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Canonical exact coherent structures embedded in high Reynolds number flows
1Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
Summary
This study explores exact coherent structures in shear flows using vortex-wave interaction theory and freestream coherent structures. These findings define new structures in unbounded flows and show broad applicability in general shear flows.
Area of Science:
- Fluid dynamics
- Asymptotic analysis
- Nonlinear dynamics
Background:
- Shear flows exhibit complex dynamics, including exact coherent structures.
- Vortex-wave interaction (VWI) theory and freestream coherent structures (FCS) are recent asymptotic descriptions of these structures.
Purpose of the Study:
- To discuss the applications and implications of VWI and FCS in shear flows.
- To present new results for canonical VWI problems in infinite regions.
- To demonstrate the occurrence of FCS in flows beyond boundary layers.
Main Methods:
- Asymptotic analysis of shear flows.
- Investigation of canonical vortex-wave interaction problems.
- Analysis of freestream coherent structures in various flow types.
Main Results:
- Exact coherent structures are defined for unbounded flows for the first time.
- VWI results confirm and extend previous findings for infinite problems.
- Freestream coherent structures are shown to exist in Burgers vortex sheets.
Conclusions:
- Both VWI and FCS canonical problems can be locally embedded in general shear flows.
- These structures possess widespread applicability in fluid dynamics.
- The study advances the understanding of exact coherent structures in fluid flows.
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