne YF. 1987. Numerical simulation of homogeneous compressible turbulence Paper presented at the 2nd International Symposium on Transport Phenomena in Turbulent Flows Tokyo: Oct. 25–29
    [Google Scholar]
  22. Deardorff JW. 1970. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41:45380
    [Google Scholar]
  23. Deardorff JW. 1971. On the magnitude of the subgrid scale eddy coefficient. J. Comput. Phys. 7:112033
    [Google Scholar]
  24. Deardorff JW. 1972. Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci. 29:91115
    [Google Scholar]
  25. Deardorff JW, Peskin RL. 1970. Lagrangian statistics from numerically integrated turbulent shear flow. Phys. Fluids 13:358495
    [Google Scholar]
  26. Ducros F, Compte P, Lesieur M 1993. Ropes and lambda vortices in direct and large-eddy simulations of a high-Mach number boundary layer over a flat plate. Turbulent Shear Flows 9: Selected Papers from the Ninth International Symposium on Turbulent Shear Flows F Durst, N Kasagi, BE Launder, FW Schmidt, K Suzuki, JH Whitelaw 283300. Berlin: Springer-Verlag
    [Google Scholar]
  27. Dumas G, Leonard A. 1994. A divergence-free spectral expansions method for three-dimensional flows in spherical-gap geometries. J. Comput. Phys. 111::20519
    [Google Scholar]
  28. Erlebacher G, Hussaini MY, Kreiss HO, Sarkar S. 1990. The analysis and simulation of compressible turbulence. Theor. Comput. Fluid Dyn. 2:7395
    [Google Scholar]
  29. Erlebacher G, Zang TA, Hussaini MY, Speziale CG 1987. Numerical simulation of homogeneous, isotropic, compressible turbulence. Numerical Methods in Laminar and Turbulent Flow C Taylor, WG Habashi, MM Hafez 193243. Swansea, UK: Pineridge Press
    [Google Scholar]
  30. Fasel H, Thumm A, Bestek H. 1993. Direct numerical simulation of transition in supersonic boundary layers: oblique breakdown Paper presented at the Fluids Engineering Conference Washington, DC: June 20–24
    [Google Scholar]
  31. Feiereisen WJ, Reynolds WC, Ferziger JH. 1981. Numerical simulation of a compressible homogeneous turbulent shear flow Rep. TF-13 Dep. Mech. Eng., Stanford Univ. Stanford, CA:
    [Google Scholar]
  32. Ferziger JH. 1977. Large eddy numerical simulation of turbulent flows. AIAA J 15:126167
    [Google Scholar]
  33. George WD, Hellums JD. 1972. Hydrodynamic stability in plane Poiseuille flow with finite amplitude disturbances. J. Fluid Mech. 51:687704
    [Google Scholar]
  34. George WD, Hellums JD, Martin B. 1974. Finite-amplitude neutral disturbances in plane Poiseuille flow. J. Fluid Mech. 63:76571
    [Google Scholar]
  35. Germano M, Piomelli U, Moin P, Cabot WH. 1991. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3:176065
    [Google Scholar]
  36. Girimaji SS, Pope SB. 1990. Material-element deformation in isotropic turbulence. J. Fluid Mech. 220::42758
    [Google Scholar]
  37. Goc KA, Lehmkuhl O, Park GI, Bose ST, Moin P. 2021. Large eddy simulation of aircraft at affordable cost: a milestone in computational fluid dynamics. Flow 1:E14
    [Google Scholar]
  38. Grotzbach G. 1981. Numerical simulation of turbulent temperature fluctuations in liquid metals. Int. J. Heat Mass Transf. 24:47590
    [Google Scholar]
  39. Grotzbach G. 1988. Turbulent heat transfer in an internally heated fluid layer Paper presented at the Third International Symposium on Refined Flow Modelling and Turbulence Measurements Tokyo: July 26–28
    [Google Scholar]
  40. Grotzbach G, Schumann U 1979. Direct numerical simulation of turbulent velocity, pressure- and temperature-fields in channel flows. Turbulent Shear Flows I: Selected Papers from the First International Symposium on Turbulent Shear Flows F Durst, BE Launder, FW Schmidt, JH Whitelaw 37085. Berlin: Springer
    [Google Scholar]
  41. Guezennec Y, Piomelli U, Kim J. 1989. On the shape and dynamics of wall structures in turbulent channel flow. Phys. Fluids A 1:76466
