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
ω
m
or a typical size
R
m
, but their product
ω
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.