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Optimal harmonic response in a confined Bödewadt boundary layer flow
Younghae Do1, Juan M Lopez, Francisco Marques
1Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
This study analyzes the Bödewadt boundary layer flow in a rotating cylinder. Harmonic modulation reveals distinct linear and nonlinear responses, with periodic forcing inducing steady streaming and period-doubling bifurcations.
Area of Science:
- Fluid dynamics
- Rotating fluid systems
- Boundary layer theory
Background:
- The Bödewadt boundary layer flow is sensitive to perturbations.
- Axisymmetric radial waves precede spiral instabilities in this flow.
- Understanding flow dynamics under modulated rotation is crucial.
Purpose of the Study:
- To analyze the sensitivity and response of finite Bödewadt flow to harmonic modulation of rotation rate.
- To explore the effects of forcing amplitude and frequency variations.
- To identify excitation mechanisms for axisymmetric radial waves.
Main Methods:
- Numerical simulation of the Bödewadt flow.
- Analysis of flow response to harmonic modulation of rotation rate.
- Computation of frequency response curves.
Main Results:
- Distinct linear and nonlinear response regimes identified, with a sharp transition at moderate amplitudes.
- Periodic forcing induces steady-streaming flow and period-doubling bifurcations.
- Specific frequency bands identified for axisymmetric radial wave excitation.
Conclusions:
- Axisymmetric waves decay when modulation ceases, indicating they are not self-sustained.
- Experimentally observed persistent circular waves are likely influenced by external factors.
- The study clarifies the dynamics of modulated Bödewadt flow and wave stability.
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