1932

Abstract

This article reviews evidence concerning the cornerstone dissipation scaling of turbulence theory: , with =const., ϵ the dissipation rate of turbulent kinetic energy , and an integral length scale characterizing the energy-containing turbulent eddies. This scaling is intimately linked to the Richardson-Kolmogorov equilibrium cascade. Accumulating evidence shows that a significant nonequilibrium region exists in various turbulent flows in which the energy spectrum has Kolmogorov's −5/3 wave-number scaling over a wide wave-number range, yet /, with ≈1≈, a global/inlet Reynolds number, and a local turbulence Reynolds number.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010814-014637
2015-01-03
2024-06-10
Loading full text...

Full text loading...

/deliver/fulltext/fluid/47/1/annurev-fluid-010814-014637.html?itemId=/content/journals/10.1146/annurev-fluid-010814-014637&mimeType=html&fmt=ahah

Literature Cited

  1. Antonia RA, Pearson BR. 2000. Effect of initial conditions on the mean energy dissipation rate and the scaling exponent. Phys. Rev. E 62:8086–90 [Google Scholar]
  2. Antonia RA, Satyaprakash BR, Hussain AKMF. 1980. Measurements of dissipation rate and some other characteristics of turbulent plane and circular jets. Phys. Fluids 23:695–700 [Google Scholar]
  3. Bai K, Meneveau C, Katz J. 2013. Experimental study of spectral energy fluxes in turbulence generated by a fractal, tree-like object. Phys. Fluids 25:110810 [Google Scholar]
  4. Barenghi CF, L'vov VS, Roche PE. 2014. Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid. Proc. Natl. Acad. Sci. USA 111:4683–90 [Google Scholar]
  5. Batchelor GK. 1953. The Theory of Homogeneous Turbulence Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  6. Boffetta G, Romano GP. 2002. Structure functions and energy dissipation dependence on Reynolds number. Phys. Fluids 14:3453–58 [Google Scholar]
  7. Bos WJT, Shao L, Bertoglio JP. 2007. Spectral imbalance and the normalized dissipation rate of turbulence. Phys. Fluids 19:045101 [Google Scholar]
  8. Braza M, Perrin R, Hoarau Y. 2006. Turbulence properties in the cylinder wake at high Reynolds numbers. J. Fluids Struct. 22:757–71 [Google Scholar]
  9. Burattini P, Lavoie P, Antonia RA. 2005. On the normalized turbulent energy dissipation rate. Phys. Fluids 17:098103 [Google Scholar]
  10. Cadot O, Couder Y, Daerr A, Douady S, Tsinober A. 1997. Energy injection in closed turbulent flows: stirring through boundary layers versus inertial stirring. Phys. Rev. E 56:427–33 [Google Scholar]
  11. Dallas V, Vassilicos JC, Hewitt GF. 2009. Stagnation point von Kármán coefficient. Phys. Rev. E 80:046306 [Google Scholar]
  12. Danaila L, Krawczynski JF, Thiesset F, Renou B. 2012. Yaglom-like equation in axisymmetric anisotropic turbulence. Physica D 241:216–23 [Google Scholar]
  13. Discetti S, Ziskin IB, Astarita T, Adrian RJ, Prestridge KP. 2013. PIV measurements of anisotropy and inhomogeneity in decaying fractal generated turbulence. Fluid Dyn. Res. 45:061401 [Google Scholar]
  14. Doering CR. 2009. The 3D Navier-Stokes problem. Annu. Rev. Fluid Mech. 41:109–28 [Google Scholar]
  15. Doering CR, Foias C. 2002. Energy dissipation in body-forced turbulence. J. Fluid Mech. 467:289–306 [Google Scholar]
  16. Douady S, Couder Y, Brachet ME. 1991. Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67:983–86 [Google Scholar]
  17. Duchon J, Robert R. 2000. Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations. Nonlinearity 13:249–55 [Google Scholar]
  18. Eyink GL. 2003. Local 4/5-law and energy dissipation anomaly in turbulence. Nonlinearity 17:137–45 [Google Scholar]
  19. Frisch U. 1995. Turbulence: The Legacy of A.N. Kolmogorov Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  20. Gad-el-Hak M, Corrsin S. 1974. Measurements of the nearly isotropic turbulence behind a uniform jet grid. J. Fluid Mech. 62:115–43 [Google Scholar]
