Incompressible Homogeneous Isotropic Turbulence

Chapter

Abstract

This chapter is devoted to isotropic incompressible turbulence. The main features of related theories are discussed, along with the recent results: energy spectrum and two-point correlations and related models, closures for non-linear terms in both physical and Fourier space, theories for grid turbulence decay including fractal grid case, non-equilibrium effects, advanced spectral theories and models for kinetic energy cascade and dynamics in physical space.

References

  1. André, J.-C., Lesieur, M.: Influence of helicity on the evolution of isotropic turbulence at high Reynolds number. J. Fluid Mech. 81, 187–207 (1977)ADSMATHCrossRefGoogle Scholar
  2. Andreotti, B.: Studying Burgers’ models to investigate the physical meaning of the alignments statistically observed in turbulence. Phys. Fluids 9, 735–742 (1997)ADSMathSciNetMATHCrossRefGoogle Scholar
  3. Antonia, R.A., Burattini, P.: Approach to the 4/5 law in homogeneous isotropic turbulence. J. Fluid Mech. 550, 175–184 (2006)ADSMATHCrossRefGoogle Scholar
  4. Bass, J.: Sur les bases mathématiques de la théorie de la turbulence. Comptes Rendus Acad. Sci. 228(3), 228–229 (1949)Google Scholar
  5. Batchelor, G.K.: Energy decay and self-preserving correlation functions in isotropic turbulence. Q. Appl. Math. 6, 97 (1948)MathSciNetMATHCrossRefGoogle Scholar
  6. Batchelor, G.K.: Pressure fluctuations in isotropic turbulence. Proc. Camb. Philos. Soc. 47, 359–374 (1951)ADSMATHCrossRefGoogle Scholar
  7. Batchelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge University Press, Cambridge (1953)MATHGoogle Scholar
  8. Benney, D.J., Newell, A.C.: Random wave closure. Stud. Appl. Math. 48, 29–53 (1969)MATHCrossRefGoogle Scholar
  9. Borue, V., Orszag, S.A.: Self similar decay of three-dimensional homogeneous turbulence with hyperviscosity. Phys. Rev. E 51(2), R856–R859 (1995a)Google Scholar
  10. Borue, V., Orszag, S.A.: Forced three-dimensional homogeneous turbulence with hyperviscosity. Europhys. Lett. 29(9), 687–692 (1995b)Google Scholar
  11. Bos, W.J.T., Bertoglio, J.-P.: Dynamics of spectrally truncated inviscid turbulence. Phys. Fluids 18, 071701 (2006a)Google Scholar
  12. Bos, W.J.T., Bertoglio, J.-P.: A single-time two-point closure based on fluid particle displacements. Phys. Fluids 18, 031706 (2006b)Google Scholar
  13. Bos, W.J.T., Rubinstein, R.: Dissipation in unsteady turbulence. Phys. Rev. Fluids 2, 022601(R) (2017)ADSCrossRefGoogle Scholar
  14. Bos, W.J.T., Shao, L., Bertoglio, J.P.: Spectral imbalance and the normalized dissipation rate of turbulence. Phys. Fluids 19, 045101 (2007)ADSMATHCrossRefGoogle Scholar
  15. Brasseur, J.G., Wei, C.H.: Interscale dynamics and local isotropy in high Reynolds number turbulence within triadic interactions. Phys. Fluids 6(2), 842–870 (1994)ADSMATHCrossRefGoogle Scholar
  16. Cambon, C., Jacquin, L.: Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317 (1989)ADSMathSciNetMATHCrossRefGoogle Scholar
  17. Cambon, C., Jeandel, D., Mathieu, M.: Spectral modelling of homogeneous non-isotropic turbulence. J. Fluid Mech. 104, 247–262 (1981)ADSMATHCrossRefGoogle Scholar
  18. Cantwell, B.J.: Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A 4, 782–793 (1992)ADSMathSciNetMATHCrossRefGoogle Scholar
  19. Chakraborty, P., Balachandar, S., Adrian, R.J.: On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214 (2005)ADSMathSciNetMATHCrossRefGoogle Scholar
