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Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Causally coherent structures in turbulent dynamical systems.

Daniele Massaro1, Saleh Rezaeiravesh2, Philipp Schlatter3

  • 1Massachusetts Institute of Technology, Department of Mechanical Engineering, Cambridge 02139, Massachusetts, USA.

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Researchers used transfer entropy (TE) to uncover causal relationships in turbulent boundary layers. This information theory approach identifies causally coherent structures and dominant flow interactions, advancing the study of chaotic systems.

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Area of Science:

  • * Physics
  • * Mathematics
  • * Engineering

Background:

  • * Extracting spatiotemporal coherence from chaotic, nonlinear dynamical systems like turbulent flows is a significant challenge.
  • * Existing methods like correlation and spectral analysis have limitations in capturing complex causality.
  • * Information theory offers novel approaches to understand system dynamics.

Purpose of the Study:

  • * To employ Shannon transfer entropy (TE) for identifying causally coherent motions in turbulent boundary layers (TBLs).
  • * To introduce and define causally coherent structures (CCS) as spatiotemporal patterns of causality.
  • * To adapt TE for wall-bounded flows and analyze information fluxes across different TBL regions.

Main Methods:

  • * Application of Shannon transfer entropy (TE), an information theory metric, to time series data from TBLs.
  • * Development of an adaptive tuning method for TE hyperparameters, specifically the Markovian order (m).
  • * Utilization of net transfer entropy flux to pinpoint source and target regions within the boundary layer.

Main Results:

  • * Successful identification of causally coherent structures (CCS) in a zero-pressure-gradient TBL.
  • * Characterization of information fluxes in the viscous, logarithmic, and outer layers of the TBL.
  • * Demonstration of dominant top-down interactions between inner and outer layers, analogous to energy cascades.

Conclusions:

  • * Transfer entropy provides a powerful, generalizable method for analyzing causality in complex dynamical systems.
  • * The concept of causally coherent structures offers new insights into the organization of turbulent flows.
  • * This approach has broad applicability beyond fluid dynamics, including cognitive sciences, systems biology, and finance.