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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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Turbulent Flows Are Not Uniformly Multifractal.

Siddhartha Mukherjee1,2, Sugan Durai Murugan1,3, Ritwik Mukherjee1

  • 1International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India.

Physical Review Letters
|May 17, 2024
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Summary
This summary is machine-generated.

Turbulence research reveals that while energy dissipation is often multifractal, large regions remain monofractal, challenging existing theories. This finding offers new insights into anomalous dissipation and intermittency.

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Area of Science:

  • Fluid Dynamics
  • Statistical Physics

Background:

  • Kolmogorov's 1941 theory posits nonintermittent energy dissipation in turbulence.
  • Empirical evidence shows intermittency, multiscaling, and multifractality, contradicting the 1941 theory.
  • Multifractality is not typically viewed as a local flow property.

Purpose of the Study:

  • To investigate local multifractality in turbulent energy dissipation.
  • To reconcile the conflict between Kolmogorov's theory and observed intermittency.
  • To explore potential links between local multifractality and anomalous dissipation or finite-time blowup.

Main Methods:

  • A simple construction was developed to model local multifractality.
  • Analysis of the energy dissipation field to identify regions of monofractality and multifractality.
  • Quantification of the relationship between multifractality strength and local energy dissipation fluctuations.

Main Results:

  • A significant portion of the energy dissipation field exhibits monofractality, consistent with Kolmogorov's theory.
  • Multifractality emerges in localized regions, described as 'small islands'.
  • The strength of multifractality increases logarithmically with local fluctuations in energy dissipation, suggesting universality.

Conclusions:

  • The findings suggest a nuanced view of turbulence, where both monofractal and multifractal characteristics coexist.
  • The localized nature of multifractality provides a new perspective on understanding singularities, anomalous dissipation, and intermittency.
  • The proposed approach is adaptable for applications in diverse fields like climate science and medical data analysis.