  20. Chandrasekhar, S.: The theory of statistical and isotropic turbulence. Phys. Rev. 76(5), 896–897 (1949)Google Scholar
  21. Chertkov, M., Pumir, A., Shraiman, B.I.: Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11, 2394–2410 (1999)ADSMathSciNetMATHCrossRefGoogle Scholar
  22. Chevillard, L., Meneveau, C., Biferale, L., Toschi, F.: Modeling the pressure Hessian and viscous Laplacian in turbulence: comparisons with direct numerical simulation and implications on velocity gradient dynamics. Phys. Fluids 20, 101504 (2008)ADSMATHCrossRefGoogle Scholar
  23. Chong, M.S., Perry, A.E., Cantwell, B.J.: A general classification of three-dimensional flow fields. Phys. Fluids 2, 765–777 (1990)ADSMathSciNetCrossRefGoogle Scholar
  24. Cichowlas, C., Bonati, P., Debbasch, F., Brachet, M.: Effective dissipation and turbulence in spectrally truncated Euler flows. Phys. Rev. Lett. 95, 264502 (2005)ADSCrossRefGoogle Scholar
  25. Clark, T.T., Zemach, C.: Symmetries and the approach to statistical equilibrium in isotropic turbulence. Phys. Fluids 31, 2395–2397 (1998)MathSciNetMATHGoogle Scholar
  26. Clark, T.T., Rubinstein, R., Weinstock, J.: Reassessment of the classical turbulence closures: the Leith diffusion model. J. Turbul. 10(35), 1–23 (2009)MathSciNetMATHGoogle Scholar
  27. Coleman, G.N., Mansour, N.N.: Modeling the rapid spherical compression of isotropic turbulence. Phys. Fluids 3, 2255–2259 (1991)ADSMATHCrossRefGoogle Scholar
  28. Comte-Bellot, G., Corrsin, S.: The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657–682 (1966)ADSCrossRefGoogle Scholar
  29. Davidson, P.A.: Turbulence. An Introduction for Scientists and Engineers. Oxford University Press, Oxford (2004)MATHGoogle Scholar
  30. Davidson, P.A.: The minimum energy decay rate in quasi-isotropic grid turbulence. Phys. Fluids 23, 085108 (2011)ADSCrossRefGoogle Scholar
  31. De Divitiis, N.: von Karman-Howarth and Corrsin equations closure based on Lagrangian description of the fluid motion. Ann. Phys. 368, 296–309 (2016)ADSMATHCrossRefGoogle Scholar
  32. Djenidi, L., Antonia, R.A.: A general self-preservation analysis for decaying homogeneous isotropic turbulence. J. Fluid Mech. 773, 345–365 (2015)Google Scholar
  33. Djenidi, L., Kamruzzaman, Md, Antonia, R.A.: Power-law exponent in the transition period of decay in grid turbulence. J. Fluid Mech. 779, 544–555 (2015)Google Scholar
  34. Donzis, D.A., Sreenivasan, K.R., Yeung, P.K.: Some results on the Reynolds number scaling of pressure statistics in isotropic turbulence. Phys. D 241, 164–168 (2012)MathSciNetCrossRefGoogle Scholar
  35. Dryden, J.L.: A review of the statistical theory of turbulence. Q. Appl. Math. 1, 7–42 (1943)MathSciNetMATHCrossRefGoogle Scholar
  36. Eyink, G.L., Thomson, D.J.: Free decay of turbulence and breakdown of self-similarity. Phys. Fluids 12(3), 477–479 (2000)ADSMathSciNetMATHCrossRefGoogle Scholar
  37. Favier, B., Godeferd, F.S., Cambon, C.: On space and time correlations of isotropic and rotating turbulence. Phys. Fluids 22, 015101 (2010)ADSMATHCrossRefGoogle Scholar
  38. Falkovich, G., Lebedev, V.: Single-point velocity distribution in turbulence. Phys. Rev. Lett. 79(21), 4159–4161 (1997)ADSCrossRefGoogle Scholar
  39. Fjortoft, R.: On the changes in spectral distributions on kinetic energy for two-dimensional, non-divergent flow. Tellus 5, 225–230 (1953)ADSMathSciNetCrossRefGoogle Scholar
