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Related Experiment Videos

Unstable periodic solutions embedded in a shell model turbulence.

Sei Kato1, Michio Yamada

  • 1Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Meguro-ku, Komaba, Tokyo 153-8914, Japan. seikato@jp.ibm.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
Summary

We propose a dynamical systems approach to shell model turbulence intermittency. Unstable solutions, including an unstable periodic orbit (UPO), reveal nonlinear scaling exponents similar to turbulent flows, explaining intermittency.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Turbulence intermittency presents a major challenge in fluid dynamics.
  • The Gledzer-Ohkitani-Yamada (GOY) shell model is a simplified system used to study turbulence.
  • Understanding intermittency requires advanced theoretical frameworks like dynamical systems theory.

Purpose of the Study:

  • To investigate the intermittency of shell model turbulence using a dynamical systems perspective.
  • To identify the dynamical mechanisms underlying intermittent behavior in the GOY model.
  • To connect the properties of unstable solutions to observed turbulence statistics.

Main Methods:

  • Analysis of unstable solutions within the Gledzer-Ohkitani-Yamada shell model.

Related Experiment Videos

  • Detection and characterization of unstable periodic orbits (UPOs).
  • Examination of scaling exponents of the structure function and phase space attractors.

    • Main Results:

    • An unstable periodic orbit (UPO) was identified in the GOY shell model.
    • This UPO exhibits intermittency with nonlinear scaling exponents, mirroring turbulence.
    • The system's attractor is approximated by solutions derived from the UPO, suggesting its significance.

    Conclusions:

    • The unstable periodic orbit (UPO) provides a dynamical explanation for intermittency in the shell model turbulence.
    • This approach offers a novel perspective on turbulence intermittency through the lens of dynamical systems.
    • The findings highlight the role of unstable dynamics in complex systems like turbulence.