Eulerian-Lagrangian scaling of the Lyapunov exponent in homogeneous turbulence

We present a heuristic derivation of the maximal Lyapunov exponent $\gamma$ of homogeneous turbulence which yields two new relations, a sweeping relation and the scaling of the uncertainty field’s integral length $L_{\mathrm{\Delta }}$. These relations and the maximal Lyapunov exponent’s scaling that they imply are confirmed by periodic turbulence simulations. As the Reynolds number $R{e}_{\text{lammbda}}$ increases, $L_{\mathrm{\Delta }}$ and ${\gamma }^{-1}$ decrease towards values smaller than the Kolmogorov length and time scales.