  40. Fournier, J.D., Frisch, U.: \(d\)-dimensional turbulence. Phys. Rev. A 17(2), 747–762 (1978)ADSMathSciNetCrossRefGoogle Scholar
  41. Frisch, U.: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge (1995)MATHGoogle Scholar
  42. George, W.K.: The decay of homogeneous turbulence. Phys. Fluids A 4(7), 1492–1509 (2000)Google Scholar
  43. George, W.K.: Asymptotic effect of initial and upstream conditions on turbulence. ASME J. Fluids Eng. 134, 061203 (2012)CrossRefGoogle Scholar
  44. George, W.K., Wang, H.: The exponential decay of homogeneous isotropic turbulence. Phys. Fluids 21, 025108 (2000)Google Scholar
  45. Girimaji, S.S., Zhou, Y.: Spectrum and energy transfer in steady Burgers turbulence. ICASE Report No. 95–13 (1995)Google Scholar
  46. Goto, S., Vassilicos, J.C.: Energy dissipation and flux laws for unsteady turbulence. Phys. Lett. A 379, 1144–1148 (2015)ADSCrossRefGoogle Scholar
  47. Guo, H., Li, C., Qu, Q., Liu, P.: Attractive fixed-point solution study of shell model for homogeneous isotropic turbulence. Appl. Math. Mech. 34, 259–268 (2013)MathSciNetMATHCrossRefGoogle Scholar
  48. He, G.W., Jin, G., Zhao, X.: Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence. Phys. Rev. E 80, 066313 (2009)ADSCrossRefGoogle Scholar
  49. Heisenberg, W.: Zur statistischen theorie der turbulenz. Zeitschrift fur Physik 124, 628–657 (1948)Google Scholar
  50. Hinze, J.O.: Turbulence. McGraw-Hill Series in Mechanical Engineering. McGraw-Hill, New York (1975)Google Scholar
  51. Horiuti, K.: A classification method for vortex sheet and tube structures in turbulent flows. Phys. Fluids 13(12), 3756–3774 (2001)ADSMathSciNetMATHCrossRefGoogle Scholar
  52. Horiuti, K., Takagi, Y.: Identification method for vortex sheet structures in turbulent flows. Phys. Fluids 17, 121703 (2005)ADSMATHCrossRefGoogle Scholar
  53. Horiuti, K., Tamaki, T.: Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation. Phys. Fluids 25, 125104 (2013)ADSCrossRefGoogle Scholar
  54. Horiuti, K., Yanagihara, S., Tamaki, T.: Nonequilibrium state in energy spectra and transfer with implications for topological transitions and SGS modeling. Fluid Dyn. Res. 48, 021409 (2016)MathSciNetCrossRefGoogle Scholar
  55. Hunt, J.C.R., Wray, A.A. Moin, P.: Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88, pp. 193–208 (1988)Google Scholar
  56. Ishida, T., Davidson, P.A., Kaneda, Y.: On the decay of isotropic turbulence. J. Fluid Mech. 564, 455–475 (2006)ADSMathSciNetMATHCrossRefGoogle Scholar
  57. Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K., Uno, A.: Energy spectrum in the near dissipation range of high resolution DNS of turbulence. J. Phys. Soc. Jpn. 74(5), 1464–1471 (2005)ADSMATHCrossRefGoogle Scholar
  58. Jeong, J., Hussain, F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)ADSMathSciNetMATHCrossRefGoogle Scholar
  59. Jimenez, J.: Kinematic alignment effects in turbulent flows. Phys. Fluids 4, 652–654 (1992)ADSCrossRefGoogle Scholar
  60. Jimenez, J., Wray, A.: On the characteristics of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255–285 (1998)ADSMathSciNetMATHCrossRefGoogle Scholar
  61. Jimenez, J., Wray, A., Saffman, P.G., Rogallo, R.: The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90 (1993)ADSMathSciNetMATHCrossRefGoogle Scholar
