Spontaneous stochasticity in the presence of intermittency

Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in the limit where the random input, namely the thermal noise, vanishes. Here, we investigate the fate of spontaneous stochasticity in the presence of spatial intermittency, with multifractal scaling of the lognormal type, as usually encountered in turbulence studies. In principle, multifractality enhances the underlying roughness, and should also favor the spontaneous stochasticity. This letter exhibits a case with a less intuitive interplay between spontaneous stochasticity and spatial intermittency. We specifically address Lagrangian transport in unidimensional multifractal random flows, obtained by decorating rough Markovian monofractal Gaussian fields with frozen-in-time Gaussian multiplicative chaos. Combining systematic Monte-Carlo simulations and formal stochastic calculations, we evidence a transition between spontaneously stochastic and deterministic behaviors when increasing the level of intermittency. While its key ingredient in the Gaussian setting, roughness here suprisingly conspires against the spontaneous stochasticity of trajectories.