An alternative definition of order dependent dissipation scales

Abstract

While Kolmogorov's similarity hypothesis suggests that velocity structure functions scale with the mean dissipation $\left< \varepsilon \right>$ and the viscosity $\nu$, we find that the $2m.$ even order scales with $\left< \varepsilon^m \right>$. This implies that there are other cut-off lengths than the Kolmogorov length $\eta$. These cut-off lengths are smaller than $\eta$ and decrease with increasing order and Reynolds-number. They are compared to a previous definition of order dependent dissipative scales by Schumacher~et.~al\cite{schumacher2007asymptotic}.