Vorticity Statistics in Fully Developed Turbulence

Conference paper


We study the statistical properties of fully developed hydrodynamical turbulence. To this end, a theoretical framework is established relating basic dynamical features of fluid flows to the shape and evolution of probability density functions of, for example, the vorticity. Starting from the basic equations of motion, the theory involves terms, which presently cannot be calculated from first principles. This missing information is taken from direct numerical simulations. A parallel pseudospectral code is used to to obtain well-resolved numerical simulations of homogeneous isotropic turbulence. The results yield a consistent description of the vorticity statistics and provide insights into the structure and dynamics of fully developed turbulence.


Direct Numerical Simulation Tracer Particle Vorticity Equation Conditional Average Homogeneous Isotropic Turbulence 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Boyd, J.: Chebyshev and Fourier Spectral Methods. www-personal.engin.umich.edu/~jpboyd/ (2000)
  2. 2.
    Canuto, C., Hussaini, M., Quarteroni, A., Zang, T.: Spectral Methods in Fluid Dynamics. Springer-Verlag, Berlin (1987) Google Scholar
  3. 3.
  4. 4.
    Frisch, U.: Turbulence - The Legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge, England (1995) MATHGoogle Scholar
  5. 5.
    Hou, T.Y., Li, R.: Computing nearly singular solutions using pseudo-spectral methods. J. Comp. Phys. 226(1), 379–397 (2007) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Lundgren, T.S.: Distribution functions in the statistical theory of turbulence. Physics of Fluids 10(5), 969–975 (1967) CrossRefGoogle Scholar
  7. 7.
    Monin, A.: Equations of turbulent motion. Prikl. Mat. Mekh. 31(6), 1057 (1967) MATHGoogle Scholar
  8. 8.
    Novikov, E.A.: Kinetic equations for a vortex field. Soviet Physics-Doklady 12(11), 1006–1008 (1967) MATHGoogle Scholar
  9. 9.
    Novikov, E.A.: A new approach to the problem of turbulence, based on the conditionally averaged Navier-Stokes equations. Fluid Dynamics Research 12(2), 107–126 (1993) CrossRefGoogle Scholar
  10. 10.
    Novikov, E.A., Dommermuth, D.: Conditionally averaged dynamics of turbulence. Mod. Phys. Lett. B 8(23), 1395 (1994) CrossRefGoogle Scholar
  11. 11.
    Pope, S.: Turbulent Flows. Cambridge University Press, Cambridge, England (2000) MATHGoogle Scholar
  12. 12.
    Shu, C., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comp. Phys. 77(12), 379–397 (1988) MathSciNetGoogle Scholar
  13. 13.
    Wilczek, M., Friedrich, R.: Dynamical origins for non-Gaussian vorticity distributions in turbulent flows. Physical Review E 80(1), 016316 (2009) CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Michael Wilczek
    • 1
  • Anton Daitche
    • 1
  • Rudolf Friedrich
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of MünsterMünsterGermany

Personalised recommendations