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Laminar chaotic saddle within a turbulent attractor.

Hibiki Kato¹, Miki U Kobayashi², Yoshitaka Saiki³

¹Faculty of Commerce and Management, <a href="https://ror.org/04jqj7p05">Hitotsubashi University</a>, Tokyo 186-8601, Japan.

Physical Review. E

|December 18, 2024

Summary

This study reveals chaotic saddles as the underlying mechanism for intermittency in high-dimensional systems like fluid turbulence. These structures, characterized by periodic orbits, persist across a wide parameter range, explaining observed chaotic state switching.

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Area of Science:

Complex Systems Dynamics
Nonlinear Physics
Fluid Turbulence

Background:

Intermittent switching between laminar and bursty states is common in high-dimensional chaotic systems, notably fluid turbulence.
This phenomenon differs from low-dimensional intermittency, often appearing across broad parameter ranges in complex systems.

Purpose of the Study:

To investigate the role of chaotic saddles in high-dimensional intermittency.
To characterize laminar states within chaotic attractors using chaotic saddle structures.
To demonstrate the presence and persistence of chaotic saddles in fluid turbulence and phase synchronization.

Main Methods:

Characterization of laminar states (L) as chaotic subsets (S) of chaotic attractors (X), denoted S ⊊ X.
Analysis of chaotic saddles, defined as sets densely filled with periodic orbits possessing varying unstable directions.
Modeling and simulation of turbulent systems to identify underlying chaotic saddle dynamics.

Main Results:

The study demonstrates that chaotic saddles underlie intermittency in fluid turbulence and phase synchronization phenomena.
Chaotic saddles were confirmed to persist across a wide range of system parameters.
A form of phase synchronization was observed to occur within the turbulent model studied.

Conclusions:

Chaotic saddles provide a robust framework for understanding intermittency in high-dimensional chaotic systems.
The persistence of chaotic saddles explains the wide parameter range over which intermittency is observed.
The findings link chaotic saddle dynamics to phenomena like phase synchronization in turbulent systems.