Anisotropy and scaling corrections in turbulence

We analyze second-order turbulent velocity moments both in r and in p space. Finite size corrections induce dramatic differences between local r- and p-space scaling exponents. As analytically accessible examples we focus on two popular parametrizations: the Batchelor parametrization for the r-space structure function and a common parametrization for the energy spectrum, E(p)∝${\mathit{p}}^{\mathrm{-}5/3}$exp(-p/${\mathit{p}}_{\mathit{d}}$). The spectral bottleneck energy pileup hidden in the Batchelor parametrization results in an extended r-space scaling range, comparable to experimental ones for the same Taylor-Reynolds number ${\mathrm{Re}}_{\lambda }$. Shear effects are discussed in terms of (global) apparent scaling correction δ${\mathrm{\zeta }}^{\mathit{app}}$(${\mathrm{Re}}_{\lambda }$) to classical scaling, which again depend on whether looked at in r or in p space. The differences can be traced back to the subtleties of the crossovers in the velocity moments. Our observations emphasize the need for more experimental information on crossovers between different subranges. © 1996 The American Physical Society.