On the importance of stochasticity in closures of turbulence

Deterministic closures for coarse-grained turbulence models help reproduce mean statistics, but often fail to capture the finite-time growth of uncertainty. Using the framework of shell models as a quantitative multi-scale testbed, we compare fully resolved simulations with large-eddy simulations using either stochastic or deterministic subgrid closures. While in the fully resolved system a single microscopic perturbation is rapidly amplified by strongly chaotic dynamics, truncation produces a strong delay and suppression of variance growth when uncertainty is introduced through initial condition perturbations only. We show that a data-driven Langevin-type stochastic closure restores the correct timing and magnitude of variance growth across scales, demonstrating that sustained stochasticity is essential for predictability in reduced turbulent dynamics.