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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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This study introduces a dynamical framework to understand intermittent reversals and excursions in turbulent circulations. It shows these events arise from unstable periodic orbits, enabling prediction and control of extreme flow fluctuations.

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Area of Science:

  • Fluid dynamics
  • Turbulence theory
  • Dynamical systems

Background:

  • Large-scale circulations in turbulence exhibit intermittent reversals and excursions (R&Es).
  • Understanding the underlying mechanisms of these extreme events is crucial for predicting and controlling turbulent flows.

Purpose of the Study:

  • To present a novel dynamical framework for analyzing intermittent reversals and excursions (R&Es) in turbulent flows.
  • To demonstrate how R&Es can be predicted and controlled using insights from dynamical systems theory.

Main Methods:

  • Developing a dynamical framework based on phase space trajectories and invariant manifolds.
  • Utilizing unstable periodic orbits (UPOs) and their associated manifolds to reconstruct flow dynamics.
  • Implementing closed-loop control strategies to preemptively avert extreme events.

Main Results:

  • R&Es occur when turbulent trajectories shadow invariant manifolds of specific unstable periodic orbits (UPOs).
  • Flow reorganization and extreme fluctuations during R&Es can be reconstructed by splicing unstable manifolds of dynamically relevant UPOs.
  • The framework enables the prediction of imminent R&Es.

Conclusions:

  • The geometrical dynamical framework provides a new perspective on intermittent extreme events in turbulence.
  • Predictive capabilities allow for preemptive control of R&Es, offering potential applications in managing turbulent systems.