We investigate the Reynolds-number dependence of the maximal Lyapunov exponent in fully developed turbulence, which quantifies the rate of chaotic divergence of nearby velocity fields. Using decorrelators constructed from infinitesimally perturbed flows, we find that the Lyapunov exponent scales with Reynolds number as $\lambda \sim {\mathrm{Re}}^{\alpha }$, with an exponent $\alpha =0.59\pm 0.04$ exceeding the classical mean-field prediction. By explicitly separating the nonlinear strain and viscous contributions to decorrelator growth, we show that this departure is associated by intermittent fluctuations of the strain-rate tensor, which dominate the short-time growth of the infinitesimal perturbations over viscous damping. Direct numerical simulations of the Navier-Stokes equations and complementary tests using a reduced shell model yield consistent scaling behavior, indicating robustness within the frameworks considered. Our results show that the dynamical origin of chaotic divergence in turbulence is closely linked to intermittent strain-rate fluctuations.

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• Chaos
• Classical statistical mechanics
• Intermittency
• Three-dimensional turbulence
• Classical fluids
• Dynamical systems