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Extreme events in transitional turbulence.

Sébastien Gomé1, Laurette S Tuckerman1, Dwight Barkley2

  • 1Laboratoire de Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris, PSL Research University, Sorbonne Université, Université de Paris, Paris 75005, France.

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Summary
This summary is machine-generated.

Turbulence in shear flows can decay or spread. This study uses a rare-event algorithm to efficiently analyze transition paths and passage times in channel flow, revealing a self-similar regime and a most-probable pathway for decay or splitting events.

Keywords:
Large Deviation theoryextreme valuesrare eventstransitional turbulence

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Area of Science:

  • Fluid dynamics
  • Turbulence theory
  • Computational physics

Background:

  • Transitional localized turbulence in shear flows exhibits two main behaviors: decay to a laminar state or proliferation via splitting.
  • Passage times between these states depend super-exponentially on the Reynolds number, indicating a critical threshold for proliferation over decay.

Purpose of the Study:

  • To efficiently study transition paths and estimate large passage times in channel flow using a rare-event algorithm.
  • To establish a connection between turbulence transitions and extreme value distributions.
  • To investigate the self-similar nature of transitions and identify most-probable pathways.

Main Methods:

  • Application of the Adaptive Multilevel Splitting (AMS) rare-event algorithm.
  • Analysis of the deterministic Navier-Stokes equations for channel flow.
  • Connection to extreme value distributions and Large Deviation theory (instantons).

Main Results:

  • Efficient estimation of large passage times for turbulence transitions in channel flow.
  • Identification of a self-similar regime mediating transitions, dependent on the Reynolds number.
  • Demonstration that super-exponential passage time variations are linked to extreme value distribution parameters.
  • Observation that decay and splitting events converge to a most-probable pathway.

Conclusions:

  • The Adaptive Multilevel Splitting algorithm provides an efficient method for studying rare events in fluid dynamics.
  • Turbulence transitions in shear flows exhibit universal characteristics related to extreme value statistics and self-similarity.
  • Understanding these pathways is crucial for predicting and controlling turbulent behavior in various flow regimes.