On exchanges between convective modes in a slightly tilted porouscavity

We use Liapunov–Schmidt reduction and singularity-theory methods to investigate the bifurcation structure of steady free convection in a finite two-dimensional saturated porous cavity heated from below. In particular, we develop a qualitative model describing the modal exchanges that occur as the aspect ratio of a slightly tilted cavity varies. ℤ2-symmetry breaking bifurcations are involved in these exchanges and the mechanism is significantly different from those in previously studied physical systems. The work is akin to, but distinct from, that of Schaeffer's on the Taylor–Couette problem. We also derive and clearly state conditions for the application of this model to modal exchange in other systems.