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Updated: May 11, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Rotating polygon instability of a swirling free surface flow
1Physics Department and Center for Fluid Dynamics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark.
Physical Review Letters
|May 28, 2013
Summary
Rotating polygon instability in swirling fluids arises from resonant wave interactions. This study models these interactions, explaining experimental results and demonstrating transient polygon formation in stirred liquid nitrogen.
Area of Science:
- Fluid dynamics
- Wave phenomena
- Nonlinear dynamics
Background:
- The rotating polygon instability observed on swirling fluid surfaces is a complex phenomenon.
- Previous studies (Vatistas, 1990; Jansson et al., 2006) have documented this instability but lacked a unified theoretical explanation.
- Understanding this instability is crucial for various applications involving free-surface flows.
Purpose of the Study:
- To elucidate the underlying mechanisms of the rotating polygon instability.
- To develop a theoretical model explaining the resonant interactions responsible for the instability.
- To validate the model against experimental observations and explore its broader applicability.
Main Methods:
- Application of potential flow theory and linearization around a potential vortex flow.
- Analysis of resonant interactions between surface gravity waves and inner centrifugal waves.
- Derivation of an analytically soluble model focusing on lowest-order wave modes.
- Estimation of circulation using angular momentum balance.
Main Results:
- Identification of unstable resonant states in the linearized potential vortex flow model.
- Successful reproduction of key features of the experimental phase diagram using the analytical model.
- Demonstration that the instability is not limited to specific boundary conditions, such as rotating bottoms.
- Transient formation of polygons observed when stirring liquid nitrogen.
Conclusions:
- The rotating polygon instability is explained by resonant interactions between gravity and centrifugal waves.
- The developed analytical model accurately captures the essential dynamics of the instability.
- The findings suggest a general mechanism for polygon formation in swirling free-surface flows, extendable to practical scenarios like stirred liquid nitrogen.
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