Extreme events in transitional turbulence

Abstract

Transitional localised turbulence in shear flows is known to either decay to an absorbing laminar state or proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare event algorithm, Adaptative Multilevel Splitting (AMS), to the deterministic Navier-Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds-number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation Theory, we show that decay or splitting events approach a most-probable pathway.

arXiv comment29 pages, 14 figures, 5 tables. Contribution to a theme issue 'Mathematical problems in fluid dynamics (part 2)'

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