    [Google Scholar]
  42. Guo Y, Adams NA. 1994. Numerical investigation of turbulent supersonic boundary layers with high wall temperature. Proceedings of the 1994 Summer Program24567. Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  43. Guo Y, Kleiser L, Adams NA. 1994. A comparison study of an improved temporal DNS and spatial DNS of compressible boundary layer transition Paper presented at the AIAA Fluid Dynamics Conference Colorado Springs, CO: AIAA Pap. 1994-2371
    [Google Scholar]
  44. Hamilton JM, Kim J, Waleffe F. 1995. Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287:31748
    [Google Scholar]
  45. Harlow FH, Welch JE. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8:12218289
    [Google Scholar]
  46. Herring JR. 2000. A brief history of the geophysical turbulence program at NCAR. IUTAM Symposium on Developments in Geophysical Turbulence RM Kerr, Y Kimura 14. Berlin: Springer Science+Business Media
    [Google Scholar]
  47. Hill EL. 1954. The theory of vector spherical harmonics. Am. J. Physics 22:21114
    [Google Scholar]
  48. Hunt JCR. 1988. Studying turbulence using direct numerical simulation: 1987 center for turbulence research NASA Ames/Stanford summer programme. J. Fluid Mech. 190:37592
    [Google Scholar]
  49. Hunt JCR. 1998. Lewis Fry Richardson and his contributions to mathematics, meteorology, and models of conflict. Annu. Rev. Fluid Mech. 30:xiiixxxvi
    [Google Scholar]
  50. Hunt JCR, Wray AA, Moin P. 1988. Eddies, streams, and convergence zones in turbulent flows. Proceedings of the 1988 Summer Program193208. Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  51. Jimenez J, Moin P. 1991. The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225:21340
    [Google Scholar]
  52. Johansson AV, Alfredsson PH, Kim J. 1991. Evolution and dynamics of shear-layer structure in near-wall turbulence. J. Fluid Mech. 224:57999
    [Google Scholar]
  53. Kaneda Y, Ishihara T, Yokokawa M, Itakura KI, Uno A. 2003. Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15:L2124
    [Google Scholar]
  54. Kasagi N, Iida O. 1999. Progress in direct numerical simulation of turbulent heat transfer Paper presented at the 5th ASME/JSME Joint Thermal Engineering Conference San Diego, CA: March 15–19
    [Google Scholar]
  55. Kasagi N, Kuroda A, Hirata M. 1989. Numerical investigation of near-wall turbulent heat transfer taking into account the unsteady heat conduction in the solid wall. ASME J. Heat Transf. 24:154144
    [Google Scholar]
  56. Kasagi N, Tomita Y, Kuroda A. 1992. Direct numerical simulation of passive scalar field in a turbulent channel flow. J. Heat Transf. 114:598606
    [Google Scholar]
  57. Kerr RM. 1985. Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 1531:3158
    [Google Scholar]
  58. Kim J. 2003. Control of turbulent boundary layers. Phys. Fluids 15:51093105
    [Google Scholar]
  59. Kim J, Bewley TR. 2007. A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39:383417
    [Google Scholar]
  60. Kim J, Moin P 1989. Transport of passive scalars in a turbulent channel flow. Turbulent Shear Flows 6: Selected Papers from the Sixth International Symposium on Turbulent Shear Flows J-C André, J Cousteix, F Durst, BE Launder, FW Schmidt, JH Whitelaw 8596. Berlin: Springer-Verlag
    [Google Scholar]
  61. Kim J, Moin P, Moser RD. 1987. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177:13366
    [Google Scholar]
  62. Kline SJ. 1987. Coherent structures and modeling: some background comments. Proceedings of the 1987 Summer Program32528. Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  63. Kline SJ, Reynolds WC, Schraub FA, Runstadler PW. 1967. The structure of turbulent boundary layers. J. Fluid Mech. 30:474173
    [Google Scholar]
  64. Kreplin HP, Eckelmann H. 1979. Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow. Phys. Fluids 22:7123339
