Large-scale flow generation in turbulent convection

In a horizontal layer of fluid heated from below and cooled from above, cellular convection with horizontal length scale comparable to the layer depth occurs for small enough values of the Rayleigh number. As the Rayleigh number is increased, cellular flow disappears and is replaced by a random array of transient plumes. Upon further increase, these plumes drift in one direction near the bottom and in the opposite direction near the top of the layer with the axes of plumes tilted in such a way that horizontal momentum is transported upward via the Reynolds stress. With the onset of this large-scale flow, the largest scale of motion has increased from that comparable to the layer depth to a scale comparable to the layer width. The condiditions for occurence and determination of the direction of this large-scale circulation are described.