Skip to main content

Turbulence in a box: quantification of large-scale resolution effects in isotropic turbulence free decay

  • M. Meldi (a1) and P. Sagaut (a2)

The effects of the finiteness of the physical domain over the free decay of homogeneous isotropic turbulence are explored in the present article. Saturation at the large scales is investigated by the use of theoretical analysis and eddy-damped quasi-normal Markovian calculations. Both analyses indicate a strong sensitivity of the large-scale features of the flow to saturation and finite Reynolds number effects. This aspect plays an important role in the general lack of agreement between grid turbulence experiments and numerical simulations. On the other hand, the statistical quantities associated with the behaviour of the spectrum in the inertial region are only marginally affected by saturation. These results suggest new guidelines for the interpretation of experimental and direct numerical simulation studies.

Corresponding author
Email address for correspondence:
Hide All
Antonia, R. A., Tang, S. L., Djenidi, L. & Danaila, L. 2015 Boundedness of the velocity derivative skewness in various turbulent flows. J. Fluid Mech. 781, 727744.
Bos, W. J. T., Shao, L. & Bertoglio, J. P. 2007 Spectral imbalance and the normalized dissipation rate of turbulence. Phys. Fluids 19 (4), 045101.
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657682.
Davidson, P. A. 2004 Turbulence. An Introduction for Scientists and Engineers. Oxford University Press.
Davidson, P. A. 2011 The minimum energy decay rate in quasi-isotropic grid turbulence. Phys. Fluids 23 (8), 085108.
Djenidi, L., Kamruzzamana, Md. & Antonia, R. A. 2015 Power-law exponent in the transition period of decay in grid turbulence. J. Fluid Mech. 779, 544555.
Eyink, G. L. & Thomson, D. J. 2000 Free decay of turbulence and breakdown of self-similarity. Phys. Fluids 12, 477479.
George, W. K. 1992 The decay of homogeneous isotropic turbulence. Phys. Fluids A 4 (7), 14921509.
George, W. K. 2012 Asymptotic effect on initial upstream conditions on turbulence. J. Fluids Engng 134, 061203.
Goto, S. & Vassilicos, J. C. 2015 Energy dissipation and flux laws for unsteady turbulence. Phys. Lett. A 379, 11441148.
Ishida, T., Davidson, P. A. & Kaneda, Y. 2006 On the decay of isotropic turbulence. J. Fluid Mech. 564, 455475.
Krogstad, P. Å. & Davidson, P. A. 2010 Is grid turbulence Saffman turbulence? J. Fluid Mech. 642, 373394.
Krogstad, P. Å. & Davidson, P. A. 2011 Freely-decaying, homogeneous turbulence generated by multi-scale grids. J. Fluid Mech. 680, 417434.
Lavoie, P., Djenidi, L. & Antonia, R. A. 2007 Effects of initial conditions in decaying turbulence generated by passive grids. J. Fluid Mech. 585, 395420.
Lesieur, M., Ossia, S. & Metais, O. 1999 Infrared pressure spectra in two- and three-dimensional isotropic incompressible turbulence. Phys. Fluids 11, 15351543.
Meldi, M. 2016 The signature of initial production mechanisms in isotropic turbulence decay. Phys. Fluids 28, 035105.
Meldi, M. & Sagaut, P. 2012 On non-self-similar regimes in homogeneous isotropic turbulence decay. J. Fluid Mech. 711, 364393.
Meldi, M. & Sagaut, P. 2013a Further insights into self-similarity and self-preservation in freely decaying isotropic turbulence. J. Turbul. 14, 2453.
Meldi, M. & Sagaut, P. 2013b Pressure statistics in self-similar freely decaying isotropic turbulence. J. Fluid Mech. 717, R2.
Meldi, M. & Sagaut, P. 2014 An adaptive numerical method for solving EDQNM equations for the analysis of long-time decay of isotropic turbulence. J. Comput. Phys. 262, 7285.
Mohamed, M. S. & Larue, J. C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195214.
Mons, V., Chasaing, J. C., Gomez, T. & Sagaut, P. 2014 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.
Mydlarski, L. & Warhaft, Z. 1996 On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech. 320, 331368.
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363386.
Sagaut, P. & Cambon, C. 2008 Homogenous Turbulence Dynamics. Cambridge University Press.
Sinhuber, M., Bodenschatz, E. & Bewley, G. P. 2015 Decay of turbulence at high Reynolds numbers. Phys. Rev. Lett. 114, 034501.
Skrbek, L., Niemela, J. J. & Donnelly, R. J. 2000 Four regimes of decaying grid turbulence in a finite channel. Phys. Rev. Lett. 85, 29732976.
Skrbek, L. & Stalp, S. R. 2000 On the decay of homogeneous isotropic turbulence. Phys. Fluids 12, 19972019.
Stalp, R. S., Skrbek, L. & Donnelly, R. J. 1999 Decay of grid turbulence in a finite channel. Phys. Rev. Lett. 82, 214503.
Thormann, A. & Meneveau, C. 2014 Decay of homogeneous, nearly isotropic turbulence behind active fractal grids. Phys. Fluids 26, 025112.
Thornber, B. 2016 Impact of domain size and statistical errors in simulations of homogeneous decaying turbulence and the Richtmyer–Meshkov instability. Phys. Fluids 28, 045106.
Valente, P. C. & Vassilicos, J. C. 2012 Universal dissipation scaling for nonequilibrium turbulence. Phys. Rev. Lett. 108, 214503.
White, C. M., Karpetis, A. N. & Sreenivasan, K. R. 2002 High-Reynolds-number turbulence in small apparatus: grid turbulence in cryogenic liquids. J. Fluid Mech. 452, 189197.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 6
Total number of PDF views: 240 *
Loading metrics...

Abstract views

Total abstract views: 423 *
Loading metrics...

* Views captured on Cambridge Core between 5th April 2017 - 23rd April 2018. This data will be updated every 24 hours.