The stability of a developing thermal front in a porous medium. II nonlinear evolution

We consider the instability of the unsteady thermal boundary that is caused by suddenly raising the temperature of the lower boundary of an otherwise cold saturated porous medium. In particular, we focus attention on strongly nonlinear two-dimensional convection. A comprehensive set of results is presented which shows the effects of varying the amplitude of the disturbance, its wave number, and the time at which the disturbance is introduced into the developing thermal boundary layer. We indicate, in detail, how the evolution of the instabilities with time is affected by nonlinearity and how the characteristics of that evolution are changed from those that arise in linearized theory. We also determine when linearized theory is inadequate to describe the global features of the evolution, such as the re stabilisation of convection. Copyright © 2006 Begell House, Inc.