Finite-size scaling of two-point statistics and the turbulent energy cascade generators

Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Feb;71(2 Pt 2):026309. doi: 10.1103/PhysRevE.71.026309. Epub 2005 Feb 28.


Within the framework of random multiplicative energy cascade models of fully developed turbulence, finite-size-scaling expressions for two-point correlators and cumulants are derived, taking into account the observationally unavoidable conversion from an ultrametric to an Euclidean two-point distance. The comparison with two-point statistics of the surrogate energy dissipation, extracted from various wind tunnel and atmospheric boundary layer records, allows an accurate deduction of multiscaling exponents and cumulants, even at moderate Reynolds numbers for which simple power-law fits are not feasible. The extracted exponents serve as input for parametric estimates of the probabilistic cascade generator. Various cascade generators are evaluated.