  21. George WK. 1989. The self-preservation of turbulent flows and its relation to initial conditions and coherent structures. Advances in Turbulence WK George, R Arndt 39–73 New York: Hemisphere [Google Scholar]
  22. George WK. 1992. The decay of homogeneous isotropic turbulence. Phys. Fluids A 4:1492–509 [Google Scholar]
  23. George WK. 2014. Reconsidering the ‘local equilibrium’ hypothesis for small scale turbulence. Turbulence Colloquium Marseille 2011: Fundamental Problems of Turbulence, 50 Years After the Marseille 1961 Conference M Farge, HK Moffatt, K Schneider Les Ulis, Fr.: EDP Sci. In press [Google Scholar]
  24. George WK, Wang H. 2009. The exponential decay of homogeneous turbulence. Phys. Fluids 21:025108 [Google Scholar]
  25. Gomes-Fernandes R, Ganapathisubramani B, Vassilicos JC. 2012. Particle image velocimetry study of fractal-generated turbulence. J. Fluid Mech. 711:306–36 [Google Scholar]
  26. Gomes-Fernandes R, Ganapathisubramani B, Vassilicos JC. 2014a. Evolution of the velocity-gradient tensor invariants in a spatially developing flow. J. Fluid Mech. 756252–92 [Google Scholar]
  27. Gomes-Fernandes R, Ganapathisubramani B, Vassilicos JC. 2014b. The energy cascade in a non-homogeneous non-isotropic turbulence. J. Fluid Mech. Submitted manuscript [Google Scholar]
  28. Goto S, Vassilicos JC. 2009. The dissipation rate is not universal and depends on the internal stagnation point structure. Phys. Fluids 21:035104 [Google Scholar]
  29. Hearst RJ, Lavoie P. 2014. Decay of turbulence generated by a square fractal-element grid. J. Fluid Mech. 741:567–84 [Google Scholar]
  30. Hill RJ. 2002. Exact second-order structure-function relationships. J. Fluid Mech. 468:317–26 [Google Scholar]
  31. Hurst D, Vassilicos JC. 2007. Scalings and decay of fractal-generated turbulence. Phys. Fluids 19:035103 [Google Scholar]
  32. Isaza JC, Salazar R, Warhaft Z. 2014. On grid-generated turbulence in the near and far field regions. J. Fluid Mech. 753402–26 [Google Scholar]
  33. Kaneda Y, Ishihara T, Yokohama M, Itakura K, Uno A. 2003. Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15:L21–24 [Google Scholar]
  34. Kistler AL, Vrebalovich T. 1966. Grid turbulence at high Reynolds numbers. J. Fluid Mech. 26:37–47 [Google Scholar]
  35. Kolmogorov AN. 1941a. Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk. SSSR 32:16–18 [Google Scholar]
  36. Kolmogorov AN. 1941b. On degeneration (decay) of isotropic turbulence in an incompressible viscous fluid. Dokl. Akad. Nauk. SSSR 31:538–40 [Google Scholar]
  37. Kolmogorov AN. 1941c. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30:301–5 [Google Scholar]
  38. Laizet S, Vassilicos JC, Cambon C. 2013. Interscale energy transfer in decaying turbulence and vorticity-strain rate dynamics in grid-generated turbulence. Fluid Dyn. Res. 45:061408 [Google Scholar]
  39. Launder BE, Spalding DB. 1972. Mathematical Models of Turbulence London: Academic [Google Scholar]
  40. Lesieur M, Metais O. 1996. New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28:45–82 [Google Scholar]
  41. Liepmann HW. 1949. Die anwendung eines satzes uber die nullstellen stochstischer functionen auf turbulenzmessungen. Helv. Phys. Acta 22:119–24 [Google Scholar]
  42. Liepmann HW, Robinson MS. 1952. Counting methods and equipment for mean-value measurements in turbulence research NACA Tech. Note 3037, Natl. Advis. Comm. Aeronaut. [Google Scholar]
  43. Lumley JL. 1992. Some comments on turbulence. Phys. Fluids A 4:201–11 [Google Scholar]
  44. Makita H. 1991. Realization of a large-scale turbulence field in a small wind tunnel. Fluid Dyn. Res. 8:53–64 [Google Scholar]
  45. Marati N, Casciola CM, Piva R. 2004. Energy cascade and spatial fluxes in wall turbulence. J. Fluid Mech. 521:191–215 [Google Scholar]
