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Stochastic-processes and Dynamical systems techniques for fluid mechanics

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Davide Faranda (CNRS-IPSL-LSCE)

We will discuss dynamical systems techniques to study predictability, metastable states and effective degrees of freedom of laboratory turbulent flows and geophysical flows. The main idea is to measure the deviations from the behavior expected by a turbulent observable when it is close to a transition between different metastable states. Whereas, far from the transitions, the dynamics can be represented by a simple Ornstein Uhlenbeck process, close to the tipping points or unstable regions of the phase space, the dynamics must be rapresented by a more complex process, that accounts for the different time-scales involved in the dynamics. We first assess the performance of our method on the Lorenz attractor and the von Karman flow. Then, we analyze few examples of geophysical flows: i) the hydrodynamic equilibrium properties of the stably stratified atmospheric boundary layer from measurements obtained in the Snow-Horizontal Array Turbulence Study (SnoHATS) campaign at the Plaine Morte Glacier in the Swiss Alps, ii) the zonal atmospheric mid-latitude flow and its transitions towards blocked states. The results show that the method recognizes subtle differences among different stable boundary layers turbulence regimes and may be used to help characterise their transitions.