Anisotropy and symmetry in porous medium convection
The authors study the linear and nonlinear stability of resting fluid (conduction solution) and of a vertical throughflow in an anisotropic porous medium between two horizontal impermeable heat-conducting walls. The model uses Darcy-Boussinesq equations with boundary conditions, which the authors recast into dimensionless form and then obtain perturbation equations. The linear stability of these equations is then performed, and sufficient conditions for which convective motions arise are determined. The nonlinear stability allows to determine conditions ensuring that the convective motions cannot arise in the layer. Further, the authors give a weighted nonlinear stability analysis of the steady-state problem, indicating the global nonlinear stability. The obtained numerical results are presented in 6 figures.
scientific article; zbMATH DE number 5648837