Scaling hypothesis leading to generalized extended self-similarity in turbulence

Hirokazu Fujisaka, Yasuya Nakayama, Takeshi Watanabe, Siegfried Grossmann

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9 Citations (Scopus)


A scaling hypothesis leading to generalized extended self-similarity (GESS) for velocity structure functions, valid for intermediate scales in isotropic, homogeneous turbulence, is proposed. By introducing an effective scale r̂, monotonically depending on the physical scale r, with the use of the large deviation theory, the asymptotic forms of the probability densities for the velocity differences ur and for the coarse-grained energy-dissipation rate fluctuations εr, compatible with this GESS, are proposed. The probability density for εr is shown to have the form P r(ε)∼ε-1(r̂/L) sr̂(zr̂(ε)) with zr̂(ε)=ln(ε/ εL)/ln(L/r̂), where L and εL are the stirring scale and the coarse-grained energy-dissipation rate over the scale L. The concave function Sr̂(z), the spectrum, plays the central role of the present approach. Comparing the results with numerical and experimental data, we explicitly obtain the fluctuation spectra Sr̂(z).

Original languageEnglish
Article number046307
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
Publication statusPublished - Apr 1 2002
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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