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Stochastic Model for Quasi-One-Dimensional Transitional Turbulence with Streamwise Shear Interactions.

Xueying Wang1, Hong-Yan Shih2, Nigel Goldenfeld1,3

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We developed a minimal model for turbulent flow transitions. This model explains how turbulent patches grow, split, and decay in pipe and Taylor-Couette flows near the critical Reynolds number.

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Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Statistical Mechanics

Background:

  • Subcritical transition to turbulence in wall-bounded flows is complex.
  • The interplay of fluctuations, pattern formation, and stochasticity is not fully understood.
  • Understanding this transition is crucial for various engineering applications.

Purpose of the Study:

  • To present a spatially extended stochastic minimal model for transitional pipe flow.
  • To investigate the dynamics of turbulent patches (puffs) during laminar-turbulent transition.
  • To extend the model to other geometries like Taylor-Couette flow.

Main Methods:

  • Developed a minimal model focusing on the energy budget.
  • Incorporated spatial extension and stochasticity.
  • Applied the model to pipe flow and quasi-one-dimensional Taylor-Couette flow.

Main Results:

  • The model successfully recapitulates puff decay, splitting, and growth with increasing Reynolds number.
  • The model reproduces the directed percolation pattern observed in turbulent patches.
  • The model accounts for flow geometry, demonstrating its versatility.

Conclusions:

  • The developed stochastic minimal model provides a framework for understanding transitional turbulence.
  • The findings offer insights into the spatio-temporal dynamics of turbulent structures.
  • The model's success in different flow geometries highlights its general applicability.