On the importance of stochasticity in closures of turbulence

TL;DR

This paper demonstrates that incorporating stochasticity into turbulence closure models is crucial for accurately capturing the growth of uncertainty and predictability in coarse-grained turbulence simulations, using shell models as a testbed.

Contribution

The study shows that a data-driven Langevin-type stochastic closure effectively restores variance growth in turbulence models, highlighting the importance of stochasticity for accurate predictions.

Findings

Stochastic closures reproduce the timing and magnitude of variance growth.

Deterministic closures delay and suppress uncertainty growth.

Stochasticity is essential for predictability in turbulence models.

Abstract

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.