High Rayleigh number convection in a porous medium containing a thin low-permeability layer

Porous geological formations are commonly interspersed with thin, roughly horizontal, low-permeability layers. Statistically steady convection at high Rayleigh number Ra is investigated numerically in a two-dimensional porous medium that is heated at the lower boundary and cooled at the upper, and contains a thin, horizontal, low-permeability interior layer. In the limit that both the dimensionless thickness h and permeability Pi of the low-permeability layer are small, the flow is described solely by the impedance of the layer Omega = h/Pi and by Ra. In the limit Omega -> 0 (i.e. h -> 0), the system reduces to a homogeneous Rayleigh-Darcy (porous Rayleigh-Benard) cell. Two notable features are observed as Omega is increased: the dominant horizontal length scale of the flow increases; and the heat flux, as measured by the Nusselt number Nu, can increase. For larger values of Omega, Nu always decreases. The dependence of the flow on Ra is explored, over the range 2500 <= Ra <= 2 x 10(4). Simple one-dimensional models are developed to describe some of the observed features of the relationship Nu(Omega).