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Finite amplitude thermal convection with continuous finite bandwidth of long wavelengthmodes in a porous layer between two horizontal poorly conducting walls is studied when spatially nonuniformtemperature is prescribed at the lower wall. The weakly nonlinear problem is solved by usingmultiple scales and perturbation techniques. The preferred long wavelength flow solutions aredetermined by a stability analysis. The case of near resonant wavelength excitation is considered todetermine the non-modal type of solutions. It is found that, under certain conditions on the form of theboundary imperfections, the preferred horizontal structure of the solutions is of the same spatial form asthat of the total or some subset of the imperfection shape function. It is composed of a multi-modalpattern with spatial variations over the fast variables and with non-modal amplitudes, which vary over theslow variables. The preferred solutions have unusual properties and, in particular, exhibit kinks incertain vertical planes which are parallel to the wave vectors of the boundary imperfections. Alongcertain vertical axes, where some of these vertical planes can intersect, the solutions exhibit multiplekinks

Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitation