Toshihico Arimitsu, Naoko Arimitsu, Hideaki Mouri
The probability density functions (PDFs) for energy dissipation rates created
from turbulence in a wind tunnel, are analyzed by multifractal probability
density function theory, and the validity of the new scaling relation is proven
in the case of experimental turbulence. The tail part of PDF, representing
intermittent coherent motion in fully developed turbulence, is determined by
Tsallis-type PDF for singularity exponents with the new scaling relation which
shows that the coherent motion is deeply related to the marginal instabilities
within a dynamical system at the $\delta^k$-period ($\delta>2$) saddle-node
bifurcation points ($k=1,2,3,...$) associated with $\delta^k$-period windows
constituting a self-similar nesting structure. For the central part PDF
representing both contributions from the coherent motion and the fluctuating
motion twining around the former, we introduced a trial function specified by
three adjustable parameters which reveal scaling behaviors in much wider area
not restricted to the inertial range. The connection point between the central
and tail parts of PDF provides us with an important information to distinguish
the characteristics of the two motions. A trial is performed how to extract the
information of incoherent motion with the help of two different ways in
creating PDFs from the observed time-series data.
View original:
http://arxiv.org/abs/1111.4229
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