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Slow diffusive structure in Nikolaevskii turbulence.

Takayuki Narumi1, Yoshiki Hidaka2

  • 1Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Ube 755-8611, Japan.

Physical Review. E
|March 15, 2020
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Summary
This summary is machine-generated.

Weak turbulence in the Nikolaevskii model exhibits superdiffusive particle motion near phase transitions. This scale-invariant diffusion suggests a hierarchical structure, simplified by a two-scale Brownian motion model.

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Area of Science:

  • Nonlinear and Nonequilibrium Physics
  • Turbulence Theory
  • Statistical Mechanics

Background:

  • Weak turbulence is crucial for understanding universal behaviors near critical points in complex systems.
  • The Nikolaevskii turbulence model provides a theoretical framework for studying one-dimensional weak turbulence.
  • Investigating ordered-disordered state transitions requires understanding underlying dynamic processes.

Purpose of the Study:

  • To theoretically analyze the one-dimensional Nikolaevskii turbulence model.
  • To elucidate the Lagrangian description of particle dynamics within this turbulent system.
  • To characterize the diffusion properties and scale invariance near transition points.

Main Methods:

  • Calculation of the velocity field for Nikolaevskii turbulence, assuming a convective structure.
  • Tagged-particle simulations within the turbulent flow to observe particle trajectories.
  • Analysis of diffusion behavior across different timescales and its dependence on control parameters.

Main Results:

  • Tagged particles exhibit superdiffusive behavior over intermediate timescales.
  • The diffusion of the slow structure follows a power law near the transition point.
  • Scale invariance of diffusive characteristics is observed for the slow structure.

Conclusions:

  • Nikolaevskii turbulence displays scale-invariant diffusive properties near phase transitions.
  • A simplified 'two-scale Brownian motion' model captures the hierarchical nature of this turbulence.
  • The findings contribute to understanding universal characteristics in nonlinear-nonequilibrium systems.