    [Google Scholar]
  65. Kwak D, Reynolds WC, Ferziger JH. 1975. Three-dimensional time dependent computation of turbulent flow Rep. TF-5 Dep. Mech. Eng., Stanford Univ. Stanford, CA:
    [Google Scholar]
  66. Le H, Moin P. 1994. Direct numerical simulation of turbulent flow over a backward-facing step Rep. TF-58 Dep. Mech. Eng., Stanford Univ. Stanford, CA:
    [Google Scholar]
  67. Le H, Moin P, Kim J. 1997. Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330:34974
    [Google Scholar]
  68. Lee S, Lele SK, Moin P. 1991. Eddy-shocklets in decaying compressible turbulence. Phys. Fluids A 3:65764
    [Google Scholar]
  69. Leith CE 1965. Numerical simulation of the Earth's atmosphere. Methods in Computational Physics. Advances in Research and Applications. Vol. 4, Applications in Hydrodynamics B Adler, S Fernbach, M Rotenberg 128. Academic New York:
    [Google Scholar]
  70. Lele SK. 1992. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103:1642
    [Google Scholar]
  71. Lele SK. 1994. Compressibility effects on turbulence. Annu. Rev. Fluid Mech. 26:21154
    [Google Scholar]
  72. Lele SK. 1997. Computational aeroacoustics: a review Paper presented at the 35th Aerospace Sciences Meeting and Exhibit Reno, NV: AIAA Pap. 1997-0018
    [Google Scholar]
  73. Leonard A. 1973. On the energy cascade in large-eddy simulations of turbulent fluid flows Rep. TF-1 Stanford Univ. Stanford, CA:
    [Google Scholar]
  74. Leonard A. 1974. Energy cascade in large-eddy simulations of turbulent fluid flows. Advances in Geophysics, Vol. 18A. International Symposium on Turbulent Diffusion and Environmental Pollution, ed. F Frenkiel, R Munn 23748. New York: Academic
    [Google Scholar]
  75. Leonard A. 2015. Large-eddy simulations of the Navier-Stokes equations: deconvolution, particle methods, and super-resolution. IUTAM Symposium on Advances in Computation, Modeling and Control of Transitional and Turbulent Flows T Sengupta 116. Singapore: World Sci.
    [Google Scholar]
  76. Leonard A, Wray A 1982. A new numerical method for the simulation of three-dimensional flow in a pipe. Eighth International Conference on Numerical Methods in Fluid Dynamics H Araki, J Ehlers, K Hepp, R Kippenhahn, HA Weidenmüller, J Zittartz 33542. Berlin: Springer
    [Google Scholar]
  77. Lilly DK. 1965. On the computational stability of numerical solutions of time-dependent non-linear geophysical fluid dynamics problems. Mon. Weather Rev. 93:11125
    [Google Scholar]
  78. Lilly DK. 1967. The representation of small-scale turbulence in numerical simulation experiments. Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences195210. White Plains, NY: IBM
    [Google Scholar]
  79. Lilly DK. 2000. The meteorological development of large eddy simulation. IUTAM Symposium on Developments in Geophysical Turbulence RM Kerr, Y Kimura 518. Berlin: Springer Science+Business Media
    [Google Scholar]
  80. Lowery PS, Reynolds WC. 1986. Numerical simulation of a spatially-developing, forced, plane mixing layer Rep. TF-26 Dep. Mech. Eng., Stanford Univ. Stanford, CA:
    [Google Scholar]
  81. Lund TS, Wu X, Squires KD. 1998. Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140::23358
    [Google Scholar]
  82. Lynch P. 2006. The Emergence of Numerical Weather Prediction: Richardson's Dream Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  83. Mansour NN, Ferziger JR, Reynolds WC. 1978. Large-eddy simulation of a turbulent mixing layer Rep. TF-11 Dep. Mech. Eng., Stanford Univ. Stanford, CA:
    [Google Scholar]
  84. Mansour NN, Moin P, Reynolds WC, Ferziger JH 1979. Improved methods for large eddy simulations of turbulence. Turbulent Shear Flows I: Selected Papers from the First International Symposium on Turbulent Shear Flows F Durst, BE Launder, FW Schmidt, JH Whitelaw 386401. Berlin: Springer
