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Transition to turbulence in a shear flow.
1Fachbereich Physik, Philipps Universität Marburg, D-35032 Marburg, Germany.
Summary
We analyzed a 19-dimensional model of parallel shear flow. Findings suggest a universal transition scenario in fluid dynamics, with fractal dependencies observed in flow perturbations.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Computational physics
Background:
- Parallel shear flows are fundamental in fluid dynamics.
- Understanding flow stability and transitions is crucial for various applications.
- Previous studies on shear flows like plane Couette flow provide context.
Purpose of the Study:
- To analyze the properties of a 19-dimensional Galerkin approximation of parallel shear flow.
- To investigate the stability of laminar flow and the occurrence of stationary flows.
- To characterize the behavior of finite amplitude perturbations.
Main Methods:
- Galerkin approximation with a 19-dimensional model.
- Analysis of flow stability across different Reynolds numbers (Re).
- Investigation of stationary flow bifurcations and perturbation lifetimes.
Main Results:
- The sinusoidal laminar flow is stable for all Reynolds numbers (Re).
- For large Re, unstable stationary flows emerge.
- Perturbation lifetimes exhibit a fractal dependence on amplitude and Reynolds number.
Conclusions:
- The observed transition scenario in parallel shear flow may be universal.
- Findings align with observations in plane Couette flow.
- The study provides insights into complex flow behavior and stability.