The onset of convection in horizontally partitioned porous layers

In this paper, the onset of convection in a horizontally partitioned porous layer is investigated. Two identical sublayers are separated by a thin impermeable barrier. There exists a background horizontal flow in one of the layers or, equivalently, flows of half that strength in each sublayer but in opposite directions. A linearised stability analysis is performed where the horizontal component of the disturbance is factored into separate Fourier modes, leaving an ordinary differential eigenvalue problem for the critical Darcy-Rayleigh number as a function of the wavenumber. The dispersion relation is derived and the neutral stability curves are obtained for a wide range of horizontal flow rates. The presence of the horizontal flow alters the morphology of the neutral curves from that which occurs when there is no flow and travelling modes may arise. We also determine the condition under which the most dangerous disturbance changes from a stationary mode to travelling mode. Some three-dimensional aspects are also considered. (C) 2011 American Institute of Physics. [doi:10.1063/1.3589864]