Statistical laws and vortex structures in fully developed turbulence

Fully developed turbulence is structured with a number of intense elongated vortices. Recognizing that statistical laws are related to such structures , the flow field is modeled by an ensemble of strained vortices (i.e. Burge rs vortices) distributing randomly in space, from which probability density functions (pdfs) for longitudinal and transversal components of velocity d ifference are derived by taking statistical averages ensuring isotropy and homogeneity for the velocity field. It is found that the pdfs tend to close -to-exponential forms at small scales, and that there exist two scaling ran ges in the structure function of every order, which are identified as the v iscous range and inertial range, respectively, with a transition scale betw een the two ranges being at the order of mean size of Burgers vortices. Vel ocity structure functions show scaling behaviors in the second interval cor responding to the inertial range with the scaling exponents close to those known in the experiments and direct numerical simulations. It is remarkable that the Kolmogorov's four-fifths law is observed to be valid in a small-s cale range. The scaling exponents of higher order structure functions are n umerically estimated up to the 25th order. It is found that asymptotic scal ing exponents, as the order increases, are in good agreement with the behav ior of a recent experiment. The above model analysis is considered to repre sent successfully the statistical behaviors at small scales (possibly less than the Taylor microscale) and higher orders. The present statistical anal ysis leads to scale-dependent probability density functions. (C) 2000 The J apan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserv ed.