2 research outputs found
Amplitude equations for weakly nonlinear two-scale perturbations of free hydromagnetic convective regimes in a rotating layer
Weakly non-linear stability of regimes of free hydromagnetic thermal
convection in a rotating horizontal layer with free electrically conducting
boundaries is considered in the Boussinesq approximation. Perturbations are
supposed to involve large spatial and temporal scales. Applying methods for
homogenisation of parabolic equations, we derive the system of amplitude
equations governing the evolution of perturbations under the assumption that
the alpha-effect is insignificant in the leading order. The amplitude equations
involve the operators of anisotropic combined eddy diffusivity correction and
advection. The system is qualitatively different from the system of mean-field
equations for large-scale perturbations of forced convective hydromagnetic
regimes. It is mixed: equations for the mean magnetic perturbation are
evolutionary, all the rest involve neither time derivatives, nor the molecular
diffusivity operator.Comment: Accepted in Geophys. Astrophys. Fluid Dyn. 24 p
Convective plan-form two-scale dynamos in a plane layer
We study generation of magnetic fields, involving large spatial scales, by
convective plan-forms in a horizontal layer. Magnetic modes and their growth
rates are expanded in power series in the scale ratio, and the magnetic eddy
diffusivity (MED) tensor is derived for flows, symmetric about the vertical
axis in a layer. For convective rolls magnetic eddy correction is demonstrated
to be always positive. For rectangular cell patterns, the region in the
parameter space of negative MED coincides with that of small-scale magnetic
field generation. No instances of negative MED in hexagonal cells are found. A
family of plan-forms with a smaller symmetry group than that of rectangular
cell patterns has been found numerically, where MED is negative for molecular
magnetic diffusivity over the threshold for the onset of small-scale magnetic
field generation.Comment: Latex. 24 pages with 3 Postscript figures, 19 references. Final
version (expanded Appendix 2, 4 references added, notation changed to a more
"user-friendly"), accepted in Geophysical and Astrophysical Fluid Dynamic