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Published on: September 28, 2021
An optimal path to transition in a duct
Damien Biau1, Alessandro Bottaro
1DICAT, University of Genova, 1 via Montallegro, Genoa, Italy. damien.biau@univ-poitiers.fr
Summary
This study investigates laminar-turbulent transition in square ducts, focusing on the bypass route. Optimal travelling waves were identified, showing similarity to minimal defect solutions and mediating transition.
Area of Science:
- Fluid dynamics
- Turbulence studies
- Nonlinear dynamics
Background:
- Laminar flow in square ducts is linearly stable, making it a model for bypass transition.
- Classical optimal perturbations (longitudinal vortices) do not effectively trigger turbulence via nonlinear response.
- Previous simulations suggest travelling waves initiate rapid breakdown through nonlinear interactions.
Purpose of the Study:
- To identify optimal travelling waves that lead to turbulence in a square duct flow.
- To investigate the relationship between optimal solutions and minimal defect states.
- To explore the role of edge states in mediating laminar-turbulent transition.
Main Methods:
- Variational approach to find optimal travelling waves by quantifying sensitivity to base flow deviations.
- Time integration of optimal solutions.
- Numerical simulations of edge states.
Main Results:
- An optimal travelling wave solution was identified, exhibiting qualitative similarity to minimal defect solutions.
- Numerical simulations of edge states were performed.
- The identified edge state mediates laminar-turbulent transition.
Conclusions:
- Optimal travelling waves play a crucial role in the bypass route to turbulence.
- Edge states are important unstable solutions that bridge laminar and turbulent flows.
- The findings provide insights into the mechanisms of transition in channel flows.
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