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Updated: Aug 8, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Square patterns in rotating Rayleigh-Bénard convection
J J Sánchez-Alvarez1, E Serre, E Crespo del Arco
1Departamento aFísica Fundamental, UNED, Apartado 60.141,28080 Madrid, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
The Küppers-Lortz instability in rotating convection typically causes spatiotemporal chaos. However, this study reveals square patterns emerge under realistic boundary conditions, challenging the established theory.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Spatiotemporal Chaos
Background:
- The Küppers-Lortz instability in rotating Rayleigh-Bénard convection is a known source of spatiotemporal chaos.
- This instability leads to continuous replacement of convection roll patterns with a 60-degree axis switch.
- Previous experiments observed unexpected square patterns in cylindrical layers, contradicting the standard Küppers-Lortz scenario.
Purpose of the Study:
- To investigate the formation of square patterns in rotating Rayleigh-Bénard convection.
- To explore the influence of realistic boundary conditions on convection patterns.
- To numerically reproduce and analyze the observed square patterns.
Main Methods:
- Solving Navier-Stokes and heat transport equations using the Oberbeck-Boussinesq approximation.
- Employing a pseudospectral numerical method with second-order time accuracy.
- Simulating convection in a cylindrical layer with realistic boundary conditions.
Main Results:
- Square patterns were successfully generated numerically.
- The rotation velocity of the square pattern increases linearly with the control parameter (epsilon).
- Square pattern velocity decreases with increasing cylinder aspect ratio, indicating lateral confinement is crucial.
Conclusions:
- Square patterns appear in laterally confined rotating convection, deviating from the Küppers-Lortz instability predictions.
- The stability range of these square patterns diminishes in more extended layers.
- Numerical results align with experimental observations of square patterns under specific conditions.
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