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The probability density functions (PDFs) for energy dissipation rates,created from time-series data of grid turbulence in a wind tunnel, are analyzedin a high precision by the theoretical formulae for PDFs within multifractalPDF theory which is constructed under the assumption that there are two mainelements constituting fully developed turbulence, i.e., coherent and incoherentelements. The tail part of PDF, representing intermittent coherent motion, isdetermined by Tsallis-type PDF for singularity exponents essentially with oneparameter with the help of new scaling relation whose validity is checked forthe case of the grid turbulence. For the central part PDF representing bothcontributions from the coherent motion and the fluctuating incoherent motionsurrounding the former, we introduced a trial function specified by threeadjustable parameters which amazingly represent scaling behaviors in much widerarea not restricted to the inertial range. From the investigation of thedifference between two difference formulae approximating velocitytime-derivative, it is revealed that the connection point between the centraland tail parts of PDF extracted by theoretical analyses of PDFs is actually theboundary of the two kinds of instabilities associated respectively withcoherent and incoherent elements.

Analyses of turbulence in a wind tunnel by a multifractal theory for probability density functions