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Characterization of the hairpin vortex solution in plane Couette flow
Sotos C Generalis1, Tomoaki Itano
1School of Engineering and Applied Sciences, Mathematics, Aston University, Birmingham, United Kingdom. s.c.generalis@aston.ac.uk
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
This study provides quantitative evidence for the hairpin vortex state (HVS) in plane Couette flow (PCF). The hairpin vortex state can be achieved through homotopy from laterally heated flow, linking to Rayleigh-Bénard convection.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Turbulence
Background:
- The hairpin vortex state (HVS) is a significant structure in turbulent flows.
- Plane Couette flow (PCF) serves as a fundamental model for studying fluid dynamics.
- Previous research explored bifurcations in laterally heated flow (LHF), but lacked quantitative evidence for HVS in PCF.
Purpose of the Study:
- To provide quantitative evidence for the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF).
- To demonstrate a method for obtaining the HVS in PCF via homotopy from LHF.
- To investigate the bifurcation pathways of the HVS.
Main Methods:
- Linear stability analysis of laterally heated flow (LHF).
- Homotopy continuation method to transition from LHF to PCF.
- Analysis of symmetry breaking in bifurcations.
Main Results:
- Quantitative evidence confirming the existence of the HVS in PCF.
- Demonstration that HVS can be obtained from LHF through homotopy.
- Identification of multiple branches arising from LHF bifurcations via symmetry breaking, connecting to the PCF manifold.
- The HVS exhibits a direct bifurcation route to Rayleigh-Bénard convection.
Conclusions:
- The hairpin vortex state (HVS) is demonstrably present in plane Couette flow (PCF).
- A novel pathway to generate HVS in PCF from LHF is established.
- The HVS serves as a crucial link between different fluid flow regimes, including Rayleigh-Bénard convection.
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