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Linear Instability of Turbulent Channel Flow.

Pavan V Kashyap1,2, Yohann Duguet1, Olivier Dauchot3

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Summary
This summary is machine-generated.

Laminar-turbulent patterns in shear flows arise from spatial modulation of turbulence, driven by a linear instability. This study accurately estimates the modulation

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Area of Science:

  • Fluid dynamics
  • Turbulence theory
  • Nonlinear dynamics

Background:

  • Subcritical plane shear flows exhibit intermittency, characterized by laminar-turbulent pattern formation.
  • Understanding the onset and dynamics of these patterns is crucial for predicting turbulent behavior.

Purpose of the Study:

  • To investigate the mechanism behind laminar-turbulent pattern formation in subcritical plane shear flows.
  • To accurately estimate the wave vector of spatial modulation at the onset of instability.

Main Methods:

  • Extensive numerical simulations of plane channel flow.
  • Sampling the linear response of the turbulent field to temporal impulses.
  • Constructing the dispersion relation from ensemble-averaged relaxation rates.

Main Results:

  • The laminar-turbulent pattern emerges from a spatial modulation of the turbulent flow.
  • This modulation is driven by a linear instability.
  • The relaxation rate of the least damped modes approaches zero as the instability threshold is neared.

Conclusions:

  • The study provides a method to accurately estimate the wave vector of modulation at onset.
  • This estimation is achieved despite turbulent fluctuations and without closure models.
  • The findings offer insights into the fundamental mechanisms of pattern formation in shear flows.