Bénard convection in a finite box: secondary and imperfect bifurcations

In the solution given by Hall & Walton (1977) for Bénard convection in a two-dimensional box with slightly imperfectly insulated side walls it was shown that there were certain critical values 2Lc of the length 2L of the box at which two modes became unstable simultaneously. In this paper we show that in the neighbourhood of Lc a secondary transition takes place which may be a bifurcation or a smooth transition depending on the boundary conditions.