The Imbalance Between Enstrophy Production and Destruction in Homogeneous Isotropic Unsteady Turbulence

  • P. C. ValenteEmail author
  • R. Onishi
  • C. B. da Silva
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 165)


We show in direct numerical simulations of homogeneous isotropic non-stationary turbulence that there is a systematic and significant imbalance between enstrophy production and its destruction which is concomitant with the previously observed imbalance between the non-linear energy cascade to fine scales and its dissipation (Valente, Onishi, da Silva, Phys Rev E 90(023003), 2014, [12]). However, contrary to the former, the imbalance between enstrophy production and destruction is affected by the ‘cascade time-lag’, i.e. the time it takes for the energy injected on the large-scales to reach the fine-scales.


Reynolds Number Direct Numerical Simulation Energy Cascade Direct Numerical Simulation Data Kinetic Energy Dissipation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Antonia, R.A., Burattini, P.: Approach to the 4/5 law in homogeneous isotropic turbulence. J. Fluid Mech. 550, 175–184 (2006)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bos, W.J.T., Shao, L., Bertoglio, J.-P.: Spectral imbalance and the normalized dissipation rate of turbulence. Phys. Fluids 19, 045101 (2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    Horiuti, K., Tamaki, T.: Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation. Phys. Fluids 25, 12104 (2013)CrossRefGoogle Scholar
  4. 4.
    Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Dokl. Akad. Nauk. SSSR 30(4) (1941). (Reprinted in 1991, Proc. R. Soc. Lond. 434, 9–13)Google Scholar
  5. 5.
    Kolmogorov, A.N.: Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk. SSSR 32(1) (1941). (Reprinted in 1991, paper 47 in Selected Works of A.N. Kolmogorov, vol. I: Mathematics and Mechanics)Google Scholar
  6. 6.
    Kraichnan, R.: On Kolmogorov’s inertial-range theories. J. Fluid Mech. 62(2), 305–330 (1974)CrossRefzbMATHGoogle Scholar
  7. 7.
    Lumley, J.L.: Some comments on turbulence. Phys. Fluids A 4(2), 203–211 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Rubinstein, R., Clark, T.T., Livescu, D., Luo, L.-S.: Time-dependent isotropic turbulence. J. Turb. 5, 11 (2004)Google Scholar
  9. 9.
    Speziale, C.G., Bernard, P.S.: The energy decay in self-preserving isotropic turbulence revisited. J. Fluid Mech. 241, 645–667 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Tchoufag, J., Sagaut, P., Cambon, C.: Spectral approach to finite Reynolds number effects on Kolmogorov’s 4/5 law in isotropic turbulence. Phys. Fluids 24, 015107 (2012)CrossRefGoogle Scholar
  11. 11.
    Tennekes, H., Lumley, J.L.: A First Course in Turbulence. MIT Press, Cambridge (1972)zbMATHGoogle Scholar
  12. 12.
    Valente, P.C., Onishi, R., da Silva, C.B.: The origin of the imbalance between energy cascade and dissipation in turbulence. Phys. Rev. E 90, 023003 (2014)CrossRefGoogle Scholar
  13. 13.
    Valente, P.C., Vassilicos, J.C.: Universal dissipation scaling for nonequilibrium turbulence. Phys. Rev. Lett. 108, 214503 (2012)CrossRefGoogle Scholar
  14. 14.
    Valente, P.C., Vassilicos, J.C.: The energy cascade in grid-generated non-equilibrium decaying turbulence (submitted) (2014). arXiv:1307.5901
  15. 15.
    Vassilicos, J.C.: Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47, 95–114 (2015)CrossRefGoogle Scholar
  16. 16.
    Yoshizawa, A.: Nonequilibrium effect of the turbulent-energy-production process on the inertial-range spectrum. Phys. Rev. E 49, 5 (1994)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.LAETA, IDMEC, Instituto Superior Técnico, Universidade de LisboaLisboaPortugal
  2. 2.Center for Earth Information Science and Technology, Japan Agency for Marine-Earth Science and TechnologyKanazawa-ku, YokohamaJapan

Personalised recommendations