Inertial range and the finite Reynolds number effect of turbulence

Abstract

The Kolmogorov law, which is the unique, exact relationship of inertial-range statistics, is applied to investigate the finite Reynolds number effect, in particular to study how the width of the inertial range of finite Reynolds number turbulence changes with the Taylor microscale Reynolds number ${\mathrm{R}}_{\ensuremath{\lambda}}$ . It is found that there is no inertial range when ${\mathrm{R}}_{\ensuremath{\lambda}}$ \ensuremath{\leqslant}2000 and, within tolerance of 1% error, ${\mathrm{R}}_{\ensuremath{\lambda}}$ should be higher than ${10}^{4}$ in order to have an inertial range wider than one decade. The so-called inertial range found in experiments and simulations is just a scaling range and is not the same as Kolmogorov's inertial range. The finite Reynolds number effect cannot be neglected within such a scaling range and should be considered in comparing experiments (or simulations) with theories of the inertial-range statistics.