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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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Visualization of High Speed Liquid Jet Impaction on a Moving Surface
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Flight-crash events in turbulence.

Haitao Xu1, Alain Pumir2, Gregory Falkovich3

  • 1International Collaboration for Turbulence Research, D-37077 Göttingen, Germany;Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany;

Proceedings of the National Academy of Sciences of the United States of America
|May 6, 2014
PubMed
Summary

Turbulence breaks detailed balance, meaning forward and backward transitions are unequal. Rare "flight-crash" events quantify this irreversibility, linking it to the range of active scales in turbulent flows.

Keywords:
Lagrangian descriptiondirect and inverse turbulent energy cascadesnonequilibrium statistical mechanicsnonequilibrium systemsturbulent mixing

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Area of Science:

  • Fluid dynamics
  • Statistical mechanics
  • Non-equilibrium systems

Background:

  • Turbulence exhibits statistical properties distinct from equilibrium systems due to energy transfer across scales.
  • Understanding the fundamental nature of turbulence requires investigating its deviation from equilibrium thermodynamics.

Purpose of the Study:

  • To elucidate the statistical differences between turbulent flows and equilibrium systems.
  • To demonstrate the breakdown of detailed balance in turbulent fluid dynamics.
  • To quantify irreversibility in turbulence using particle energy fluctuations.

Main Methods:

  • Experimental and numerical studies of fluid particle energy fluctuations in turbulent flows.
  • Analysis of the probabilities of forward and backward transitions.
  • Investigating the statistical signature of rare deceleration events.

Main Results:

  • Demonstrated the breaking of detailed balance in turbulence, with unequal forward and backward transition probabilities.
  • Observed that fluid elements decelerate more frequently than they accelerate.
  • Quantified irreversibility via the third moment of power fluctuations, showing a power-law dependence on Reynolds number.

Conclusions:

  • The breakdown of detailed balance is a key characteristic of turbulence, linked to the range of active scales.
  • Rare deceleration events serve as a statistical signature for quantifying irreversibility.
  • This breakdown of detailed balance may be a general feature of systems far from equilibrium with wide scale ranges.