Nonlinear phase synchronization and the role of spacing in shell models

Area of Science:

• * Physics
• * Fluid Dynamics
• * Complex Systems

Background:

• * Shell models represent turbulent energy cascades as chains of interacting nonlinear oscillators.
• * Phase dynamics and synchronization are crucial for understanding energy transfer in these systems.
• * Intermittency, characterized by burst-like events, is a key feature of turbulence.

Purpose of the Study:

• * To investigate the relationship between phase dynamics, synchronization, and intermittency in shell models.
• * To explore how phase alignment influences energy transfer and cascade processes.
• * To analyze the role of phase organization in both forward and inverse energy cascades.

Main Methods:

• * Simulation of interacting nonlinear oscillators (triads) within a shell model framework.
• * Application of the Kuramoto order parameter to quantify global and local phase coherence.
• * Analysis of probability distribution functions (PDFs) of triadic phases.

Main Results:

• * Synchronization is linked to increased energy transfer and intermittency.
• * Decreased shell spacing leads to increased intermittency due to enhanced phase alignment.
• * Local phase-locked states correlate with extreme energy flux events.
• * Reduced phase coherence in helical models suppresses intermittency.
• * Specific phase organizations are necessary for sustaining inverse energy cascades.

Conclusions:

• * Phase dynamics play a critical role in mediating energy transfer and intermittency in turbulent systems.
• * The Kuramoto order parameter effectively quantifies phase coherence at different scales.
• * Triadic phase organization is key to controlling the direction and efficiency of energy cascades.