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Wall-bounded flows are extensively studied to understand the fundamental mechanisms and phenomena that occur in diverse applications involving shear flows.

These classical flows, such as pipelines and channel flows, serve as simple models for different physical scenarios. Some of the most interesting examples include transport systems in engineering, aerodynamics in the development of wind turbines, and climate studies, particularly modeling the planetary boundary layer, which is crucial for understanding air pollution dispersion.

This work focuses on the transition to turbulence in the plane Couette-Poiseuille flow (CPF), analyzing the mainly streamwise coherent structures that interact with each other, leading to turbulence in a process known as the Self-Sustaining Process (SSP) [1].

In [2], a simplified dynamical model capturing essential nonlinear physics was sugested to study the relationships between certain dynamic variables of the structures involved in this phenomenon such as rolls, streaks and ondulations of structures.

In this study, we performed direct numerical simulations of the CPF to observe how the physics described by the model manifests in the transition to turbulence and turbulence itself. Our results suggest a good agreement in the proposed relationship for some of the variables involved in the SSP and compare these with recent experimental results [3].

 

[1] Hamilton JM, Kim J, Waleffe F. Regeneration mechanisms of near-wall turbulence structures. Journal of Fluid Mechanics. 1995;287:317-348. https://doi.org/10.1017/S0022112095000978

[2] Fabian Waleffe; On a self-sustaining process in shear flows. Physics of Fluids 1 April 1997; 9 (4): 883–900. https://doi.org/10.1063/1.869185

[3] Liu T., Semin B., Godoy-Diana R., Wesfreid JE., Lift-up and streaks wavines drive the self-sustained process in wall-bounded transition to turbulence. Physical Review Fluids 9, March 2024; 9, 033901. https://doi.org/10.1103/PhysRevFluids.9.033901