On the complex Ginzburg-Landau system of modulation
equations for a rotating annulus with radial magnetic field
Milos Revallo and Daniel Sevcovic
Abstract
The problem of convection in a rotating annulus in the presence
of a radial magnetic field is considered in a local Cartesian
approximation. Linear stability analysis known from earlier studies
shows the formation of two minima of the
dispersion relation at the onset of stability. This corresponds to two
convective modes having the form of traveling waves. Within certain
parametric range the two modes emerge at the same Rayleigh number.
In this paper the problem is extended to the weakly nonlinear regime
when the coupling of the modes can be studied. A system of
Ginzburg-Landau equations for the mode coupling is derived and the
coefficients are computed analytically for high rotation rates.
The properties of the coupled system of Ginzburg-Landau equations are
discussed and the conditions for existence of the global attractor and
inertial manifold are found.
Keywords:
magnetoconvection, weakly nonlinear analysis, Ginzburg-Landau equations,
compact global attractor, inertial manifold
PACS: 47.20.-k, 47.20.Ky, 47.27.Te, 47.60.+i
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