Extreme events in transitional turbulence

TL;DR

This study uses a rare event algorithm to analyze transition paths in shear flow turbulence, revealing how extreme value distributions and self-similar regimes influence the super-exponential dependence of transition times on Reynolds number.

Contribution

It introduces the application of the Adaptative Multilevel Splitting algorithm to deterministic Navier-Stokes equations for studying transition paths in turbulence.

Findings

Transition times depend super-exponentially on Reynolds number.

Transition pathways are self-similar and linked to extreme value distributions.

Decay and splitting events follow most-probable pathways akin to instantons.

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.