    [Google Scholar]
  85. Metcalfe RW, Orszag SA, Brachet ME, Menon S, Riley JJ. 1987. Secondary instability of a temporally growing mixing layer. J. Fluid Mech. 184:20743
    [Google Scholar]
  86. Moin P, Kim J. 1982. Numerical investigation of turbulent channel flow. J. Fluid Mech. 118:34177
    [Google Scholar]
  87. Moin P, Mahesh K 1998. Direct numerical simulation of turbulence: a tool in turbulence research. Annu. Rev. Fluid Mech. 30:53078
    [Google Scholar]
  88. Moin P, Reynolds WC, Ferziger JH. 1978. Large eddy simulation of incompressible turbulent channel flow Rep. TF-12 Dep. Mech. Eng., Stanford Univ. Stanford, CA:
    [Google Scholar]
  89. Moin P, Reynolds WC, Kim J. 1987. Preface. Proceedings of the 1987 Summer Program1 Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  90. Moser RD, Moin P. 1984. Direct numerical simulation of curved turbulent channel flow NASA TM-85974 Ames Res. Cent. Moffett Field, CA:
    [Google Scholar]
  91. Moser RD, Moin P. 1987. The effects of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175:479510
    [Google Scholar]
  92. Moser RD, Moin P, Leonard A. 1983. A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow. J. Comput. Phys. 52:52444
    [Google Scholar]
  93. Moser RD, Rogers MM. 1991. Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A 3:112834
    [Google Scholar]
  94. Moser RD, Rogers MM. 1993. The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence. J. Fluid Mech. 247:275320
    [Google Scholar]
  95. Moser RD, Rogers MM. 1994. Direct simulation of a self-similar plane wake NASA TM-108815 Ames Res. Cent. Moffett Field, CA:
    [Google Scholar]
  96. Orszag SA. 1971a. Numerical simulation of incompressible flows within simple boundaries: accuracy. J. Fluid Mech. 49:75112
    [Google Scholar]
  97. Orszag SA. 1971b. Numerical simulation of incompressible flows within simple boundaries. I. Galerkin (spectral) representations. Stud. Appl. Math. 50:293327
    [Google Scholar]
  98. Orszag SA, Kells LC. 1980. Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96:159205
    [Google Scholar]
  99. Orszag SA, Patterson GS Jr. 1971. Numerical simulation of turbulence. Statistical Models and Turbulence J Ehlers, K Hepp, HA Weidenmüller 12747. Berlin: Springer-Verlag
    [Google Scholar]
  100. Orszag SA, Patterson GS Jr. 1972. Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28:7679
    [Google Scholar]
  101. Patera AT. 1984. A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54::46888
    [Google Scholar]
  102. Patterson GS Jr., Orszag SA. 1971. Spectral calculations of isotropic turbulence: efficient removal of aliasing interactions. Phys. Fluids 14:253841
    [Google Scholar]
  103. Phillips NA. 1959. An example of non-linear computational instability. The Atmosphere and the Sea in Motion B Bolin 5014. New York: Rockefeller Press
    [Google Scholar]
  104. Rai MM, Gatski TB, Erlebacher G. 1995. Direct simulation of spatially evolving compressible turbulent boundary layers Paper presented at 33rd Aerospace Sciences Meeting and Exhibit Reno, NV: AIAA Pap. 1995-0583
    [Google Scholar]
  105. Richardson LF. 1922. Weather Prediction by Numerical Process. Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  106. Riley JJ, Metcalfe RW. 1980. Direct numerical simulation of a perturbed, turbulent mixing layer Paper presented at 18th Aerospace Sciences Meeting Pasadena, CA: AIAA Pap. 1980-0274
    [Google Scholar]
  107. Riley JJ, Metcalfe RW, Orszag SA. 1986. Direct numerical simulation of chemically reacting turbulent mixing layers. Phys. Fluids 29:40622
    [Google Scholar]
  108. Riley JJ, Patterson GS. 1974. Diffusion experiments with numerically integrated isotropic turbulence. Phys. Fluids 17:29297
    [Google Scholar]
  109. Robinson SK. 1991. Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23:60139