  62. Kaneda, Y.: Lagrangian and Eulerian time correlations in turbulence. Phys. Fluids A 5(11), 2835–2845 (1993)ADSMATHCrossRefGoogle Scholar
  63. Kaneda, Y., Ishihara, T., Gotoh, K.: Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. Phys. Fluids 11, 2154–2166 (1999)ADSMathSciNetMATHCrossRefGoogle Scholar
  64. Kida, S., Ohkitani, K.: Spatiotemporal intermittency and instability of a forced turbulence. Phys. Fluids 4, 1018–1027 (1992a)ADSMATHCrossRefGoogle Scholar
  65. Kida, S., Ohkitani, K.: Fine structure of energy transfer in turbulence. Phys. Fluids 4, 1602–1604 (1992b)ADSCrossRefGoogle Scholar
  66. Kovasznay, L.S.G.: The spectrum of locally isotropic turbulence. Phys. Rev. 73(9), 1115–1116 (1948)Google Scholar
  67. Kraichnan, R.H.: The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5(4), 497–543 (1959)Google Scholar
  68. Kraichnan, R.H.: Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423 (1967)ADSMathSciNetCrossRefGoogle Scholar
  69. Kraichnan, R.H.: Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech. 47, 525–535 (1971)ADSMATHCrossRefGoogle Scholar
  70. Kraichnan, R.H.: Eddy-viscosity in two and three dimensions. J. Atmos. Sci 33, 1521–1536 (1976)ADSCrossRefGoogle Scholar
  71. Kraichnan, R.H., Panda, R.: Depression of nonlinearity in decaying isotropic turbulence. Phys. Fluids 31, 2395–2397 (1988)ADSMATHCrossRefGoogle Scholar
  72. Krogstad, P.A., Davidson, P.A.: Near-field investigation of turbulence produced by multi-scale grids. Phys. Fluids 24, 035103 (2012)ADSCrossRefGoogle Scholar
  73. Lamorgese, A.G., Caughey, D.A., Pope, S.B.: Direct numerical simulation of homogeneous turbulence with hyperviscosity. Phys. Fluids 17, 015106 (2005)ADSMathSciNetMATHCrossRefGoogle Scholar
  74. Lesieur, M.: Turbulence in fluids, 3rd edn. Kluwer Academic Publishers, Dordrecht (1997)MATHCrossRefGoogle Scholar
  75. Lesieur, M., Schertzer, D.: Amortissement auto-similaire d’une turbulence à grand nombre de Reynolds. J. Méc. 17, 609–646 (1978). (in french)MATHGoogle Scholar
  76. Lesieur, M., Ossia, S., Metais, O.: Infrared pressure spectra in two- and three-dimensional isotropic incompressible turbulence. Phys. Fluids 11, 1535–1543 (1999)ADSMathSciNetMATHCrossRefGoogle Scholar
  77. Lindborg, E.: Correction to four-fifths law due to variations of the dissipation. Phys. Fluids 11(3) , 510–512 (1999)Google Scholar
  78. Llor, A., Soulard, O.: Comment on “Energy spectra at low wavenumbers in homogeneous incompressible turbulence” (Phys. Lett. A 375, 2850 (2011)). Phys. Lett. A 377, 1157–1159 (2013)Google Scholar
  79. Lund, T.S., Rogers, M.M.: An improved measure of strain rate probability in turbulent flows. Phys. Fluids 6, 1838–1847 (1994)ADSMATHCrossRefGoogle Scholar
  80. Lundgren, T.S.: Kolmogorov two-thirds law by matched asymptotic expansions. Phys. Fluids 14, 638–642 (2002)Google Scholar
  81. Lundgren, T.S.: Kolmogorov turbulence by matched asymptotic expansion. Phys. Fluids 15, 1074–1081 (2003)Google Scholar
  82. Manley, O.P.: The dissipation range spectrum. Phys. Fluids 4(6), 1320–1321 (1992)ADSCrossRefGoogle Scholar
  83. Martins-Afonso, M., Meneveau, C.: Recent fluid deformation closure for velocity gradient tensor dynamics in turbulence: timescale effects and expansions. Phys. D 239, 1241–1250 (2010)MATHCrossRefGoogle Scholar
  84. Mazzi, B., Vassilicos, J.C.: Fractal-generated turbulence. J. Fluid Mech. 502, 65–87 (2004)ADSMathSciNetMATHCrossRefGoogle Scholar
