Stochastic Chaos in a Turbulent Swirling Flow

LML External Fellow Yuzuru Sato has recently reported the experimental evidence of the existence of stochastic chaos in a turbulent swirling flow.  Together with co-authors (D. Faranda, B. Saint-Michel, C. Wiertel, V. Padilla, B. Dubrulle, and F. Daviaud), he shows that the experimental attractor can be modeled by a random strange attractor in stochastic Duffing equations. The article is published in Physical Review Letters:
In 1963, Lorenz constructed a simple model of dissipative hydrodynamic flows such as those encountered in atmospheric motions.  To his great surprise, he found that the possible solutions of his simple system were very sensitive to small perturbations of the initial conditions (i.e. deterministic chaos) but that, at the same time, their evolution always followed well-defined deterministic paths along a geometric object (i.e. the strange attractor) that looks like a butterfly.  For atmospheric motions, he conjectured the sensitivity of weather forecasts to small perturbations and that possible weathers would settle on strange attractors.  Until now, we have only been able to verify the first conjecture about weather sensitivity, whereas nobody was ever able to construct the “climate attractor.”  One explanation is provided by Landau’s observation that the dynamics of the turbulent flows which is responsible for the weather or climate dynamics can only be described by an enormous number of variables, thereby preventing description by any low dimensional attractors.
In our paper, we extend Landau’s view by revealing the existence of a “random strange attractor” in a turbulent laboratory flow, characterized by a huge number of variables, like in weather or climate flows.  Nevertheless, the attractors can be described via a random dynamical system with only three variables, like Lorenz’s toy model of atmosphere.  Our model however displays a new feature with respect to Lorenz’s model, namely a random component which encompasses the huge number of small scale degrees of freedom – the stochastic chaos.  Our work opens a new hunting season for stochastic butterflies in weather or climate dynamics.

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