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Aging and memory of transitional turbulence.

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Turbulence onset in channel flow is not memoryless, challenging the directed percolation model. Localized turbulent stripes exhibit aging, diverging from theoretical predictions for pipe and Couette flows.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • The transition to turbulence in shear flows is often modeled as a directed percolation (DP) phase transition.
  • A key assumption of the DP analogy is the memoryless nature of turbulent sites.

Purpose of the Study:

  • To investigate the memory properties of turbulent stripe decay and proliferation in channel flow.
  • To assess the validity of the directed percolation analogy for channel flow turbulence onset.
  • To explore the applicability of the chaotic saddle interpretation to localized turbulent stripes.

Main Methods:

  • Analysis of survival curves for isolated turbulent stripes in channel flow.
  • Comparison of channel flow dynamics with established models for pipe and Couette flows.

Main Results:

  • Turbulent stripe decay and proliferation in channel flow are not memoryless.
  • Isolated channel stripes exhibit aging near the critical point.
  • The one-to-one mapping between turbulent stripes and DP sites is not fulfilled in this regime.
  • The chaotic saddle interpretation does not apply to individual localized stripes.

Conclusions:

  • The directed percolation analogy, based on memoryless sites, is inadequate for channel flow turbulence onset.
  • Geometric differences in shear flows can fundamentally alter turbulence transition mechanisms.
  • Localized turbulent structures in channel flow possess distinct dynamics compared to idealized DP models.