  85. Mathieu, J., Scott, J.: An Introduction to Turbulent Flow. Cambridge University Press, Cambridge (2000)Google Scholar
  86. Martin, J., Dopazo, C., Valino, L.: Dynamics of velocity gradient invariants in turbulence: restricted Euler and linear diffusion models. Phys. Fluids 10, 2012–2025 (1998)ADSMathSciNetMATHCrossRefGoogle Scholar
  87. Mazellier, N., Vassilicos, J.C.: The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topology. Phys. Fluids 20, 015101 (2008)ADSMATHCrossRefGoogle Scholar
  88. Meldi, M., Sagaut, P.: On non-self similar regimes in homogeneous isotropic turbulence decay. J. Fluid Mech. 711, 364–393 (2012)ADSMathSciNetMATHCrossRefGoogle Scholar
  89. Meldi, M., Sagaut, P.: Further insights into self-similarity and self-preservation in freely decaying isotropic turbulence. J. Turbul. 14(8), 24–53 (2013a)ADSMathSciNetMATHCrossRefGoogle Scholar
  90. Meldi, M., Sagaut, P.: Pressure statistics in self-similar freely decaying isotropic turbulence. J. Fluid Mech. 717, R2-1–R2-12 (2013b)Google Scholar
  91. Meldi, M., Sagaut, P.: Turbulence in a box: quantification of large-scale resolution effects in isotropic turbulence free decay. J. Fluid Mech. 818, 697–715 (2017)ADSMathSciNetCrossRefGoogle Scholar
  92. Meldi, M., Sagaut, P., Lucor, D.: A stochastic view of isotropic turbulence decay. J. Fluid Mech. 668, 351–362 (2011)ADSMATHCrossRefGoogle Scholar
  93. Meldi, M., Lejemble, H., Sagaut, P.: On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence. J. Fluid Mech. 756, 816–843 (2014)ADSMathSciNetCrossRefGoogle Scholar
  94. Meneveau, C.: Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Ann. Rev. Fluid Mech. 43, 219–245 (2011)ADSMathSciNetMATHCrossRefGoogle Scholar
  95. Meyers, J., Meneveau, C.: A functional form for the energy spectrum parametrizing bottleneck and intermittency effects. Phys. Fluids 20(6), 065109 (2008)Google Scholar
  96. Millionschikov, M.D.: Theory of homogeneous isotropic turbulence. Dokl. Akad. Nauk. SSSR 32, 22–24 (1941)Google Scholar
  97. Mohamed, M.S., Larue, J.C.: The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214 (1990)ADSCrossRefGoogle Scholar
  98. Moisy, F.: Kolmogorov equation in a fully developed turbulence experiment. Phys. Rev. Lett. 82(20), 3994–3997 (1999)Google Scholar
  99. Moisy, F., Jimenez, J.: Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111–133 (2004)ADSMATHCrossRefGoogle Scholar
  100. Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics, vol. 1. MIT Press, Cambridge (1975)Google Scholar
  101. Mons, V., Chassaing, J.C., Gomez, T., Sagaut, P.: Is isotropic turbulence decay governed by asymptotic behavior of large scales? An eddy-damped quasi-normal Markovian-based data assimilation study. Phys. Fluids 26, 115105 (2014)CrossRefGoogle Scholar
  102. Nomura, K.K., Post, G.K.: The structure and the dynamics of vorticity and rate of strain in incompressible homogeneous turbulence. J. Fluid Mech. 377, 65–97 (1998)ADSMathSciNetMATHCrossRefGoogle Scholar
  103. Noullez, A., Pinton, J.F.: Global fluctuations in decaying Burgers turbulence. Eur. Phys. J. B. 28, 231–241 (2002)ADSCrossRefGoogle Scholar
  104. Noullez, A., Vergassola, M.: A fast Legendre transfrom algorithm and applications to the adhesion model. J. Sci. Comput. 9(3), 259–281 (1994)MathSciNetMATHCrossRefGoogle Scholar
