17 Feb 2024 | Dmytro Bandak, Alexei Mailybaev, Gregory L. Eyink, and Nigel Goldenfeld
The paper explores the phenomenon of spontaneous stochasticity in turbulent flows, where small-scale noise can trigger unpredictable and stochastic behavior at large scales. The authors use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the non-uniqueness of solutions to the Euler equation, leads to universal statistics at finite times, even though individual flow realizations are not predictable. They show that thermal noise alone, without any larger disturbances, can trigger spontaneous stochasticity. The findings suggest that intrinsic stochasticity in turbulent fluid motions at all scales can be triggered by molecular noise, with implications for modeling in various fields such as engineering, climate, astrophysics, and cosmology. The study uses a simplified dynamical model, the Sabra model, to demonstrate that the probability distributions of relevant flow quantities exhibit universal, non-delta-function forms at large but finite Reynolds numbers. This work provides crucial evidence for the existence of spontaneous stochasticity in turbulent flows and highlights its potential impact on the predictability of complex systems.The paper explores the phenomenon of spontaneous stochasticity in turbulent flows, where small-scale noise can trigger unpredictable and stochastic behavior at large scales. The authors use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the non-uniqueness of solutions to the Euler equation, leads to universal statistics at finite times, even though individual flow realizations are not predictable. They show that thermal noise alone, without any larger disturbances, can trigger spontaneous stochasticity. The findings suggest that intrinsic stochasticity in turbulent fluid motions at all scales can be triggered by molecular noise, with implications for modeling in various fields such as engineering, climate, astrophysics, and cosmology. The study uses a simplified dynamical model, the Sabra model, to demonstrate that the probability distributions of relevant flow quantities exhibit universal, non-delta-function forms at large but finite Reynolds numbers. This work provides crucial evidence for the existence of spontaneous stochasticity in turbulent flows and highlights its potential impact on the predictability of complex systems.