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Interoccurrence time statistics in fully-developed turbulence.

Pouya Manshour1, Mehrnaz Anvari2, Nico Reinke2

  • 1Department of Physics, Faculty of Sciences, Persian Gulf University, Bushehr 75169, Iran.

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Summary
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Extreme events in turbulent flows follow a universal pattern. The time intervals between these events are described by a q-exponential function, offering new insights into complex dynamical systems.

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Area of Science:

  • Physics
  • Complex Systems
  • Fluid Dynamics

Background:

  • Extreme events are characteristic of complex dynamical systems.
  • Understanding the statistics of time intervals between extreme events is crucial for analyzing stochastic dynamics.

Purpose of the Study:

  • To investigate the statistical properties of interoccurrence times for extreme events in turbulent flows.
  • To determine if a universal function describes these time intervals across different turbulent flow configurations.

Main Methods:

  • Analysis of extensive experimental data from various turbulent flow setups (grid, cylinder, helium jet, air jet).
  • Calculation of Taylor Reynolds numbers (Reλ) ranging from 166 to 893.
  • Statistical analysis of interoccurrence time distributions P(τ) above a positive threshold Q in the inertial range.

Main Results:

  • The interoccurrence time distributions P(τ) in the inertial range of turbulent flows are universally described by a q-exponential function.
  • The derived universal function is P(τ) = β(2-q)[1-β(1-q)τ](1/(1-q)).
  • This universality may stem from the superstatistical nature of extreme event occurrences.

Conclusions:

  • A universal statistical description for extreme events in turbulent flows has been established.
  • The findings contribute to a deeper understanding of the stochastic dynamics in complex systems.
  • The q-exponential function provides a powerful tool for characterizing extreme events in turbulence.