    [Google Scholar]
  110. Rogallo RS. 1981. Numerical experiments in homogeneous turbulence NASA TM-81315 Ames Res. Cent. Moffett Field, CA:
    [Google Scholar]
  111. Rogallo RS, Moin P. 1984. Numerical simulation of turbulent flows. Annu. Rev. Fluid Mech. 16:99137
    [Google Scholar]
  112. Rogers MM, Moser RD. 1992. The three-dimensional evolution of a plane mixing layer. J. Fluid Mech. 243:183226
    [Google Scholar]
  113. Schumann U. 1975. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18:376404
    [Google Scholar]
  114. Siggia ED. 1981. Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107:375406
    [Google Scholar]
  115. Siggia ED, Patterson GS Jr. 1978. Intermittency effects in a numerical simulation of stationary three-dimensional turbulence. J. Fluid Mech. 86:56792
    [Google Scholar]
  116. Smagorinsky J. 1963. General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weather Rev. 91:99164
    [Google Scholar]
  117. Smagorinsky J, Manabe S, Holloway JL. 1965. Numerical results from a nine-level general circulation model of the atmosphere. Mon. Weather Rev. 93:72768
    [Google Scholar]
  118. Sommeria G. 1976. Three-dimensional simulation of turbulent processes in an undisturbed trade wind boundary layer. J. Atmos. Sci. 33:21641
    [Google Scholar]
  119. Spalart PR. 1986a. Numerical simulation of boundary layers: part 1. Weak formulation and numerical method NASA TM-88222 Ames Res. Cent. Moffett Field, CA:
    [Google Scholar]
  120. Spalart PR. 1986b. Numerical study of sink-flow boundary layers. J. Fluid Mech. 172:30728
    [Google Scholar]
  121. Spalart PR. 1988. Direct numerical simulation of a turbulent boundary layer up to 1410. J. Fluid Mech. 187:6198
    [Google Scholar]
  122. Spalart PR, Leonard A. 1985. Direct numerical simulation of equilibrium turbulent boundary layers Paper presented at the 5th Symposium on Turbulent Shear Flows Ithaca, NY: Aug. 7–9
    [Google Scholar]
  123. Spalart PR, Moser RD, Rogers MM. 1991. Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96:297324
    [Google Scholar]
  124. Stolz S, Adams NA, Kleiser L. 2001. An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Phys. Fluids 13:9971015
    [Google Scholar]
  125. Tavoularis S, Corrsin S. 1981. Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104:31147
    [Google Scholar]
  126. Taylor GI. 1922. Diffusion by continuous movements. Proc. Lond. Math. Soc. s2-20:196212
    [Google Scholar]
  127. Vervisch L, Poinsot T. 1998. Direct numerical simulation of non-premixed turbulent flames. Annu. Rev. Fluid Mech. 30:65591
    [Google Scholar]
  128. von Neumann J. 1949. Recent theories of turbulence. Collected Works of John von Neumann, Volume 6: Theory of Games, Astrophysics, Hydrodynamics and Meteorology A Taub 43772. New York: Pergamon Press
    [Google Scholar]
  129. von Neumann J, Richtmyer RD. 1950. A method for the numerical calculation of hydrodynamical shocks. . J. Appl. Phys. 21::23237
    [Google Scholar]
  130. Wallace JM, Foss JF. 1995. The measurement of vorticity in turbulent flows. Annu. Rev. Fluid Mech. 27:469514
    [Google Scholar]
  131. Williamson JH. 1980. Low-storage Runge-Kutta schemes. J. Comput. Phys. 35:4856
    [Google Scholar]
  132. Yeung PK, Pope SB. 1989. Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207:53186
    [Google Scholar]
  133. Yeung PK, Pope SB, Sawford BL. 2006. Reynolds number dependence of Lagrangian statistics in large numerical simulations of isotropic turbulence. J. Turbul. 7:N58
    [Google Scholar]
  134. Yeung PK, Zhai XM, Sreenivasan KR. 2015. Extreme events in computational turbulence. PNAS 112:1263338
    [Google Scholar]
  135. Zang TA. 1991. On the rotation and skew-symmetric forms for incompressible flow simulations. Appl. Numer. Math. 7:2740
    [Google Scholar]
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