Tertiary and quarternary solutions for convection in a vertical fluid layer heated from the side

In many fluid systems the evolution from simple to complex forms of flow can be followed through a sequence of supercritical bifurcations. Each of the bifurcations is characterized by the breaking of symmetries and the occupation of new degrees-of-freedom by the fluid motion. The problem of fluid flow in a vertical layer subjected to a horizontal temperature gradient is considered in this paper. The sequence of solutions starts with the cubic profile flow as primary solution, which becomes unstable to steady transverse rolls for Prandtl numbers less than 12.45. A tertiary steady three-dimensional flow in the form of staggered vortices follows, which is replaced by a drifting pattern as the Grashof number is increased even further. It is proposed that the regular periodic solutions are representative for the coherent structures observed in experimental realizations of the problem.