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Critical "dimension" in shell model turbulence.

Paolo Giuliani1, Mogens H Jensen, Victor Yakhot

  • 1Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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Researchers explored the Gledzer-Ohkitani-Yamada (GOY) shell model at a critical dimension in turbulence. They found a critical point where energy flux reverses and helicity flux diverges, impacting turbulent scaling and thermal equilibrium.

Area of Science:

  • Fluid Dynamics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Fully developed turbulence exhibits complex dynamics governed by energy transfer across scales.
  • The Gledzer-Ohkitani-Yamada (GOY) shell model provides a simplified framework for studying turbulence.
  • Investigating turbulence at critical dimensions can reveal fundamental properties and phase transitions.

Purpose of the Study:

  • To analyze the Gledzer-Ohkitani-Yamada (GOY) shell model at a critical dimension.
  • To identify the behavior of energy and helicity fluxes near this critical point.
  • To understand the interplay between turbulent scaling, thermal equilibrium, and intermittency corrections.

Main Methods:

  • Numerical simulations of the GOY shell model with varying conserved quantities to adjust the effective dimension.

Related Experiment Videos

  • Analysis of energy and helicity flux behavior as the system approaches the critical dimension.
  • Examination of energy spectra and intermittency corrections near the critical point.
  • Application of scaling laws and rescaling arguments to derive critical exponent relations.

    • Main Results:

    • A critical point was identified where the energy flux changes sign and the helicity flux diverges.
    • The energy spectrum shows a turbulent scaling regime followed by a thermal equilibrium plateau near the critical point.
    • Intermittency corrections were found to persist even close to the critical point.
    • Scaling laws and a rescaling argument were used to establish relations between critical exponents.

    Conclusions:

    • The critical dimension in the GOY shell model signifies a transition in turbulent energy transfer.
    • The observed phenomena, including sign reversal of energy flux and spectral behavior, offer insights into turbulence theory.
    • The persistence of intermittency corrections highlights the complexity of turbulent systems even at critical points.