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

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.