We consider stability of regimes of hydromagnetic thermal convection in arotating horizontal layer with free electrically conducting boundaries, toperturbations involving large spatial and temporal scales. Equations governingthe evolution of weakly nonlinear mean perturbations are derived under theassumption that the alpha-effect is insignificant in the leading order (e.g.,due to a symmetry of the system). The mean-field equations generalise thestandard equations of hydromagnetic convection: New terms emerge -- asecond-order linear operator representing the combined eddy diffusivity, andquadratic terms associated with the eddy advection. If the perturbed CHM regimeis non-steady and insignificance of the alpha-effect in the system does notrely on the presence of a spatial symmetry, the combined eddy diffusivityoperator also involves a non-local pseudodifferential operator. If theperturbed CHM state is almost symmetric, alpha-effect terms appear in themean-field equations as well. Near a point of a symmetry-breaking bifurcation,cubic nonlinearity emerges in the equations. All the new terms are in generalanisotropic. A method for evaluation of their coefficients is presented; itrequires solution of a significantly smaller number of auxiliary problems thanin a straightforward approach.
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