Is there a Markov length in fully developed turbulence?
T. Kambe (Tokyo)
Fully developed turbulence (FDT) is structured with a number of elongated
intense vortices. In addition to the various DNS analyses of coherent
structures of FDT, there are observational evidences  of existence of
a Markov length of the order of Taylor microscale, over which the turbulence
cascade is regarded as a Markov process.
Considering that this length is closely related with the coherent
structures, a model of structured turbulence is proposed which is an ensemble
of strained vortices (i.e. Burgers vortices) distributing randomly in space,
in order to get leading order representation of statistics at small scales
(less than the Taylor microscale) and higher order moments in FDT. It is
found  that probability density functions of longitudinal velocity
differences and higher-order structure functions thus obtained are in good
agreement with known results.
 Friedrich, Zeller and Peinke (1998) Europhys. Lett. vol.41, 143;
Friedrich, Lueck, Renner and Peinke (2000) in 'Proc. of IUTAM Symposium
on Geometry and Statistics of Turbulence'.
 Kambe and Hatakeyama (2000) to appear in Fluid Dynamics Research.
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