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Wake dynamics in buoyancy-driven flows: Steady-state-Hopf-mode interaction with O(2) symmetry revisited
Javier Sierra-Ausin1,2, David Fabre1, Edgar Knobloch3
1UPS-IMFT, Allée du Professeur Camille Soula, 31000 Toulouse, France.
Physical Review. E
|February 17, 2024
Summary
This study uses mathematical analysis to understand flow bifurcations in stratified wakes. Researchers found attracting heteroclinic cycles, validating predictions with flow simulations.
Area of Science:
- Fluid dynamics
- Mathematical physics
Background:
- Wake flow past axisymmetric bodies exhibits complex bifurcations.
- Thermal stratification significantly influences wake dynamics.
Purpose of the Study:
- To mathematically model bifurcations in stratified wake flows.
- To analyze the role of symmetry in these bifurcations.
- To identify and characterize attracting robust heteroclinic cycles.
Main Methods:
- Abstract normal form analysis was employed.
- Bifurcation diagrams were constructed in parameter space.
- Normal form coefficients were computed for specific geometries (disks, spheres).
Main Results:
- Identified possible bifurcations and their diagrams.
- Interpreted bifurcations using symmetry principles.
- Confirmed the presence of attracting robust heteroclinic cycles in certain regimes.
Conclusions:
- Mathematical normal form analysis accurately predicts bifurcations in stratified wake flows.
- Direct numerical simulations validated the theoretical predictions.
- The study provides a robust framework for understanding complex fluid phenomena.
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