Nonlinear Convection in a Partitioned Porous Layer

Convection in a partitioned porous layer is considered where the thin partition causes a mechanical isolation of the two identical sublayers from one another, but heat may neveretheless conduct freely. An unsteady solver that employs the multigrid method is employed to determine steady-state strongly nonlinear for values of the Darcy–Rayleigh number up to eight times its critical value. The predictions of linear stability theory are confirmed and the accuracy of the computations are carefully monitored and controlled. It is found that the wavenumber for which the maximum rate of heat transfer is attained at any chosen value of the Darcy–Rayleigh number, Ra increases quite strongly from roughly 2.33 at onset to 6.25 when Ra = 200. It is also found that convection generally cannot take place with wavenumbers which are close to the left-hand branch of the neutral stability curve because nonlinear interactions favour modes selected from higher harmonics.