  105. Noullez, A., Wallace, G., Lempert, W., Miles, R.B., Frisch, U.: Transverse velocity increments in turbulent flow using the RELIEF technique. J. Fluid Mech. 339, 287–307 (1997)ADSMathSciNetMATHCrossRefGoogle Scholar
  106. Noullez, A., Gurbatov, S.N., Aurell, E., Simdyankin, S.I.: Global picture of self-similar and non-self-similar decay in Burgers turbulence. Phys. Rev. E 71, 056305 (2005)ADSMathSciNetCrossRefGoogle Scholar
  107. Oberlack, M.: On the decay exponent of isotropic turbulence. Proc. Appl. Math. Mech. 1, 294–297 (2002)MATHCrossRefGoogle Scholar
  108. O’Brien, E.F., Francis, G.C.: A consequence of the zero fourth cumulant approximation. J. Fluid Mech. 13, 369–382 (1963)MathSciNetMATHCrossRefGoogle Scholar
  109. Ogura, Y.: A consequence of the zero fourth cumulant approximation in the decay of isotropic turbulence. J. Fluid Mech. 16, 33–40 (1963)ADSMATHCrossRefGoogle Scholar
  110. Orszag, S.A.: Analytical theories of turbulence. J. Fluid Mech. 41, 363–386 (1970)ADSMATHCrossRefGoogle Scholar
  111. Park, N., Mahesh, K.: Analysis of statistical errors in large-eddy simulation using statistical closure theory. J. Comput. Phys. 222(1), 194–216 (2007)ADSMathSciNetMATHCrossRefGoogle Scholar
  112. Pao, Y.M.: Structure of turbulent velocity and scalar fields at large wavenumbers. Phys. Fluids 8(6), 1063–1075 (1965)Google Scholar
  113. Piquet, J.: Turbulent flows. Models and Physics, 2nd edn. Springer, Berlin (2001)Google Scholar
  114. Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)Google Scholar
  115. Pouquet, A., Lesieur, M., André, J.-C., Basdevant, C.: Evolution of high Reynolds number two-dimensional turbulence. J. Fluid Mech. 75, 305–319 (1975)ADSMATHGoogle Scholar
  116. Qian, J.: Universal equilibrium range of turbulence. Phys. Fluids 27(9), 2229–2233 (1984)Google Scholar
  117. Qian, J.: Slow decay of the finite Reynolds number effect of turbulence. Phys. Rev. E 60(3), 3409–3412 (1999)Google Scholar
  118. Ristorcelli, J.R.: The self-preserving decay of isotropic turbulence: analytic solutions for energy and dissipation. Phys. Fluids 15, 3248–3250 (2003)ADSMathSciNetMATHCrossRefGoogle Scholar
  119. Ristorcelli, J.R.: Passive scalar mixing: analytic study of time scale ratio, variance, and mix rate. Phys. Fluids 18, 075101 (2006)ADSMathSciNetMATHCrossRefGoogle Scholar
  120. Ristorcelli, J.R., Livescu, D.: Decay of isotropic turbulence: fixed points and solutions for nonconstant \(G \sim R_\lambda \) palinstrophy. Phys. Fluids 16, 3487–3490 (2004)ADSMathSciNetMATHCrossRefGoogle Scholar
  121. Rossi, M.: Of vortices and vortical layers: an overview. In: Maurel, A., Petitjeans, P. (eds.) Vortex Structure and Dynamics. Lecture Notes in Physics, pp. 40–123. Springer, Berlin (2000)Google Scholar
  122. Saffman, P.G.: On the fine scale structure of vector fields convected by a turbulent fluid. J. Fluid Mech. 16(4), 545–572 (1963)Google Scholar
  123. Siggia, E.D.: Numerical study of small scale intermittency in three dimensional turbulence. J. Fluid Mech. 107, 375–406 (1981)ADSMATHCrossRefGoogle Scholar
  124. Skrbek, L., Stalp, S.R.: On the decay of homogeneous isotropic turbulence. Phys. Fluids 12(8), 1997–2019 (2000)ADSMATHCrossRefGoogle Scholar
  125. Speziale, C.G., Bernard, P.S.: The energy decay in self-preserving isotropic turbulence revisited. J. Fluid Mech. 241, 645–667 (1992)ADSMathSciNetMATHCrossRefGoogle Scholar
  126. Sreenivasan, K.R.: On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784 (1995)Google Scholar
