A Non-normal-Mode Marginal State of Convection in a Porous Rectangle

Author's accepted manuscript (postprint). This is a post-peer-review, pre-copyedit version of an article published in Transport in Porous Media. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11242-019-01263-5. The fourth-order Darcy–Bénard eigenvalue problem for onset of thermal convection in a 2D rectangular porous box is investigated. The conventional type of solution has normal-mode dependency in at least one of the two spatial directions. The present eigenfunctions are of non-normal-mode type in both the horizontal and the vertical direction. A numerical solution is found by the finite element method, since no analytical method is known for this non-…