  46. Mazellier N, Vassilicos JC. 2008. The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topology. Phys. Fluids 20:015101 [Google Scholar]
  47. Mazellier N, Vassilicos JC. 2010. Turbulence without Richardson-Kolmogorov cascade. Phys. Fluids 22:075101 [Google Scholar]
  48. McComb WD, Berera A, Salewski M, Yoffe S. 2010. Taylor's (1935) dissipation surrogate reinterpreted. Phys. Fluids 22:061704 [Google Scholar]
  49. Meneveau C, Katz J. 2000. Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 232:1–32 [Google Scholar]
  50. Mouri H, Hori A, Kawashima Y, Hashimoto K. 2012. Large-scale length that determines the mean rate of energy dissipation in turbulence. Phys. Rev. E 86:026309 [Google Scholar]
  51. Nagata K, Sakai Y, Inaba T, Suzuki H, Terashima O, Suzuki H. 2013. Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence. Phys. Fluids 25:065102 [Google Scholar]
  52. Nedic J, Vassilicos JC, Ganapathisubramani B. 2013. Axisymmetric turbulent wakes with new non-equilibrium similarity scalings. Phys. Rev. Lett. 111:144503 [Google Scholar]
  53. Nie Q, Tanveer S. 1999. A note on third-order structure functions in turbulence. Proc. R. Soc. Lond. A 455:1615–35 [Google Scholar]
  54. Pope SB. 2000. Turbulent Flows Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  55. Richardson LF. 1922. Weather Prediction by Numerical Process Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  56. Rollin B, Dubief Y, Doering CR. 2011. Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles. J. Fluid Mech. 670:204–13 [Google Scholar]
  57. Saffman PG. 1968. Lectures on homogeneous turbulence. Topics in Nonlinear Physics N Zabuski 485–614 Berlin: Springer-Verlag [Google Scholar]
  58. Seoud RE, Vassilicos JC. 2007. Dissipation and decay of fractal-generated turbulence. Phys. Fluids 19:105108 [Google Scholar]
  59. Sreenivasan KR. 1984. On the scaling of the turbulence energy dissipation rate. Phys. Fluids 27:1048–59 [Google Scholar]
  60. Sreenivasan KR. 1995. The energy dissipation in turbulent shear flows. Symposium on Developments in Fluid Dynamics and Aerospace Engineering SM Deshpande, A Prabhu, KR Sreenivasan, PR Viswanath 159–90 Bangalore: Interline [Google Scholar]
  61. Sreenivasan KR. 1998. An update on the energy dissipation rate in isotropic turbulence. Phys. Fluids 10:528–29 [Google Scholar]
  62. Taylor GI. 1935. Statistical theory of turbulence. Proc. R. Soc. Lond. A 151:421–44 [Google Scholar]
  63. Tchoufag J, Sagaut P, Cambon C. 2012. Spectral approach to finite Reynolds number effects on Kolmogorov's 4/5 law in isotropic turbulence. Phys. Fluids 24:015107 [Google Scholar]
  64. Tennekes H, Lumley JL. 1972. A First Course in Turbulence Cambridge, MA: MIT Press [Google Scholar]
  65. Thiesset F, Antonia RA, Danaila L. 2013. Scale-by-scale turbulent energy budget in the intermediate wake of two-dimensional generators. Phys. Fluids 25:115105 [Google Scholar]
  66. Thormann A, Meneveau C. 2014. Decay of homogeneous nearly isotropic turbulence behind active fractal grids. Phys. Fluids 26:025112 [Google Scholar]
  67. Townsend AA. 1976. The Structure of Turbulent Shear Flow Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  68. Valente P, Vassilicos JC. 2011. The decay of turbulence generated by a class of multi-scale grids. J. Fluid Mech. 687:300–40 [Google Scholar]
  69. Valente P, Vassilicos JC. 2012. Universal dissipation scaling for nonequilibrium turbulence. Phys. Rev. Lett. 108:214503 [Google Scholar]
  70. Valente P, Vassilicos JC. 2014. The non-equilibrium region of grid-generated decaying turbulence. J. Fluid Mech. 744:5–37 [Google Scholar]
/content/journals/10.1146/annurev-fluid-010814-014637
Loading
/content/journals/10.1146/annurev-fluid-010814-014637
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error