The statistical properties of fully developed hydrodynamic turbulence
can be well understood using techniques from a generalized version of statistical mechanics,
so-called nonextensive statistical mechanics.

The following picture shows probability densities of velocity differences as measured on various scales in a
turbulent Taylor-Couette flow, and the theoretical predictions of a model based on nonextensive statistical mechanics.
There is excellent agreement. Other theoretical models for probability densities in turbulent flows do not yield anything of similar precision. Turbulent velocity differences u

The measurements were made by Greg Lewis and Harry Swinney at the
Center for Nonlinear Dynamics, University of Texas at Austin.

More details can be found in the following references:

  • C. Beck, G.S. Lewis, and H.L. Swinney, Measuring non-extensitivity parameters in a turbulent Couette-Taylor flow, Phys. Rev 63E , 035303(R) (2001)
    ps file available

  • C. Beck, Dynamical foundations of nonextensive statistical mechanics, Phys. Rev. Lett. 87 , 180601 (2001)
    ps file available

  • Here is a link to a popular science article on my turbulence work.

    A recent article in the SCIENCE magazin (23 August 2002) also mentions this.