Rayleigh-Benard convection with experimental boundary conditions

The onset of convection in systems that are heated via current dissipation in the lower boundary or that lose heat from the top boundary via Newton's law of cooling is formulated as a bifurcation problem. The Rayleigh number as usually defined is shown to be inappropriate as a bifurcation parameter since the temperature across the layer depends on the amplitude of convection and hence changes as convection evolves at fixed external parameter values. Moreover, the final state of the system is also different since it depends on the details of the applied boundary conditions. A modified Rayleigh number is introduced that does remain constant even when the system is evolving, and solutions obtained with the standard formulation are compared with those obtained via the new one.