Mean-field equations for weakly nonlinear two-scale perturbations of forced hydromagnetic convection in a rotating layer

摘要: We consider stability of regimes hydromagnetic thermal convection in a rotating horizontal layer with free electrically conducting boundaries, to perturbations involving large spatial and temporal scales. Equations governing the evolution weakly nonlinear mean are derived under assumption that alpha-effect is insignificant leading order (e.g., due symmetry system). The mean-field equations generalise standard convection: New terms emerge -- second-order linear operator representing combined eddy diffusivity, quadratic associated advection. If perturbed CHM regime non-steady insignificance system does not rely on presence symmetry, diffusivity also involves non-local pseudodifferential operator. state almost symmetric, appear as well. Near point symmetry-breaking bifurcation, cubic nonlinearity emerges equations. All new general anisotropic. A method for evaluation their coefficients presented; it requires solution significantly smaller number auxiliary problems than straightforward approach.