2008/04/15 by Vladislav Zheligovsky, V. Zheligovsky
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Physics and Astronomy · #Convection #Eddy diffusion #Fluid Dynamics and Turbulent Flows #Geomagnetism and Paleomagnetism Studies #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Operator (biology) #Quadratic equation #Stability (learning theory) #Symmetry (geometry) #Thermal diffusivity #nlin.CD
paper · pdf · doi:10.1080/03091920802137573
published as Geophysical and Astrophysical Fluid Dynamics, 102 (5), 489-540, 2008 · 54 pages, Latex, no figures. Accepted in Geophysical Astrophysical Fluid Dynamics
arxiv created 2008/04/15 · openalex publication_date 2008/09/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider stability of regimes of 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 of weakly nonlinear mean perturbations are derived under the assumption that the α-effect is insignificant in the leading-order (e.g. due to a symmetry of the system). The mean-field equations generalise the standard equations of hydromagnetic convection: New terms emerge – a second-order linear operator representing the combined eddy diffusivity and quadratic terms associated with the eddy advection. If the perturbed CHM regime is nonsteady and insignificance of the α-effect in the system does not rely on the presence of a spatial symmetry, the combined eddy diffusivity operator also involves a nonlocal pseudodifferential operator. If the perturbed CHM state is almost symmetric, α-effect terms appear in the mean-field equations as well. Near a point of a symmetry-breaking bifurcation, cubic nonlinearity emerges in the equations. All the new terms are in general anisotropic. A method for evaluation of their coefficients is presented; it requires solution of a significantly smaller number of auxiliary problems than in a straightforward approach.