Finite size corrections to scaling in high Reynolds number turbulence.

Abstract

We study analytically and numerically the corrections to scaling in turbulence which arise due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations \ensuremath{\delta}${\mathrm{\ensuremath{\zeta}}}_{\mathit{m}}$ from the classical Kolmogorov scaling ${\mathrm{\ensuremath{\zeta}}}_{\mathit{m}}$=m/3 of the velocity moments 〈\ensuremath{\Vert}u(k)${\mathrm{\ensuremath{\Vert}}}^{\mathit{m}}$〉\ensuremath{\propto}${\mathit{k}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\zeta}}\mathit{m}}$ decrease like \ensuremath{\delta}${\mathrm{\ensuremath{\zeta}}}_{\mathit{m}}$(Re)=${\mathit{c}}_{\mathit{m}}$${\mathrm{Re}}^{\mathrm{\ensuremath{-}}3/10}$. If, on the contrary, anomalous scaling in the inertial subrange can experimentally be verified in the large Re limit, this will support the suggestion that small scale structures should be responsible, originating form viscous effects either in the bulk (vortex tubes or sheets) or from the boundary layers (plumes or swirls), as both are underestimated in our reduced wave vector set approximation of the Navier-Stokes dynamics.