Eulerian-Lagrangian scaling of the Lyapunov exponent in homogeneous turbulence

Abstract

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 $L_{\Delta }$. These relations and the maximal Lyapunov exponent's scaling that they imply are confirmed by periodic turbulence simulations. As the Reynolds number $Re_\lammbda$ increases, $L_{\Delta }$ and ${\gamma }^{-1}$ decrease towards values smaller than the Kolmogorov length and time scales.

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