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Taylor-Couette flow in the narrow-gap limit
1Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, Japan.
Summary
This study explores Taylor-Couette flow dynamics in a narrow gap. Results show how cylinder rotation ratios influence flow structures and instability onset, recovering plane Couette flow in a limiting case.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Hydrodynamic Stability
Background:
- The Taylor-Couette system, with its rich history stemming from G.I. Taylor's work, is crucial for understanding fluid instabilities.
- Investigating the vanishing gap limit is essential for simplifying complex flow behaviors and revealing fundamental dynamics.
Purpose of the Study:
- To present a Cartesian representation of the Taylor-Couette system in the vanishing gap limit.
- To analyze the effect of the ratio of angular velocities on axisymmetric flow structures.
- To investigate the onset of axisymmetric instability and nonlinear flow behaviors.
Main Methods:
- Numerical stability analysis to determine critical Taylor numbers.
- Development of a numerical code for calculating nonlinear axisymmetric flows.
- Cartesian representation of the system to analyze flow characteristics.
Main Results:
- The study confirms previous findings for the critical Taylor number for axisymmetric instability.
- Identified the instability region as [Formula: see text] with a finite product of [Formula: see text] and [Formula: see text].
- Observed antisymmetric mean flow distortion for [Formula: see text] and additional symmetric distortion for [Formula: see text].
Conclusions:
- Axisymmetric flow structures are significantly influenced by the ratio of angular velocities in the vanishing gap limit.
- The system recovers plane Couette flow as the gap vanishes for finite rotation numbers.
- The numerical code provides a robust tool for studying nonlinear axisymmetric flows in confined geometries.
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