The sequence-of-bifurcations approach towards understanding turbulent fluid flow

The sequence-of-bifurcations approach for the analysis of transitions from simple to complex forms of fluid flow is described. Formulated for fluid systems with external conditions that are homogeneous in two spatial dimensions and in time, this approach determines bifurcations through their symmetry breaking properties. Solutions that are periodic in the homogeneous dimensions and in time are generated in this way. While the secondary solution induced by the instability of the basic homogeneous state generically assumes the form of rolls or stripes, higher bifurcations introduce solutions exhibiting structures specific for the physical system under consideration. These structures often persist in the form of coherent structures in the turbulent state of the system. Examples from the case of thermal convection in a layer heated from below are used to illustrate the sequence-of-bifurcations approach.