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Updated: Jul 3, 2026
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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Probability distributions of turbulent energy
Mahdi Momeni1, Wolf-Christian Müller
1Faculty of Physics, Tabriz University, Tabriz 51664, Iran.
Summary
Energy fluctuations in turbulent systems, including magnetohydrodynamics (MHD), show self-similar patterns across all scales. These patterns resemble Lévy distributions, offering new insights into energy transfer in turbulence.
Area of Science:
- Fluid Dynamics
- Plasma Physics
- Statistical Mechanics
Background:
- Turbulence involves complex energy transfer across various scales.
- Understanding the statistical properties of these fluctuations is crucial for modeling turbulent phenomena.
- Previous studies on turbulent velocity fluctuations show scale-dependent probability density functions (PDFs).
Purpose of the Study:
- To investigate the probability density functions (PDFs) of scale-dependent energy fluctuations.
- To compare these PDFs in Navier-Stokes and magnetohydrodynamic (MHD) turbulence with and without a mean magnetic field.
- To analyze the self-similarity and scaling properties of energy fluctuations.
Main Methods:
- High-resolution direct numerical simulations of Navier-Stokes and incompressible MHD turbulence.
- Analysis of energy fluctuation PDFs, P[deltaE(l)], across different scales.
- Comparison of simulation results with solar-wind measurements.
Main Results:
- PDFs of inertial range energy fluctuations exhibit self-similarity and monoscaling in all simulated systems.
- Energy PDFs show consistent similarity across all scales, unlike turbulent velocity PDFs.
- The observed PDFs approximate Lévy-type gamma distributions, P[deltaE(l)] ~ |deltaE|{-gamma} exp(-|deltaE|/Delta).
Conclusions:
- The study confirms monoscaling and self-similarity of energy fluctuations in turbulent systems.
- Lévy-type distributions characterize energy fluctuations, suggesting a universal behavior in energy transfer.
- Findings align with solar-wind measurements and provide a basis for turbulence modeling.
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