THE 3-DIMENSIONAL DEVELOPMENT OF THE SHEARING INSTABILITY OF CONVECTION

Two-dimensional convection can become unstable to a mean shear flow. I n three dimensions, with periodic boundary conditions in the two horiz ontal directions, this instability can cause the alignment of convecti on rolls to alternate between the x and y axes. Rolls with their axes in the y-direction become unstable to a shear flow in the x-direction that tilts and suppresses the rolls, but this flow does not affect rol ls whose axes are aligned with it. New rolls, orthogonal to the origin al rolls, can grow, until they in turn become unstable to a shear flow . This behavior is illustrated through numerical simulations and low-o rder models, and the sequence of local and global bifurcations is dete rmined. (C) 1996 American Institute of Physics.