  127. Suzuki, E., Nakano, T., Takashi, N., Gotoh, T.: Energy transfer and intermittency in four-dimensional turbulence. Phys. Fluids 17, 081702 (2005)ADSMATHCrossRefGoogle Scholar
  128. Tanaka, M., Kida, S.: Characterization of vortex tubes and sheets. Phys. Fluids 5(9), 2079–2082 (1993)ADSCrossRefGoogle Scholar
  129. Tatsumi, T.: The theory of decay process of incompressible isotropic turbulence. Proc. R. Soc. Lond. A 239, 16 (1957)ADSMathSciNetMATHCrossRefGoogle Scholar
  130. Taylor, G.I.: Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421–444 (1935)Google Scholar
  131. Tchoufag, J., Sagaut, P., Cambon, C.: A spectral approach to finite Reynolds number effects on Kolmogorov’s 4/5 law in isotropic turbulence. Phys. Fluids 24, 015107 (2012)ADSCrossRefGoogle Scholar
  132. Thiesset, F., Antonia, R.A., Danaila, L., Djenidi, L.: Karman-Howarth closure equation on the basis of a universal eddy viscosity. Phys. Rev. E 88, 011003 (2013)ADSCrossRefGoogle Scholar
  133. Tsinober, A.: An Informal Introduction to Turbulence. Kluwer Academic Publishers, Dordrecht (2001)MATHGoogle Scholar
  134. Vassilicos, J.C.: Dissipation in turbulent flows. Ann. Rev. Fluid Mech.47, 95–114 (2015)Google Scholar
  135. Verzicco, R., Jimenez, J., Orlandi, P.: Steady columnar vortices under local compression. J. Fluid Mech. 299, 367–388 (1995)ADSMathSciNetMATHCrossRefGoogle Scholar
  136. Vignon, J.-M., Cambon, C.: Thermal spectral calculation using eddy-damped quasi-normal Markovian theory. Phys. Fluids 23, 1935–1937 (1980)Google Scholar
  137. Von Karman, T., Howarth, L.: On the statistical theory of isotropic turbulence. Proc. R. Soc. A 164, 192–215 (1938)ADSMATHCrossRefGoogle Scholar
  138. Von Karman, T., Lin, C.C.: On the concept of similarity in the theory of isotropic turbulence. Rev. Mod. Phys. 21(3), 516–519 (1949)ADSMathSciNetMATHCrossRefGoogle Scholar
  139. Waleffe, F.: The nature of triad interactions in homogeneous turbulence. Phys. Fluids 4, 350–363 (1992)ADSMathSciNetMATHCrossRefGoogle Scholar
  140. Waleffe, F.: Inertial transfers in the helical decomposition. Phys. Fluids 5, 677–685 (1993)ADSMATHCrossRefGoogle Scholar
  141. Wilczek, M., Meneveau, M.: Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields. J. Fluid Mech. 756, 191–225 (2014)ADSMathSciNetMATHCrossRefGoogle Scholar
  142. Woodruff, S.L., Rubinstein, R.: Multiplescale perturbation analysis of slowly evolving turbulence. J. Fluid Mech. 565, 95–103 (2006)ADSMathSciNetMATHCrossRefGoogle Scholar
  143. Wylczek, M., Narita, Y.: Wave-number?frequency spectrum for turbulence from a random sweeping hypothesis with mean flow. Phys. Rev. E 86, 066308 (2012)ADSCrossRefGoogle Scholar
  144. Zakharov, V.E., Lvov, V., Falkowitch, G.: Wave Turbulence. Springer, Berlin (1992)Google Scholar
  145. Zhao, X., He, G.W.: Space-time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E 79, 046316 (2009)ADSCrossRefGoogle Scholar
  146. Zhou, J., Adrian, R.J., Balachandar, S., Kendall, T.M.: Mechanisms for generating coherent packets of hairpin vortices. J. Fluid Mech. 387, 353–396 (1999)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mécanique, Modélisation et Procédés Propres, UMR CNRS 7340, Ecole Centrale de MarseilleAix-Marseille UniversitéMarseilleFrance
  2. 2.Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509Ecole Centrale de LyonÉcullyFrance

Personalised recommendations