Finite size corrections to scaling in high Reynolds number turbulence
Siegfried Grossmann, Detlef Lohse, Victor L'vov, Itamar Procaccia
Abstract
We study analytically and numerically the corrections to scaling in turbulence which arise due to the finite ratio of the outer scale
L
of turbulence to the viscous scale
η
, i.e., they are due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations $\dzm$ from the classical Kolmogorov scaling
ζ
m
=m/3
of the velocity moments $\langle |\u(\k)|^m\rangle \propto k^{-\zeta_m}$ decrease like
δ
ζ
m
(Re)=
c
m
R
e
−3/10
. Our numerics employ a reduced wave vector set approximation for which the small scale structures are not fully resolved. Within this approximation we do not find
Re
independent anomalous scaling within the inertial subrange. If anomalous scaling in the inertial subrange can be verified in the large
Re
limit, this supports the suggestion that small scale structures should be responsible, originating from viscosity either in the bulk (vortex tubes or sheets) or from the boundary layers (plumes or swirls).