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Updated: Jul 15, 2026

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Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Explicit analytic formulas for Newtonian Taylor-Couette primary instabilities
1Department of Chemical Engineering, University of California at Berkeley, Berkeley, California 94720, USA.
Summary
This study reveals self-similar stability boundaries for fluid flow between rotating cylinders. New formulas predict critical Reynolds numbers for Taylor vortex and spiral vortex flows, simplifying stability analysis.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Experimental Physics
Background:
- The stability of flow between rotating cylinders is crucial in fluid mechanics.
- Existing data on primary stability boundaries exhibit complex dependencies on radius and rotation ratios.
- Understanding transitions to Taylor vortex flow and spiral vortex flow is key.
Purpose of the Study:
- To identify self-similar parameters for primary stability boundaries in concentric cylinder flows.
- To develop explicit analytic formulas for critical Reynolds numbers across various flow conditions.
- To experimentally validate the influence of nodal surfaces on flow stability.
Main Methods:
- Analysis of existing primary stability boundary data.
- Application of a combination of variables technique for data collapse.
- Empirical fitting of collapsed data to derive analytic formulas.
- Experimental investigation of nodal surface influence for specific rotation ratios.
Main Results:
- Primary stability boundary data exhibit self-similarity in a defined parameter space.
- Experimental results for Taylor vortex and spiral vortex flows collapse onto a single curve.
- Explicit analytic formulas for critical Reynolds numbers were derived for counter-rotating and co-rotating cylinders.
- Nodal surface influence was experimentally confirmed for micro approximately equal -1.7.
Conclusions:
- The study successfully established self-similar relationships for flow stability boundaries.
- The derived analytic formulas provide accurate predictions for critical Reynolds numbers.
- Findings offer a simplified approach to understanding and predicting flow instabilities in concentric cylinders.
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