Convection in a layer heated from below with a nearly insulating boundary

The problem of two- and three-dimensional finite amplitude thermal convection in a fluid layer heated from below is analyzed in the case when one boundary has a much higher and the other boundary has a much lower thermal conductivity than the fluid. Both stress-free and no-slip boundary conditions for the velocity field are considered. It is shown that two-dimensional convection rolls are stable for Rayleigh numbers not too far above the critical value Rc for the onset of convection. But at a Rayleigh number RII less than twice the critical value they become unstable and are replaced by hexaroll convection. (Here ``hexarolls'' denotes a new planform intermediate to hexagons and rolls.) At an even higher value of R time dependent convection is found.