Gill's stability problem may be unstable with horizontal heterogeneity in permeability

Abstract

The linear stability of thermal buoyant flow in a fluid-saturated vertical porous slab is studied under the assumption of weak and strong horizontal heterogeneities of the permeability. The two end vertical isothermal boundaries are impermeable and some paradigmatic cases of linear, quadratic and exponential heterogeneity models are deliberated. The stability/instability of the basic flow is examined by carrying out a numerical solution of the governing equations for the disturbances as Gill's proof (A.E. Gill, J. Fluid Mech, vol. 35, 1969, pp. 545–547) of linear stability is found to be ineffective. The possibilities of base flow becoming unstable due to heterogeneity in permeability are recognized, in contrast to Gill's stability problem. The neutral stability curves are presented and the critical Darcy–Rayleigh number for the onset of convective instability is computed for different values of the variable permeability constant. The similarities and differences between different heterogeneity models on the stability of fluid flow are clearly discerned.