On the onset of convection in a highly permeable vertical porous layer with open boundaries

The unstable nature of buoyant flow in a vertical porous slab with a pure conduction temperature distribution is investigated. The permeable and isothermal boundaries are subject to a temperature difference, which is responsible for the basic stationary and parallel vertical flow in the slab. The momentum transfer is modeled by adopting the Darcy-Forchheimer law, thus including the quadratic form-drag contribution. The instability to small-amplitude perturbations is tested by parameterizing the basic stationary flow through the Darcy-Rayleigh number and the form-drag number. The modal analysis is carried out numerically with a pressure-temperature formulation of the governing equations for the perturbations. The neutral stability curves and the critical values of the wave number and of the Darcy-Rayleigh number are obtained for different prescribed values of the form-drag number.