Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection

Abstract

Explicit formulas for the rotation frequency and the long-wavenumber diffusion coefficients of global spirals with $m$ arms in Rayleigh-Benard convection are obtained. Global spirals and parallel rolls share exactly the same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals seem not to have a characteristic frequency ${\omega }_m$ or a typical size $R_m$, but their product ${\omega }_m{R}_m$ is a constant under given experimental conditions. The ratio $R_i/R_j$ of the radii of any two dislocations ($R_i$, $R_j$) inside a multi-armed spiral is also predicted to be constant. Some of these results have been tested by our numerical work.

To appear in Phys. Rev. E as Rapid Communications

References in corpus (5)

• Spiral Defect Chaos in Large Aspect Ratio Rayleigh-Benard Convection
• Spiral defect chaos in a model of Rayleigh-Benard convection
• Defect Dynamics for Spiral Chaos in Rayleigh-Benard Convection
• Study of spiral pattern formation in Rayleigh-Benard convection
• Numerical study of pattern formation following a convective instability in non-Boussinesq fluids

Cited by in corpus (3)

• Dynamics and Selection of Giant Spirals in Rayleigh-Benard Convection
• Nature of Roll to Spiral-Defect-Chaos Transition
• Spiral Instabilities in Rayleigh-Bénard Convection under Localized Heating