Anisotropy and scaling corrections in turbulence

Abstract

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)\ensuremath{\propto}${\mathit{p}}^{\mathrm{\ensuremath{-}}5/3}$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 ${\mathrm{Re}}_{\ensuremath{\lambda}}$. Shear effects are discussed in terms of (global) apparent scaling correction \ensuremath{\delta}${\mathrm{\ensuremath{\zeta}}}^{\mathit{app}}$(${\mathrm{Re}}_{\ensuremath{\lambda}}$) 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. \textcopyright{} 1996 The American Physical Society.