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Talk

Spontaneous stochasticity in intermittent random flows

  • André Considera (IMPA / Université Paris-Saclay)
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Abstract

pontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that particles advected by rough turbulent flows and subjected to additional thermal noise remain non-deterministic in the limit where the random input — namely, the thermal noise — vanishes.

In this talk, we investigate the spontaneous stochasticity of Lagrangian particles advected by one-dimensional, white-in-time, and intermittent-in-space velocity fields constructed using Gaussian multiplicative chaos (GMC) theory. This framework generalizes the classical Kraichnan model of turbulent transport by introducing intermittency in the spatial variable.

In an averaged sense, our intermittent fields are rougher than their Gaussian counterparts. Considerations from the Kraichnan model suggest that this increased roughness should render the spontaneous stochastic nature of particles more pronounced in intermittent flows. However, systematic Monte Carlo simulations reveal a less intuitive interplay, namely, a transition between spontaneously stochastic and deterministic behaviors as the level of intermittency increases. The numerical evidence is supplemented with a theoretical analysis that views particle dynamics as random motion in a random environment induced by the GMC. This approach allows us to establish the aforementioned phase transition at a theoretical level.

While its key ingredient in the Gaussian setting, surprisingly, roughness here conspires against the spontaneous stochasticity of trajectories.

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