The Sequence-of-Bifurcations Approach towards Understanding Turbulent Fluid Flow

The sequence-of-bifurcations approach for the analysis of transitionsfrom simple to complex forms of fluid flow is described.Formulated for fluid systemswith external conditions that are homogeneous in two spatial dimensionsand in time,this approach determines bifurcations through theirsymmetry breaking properties.Solutions that are periodic in the homogeneous dimensionsand in time are generatedin this way. While the secondary solution induced by theinstability of the basichomogeneous state generically assumes the form of rolls orstripes, higher bifurcationsintroduce solutions exhibiting structures specific for thephysical system underconsideration. These structures often persist in the formof coherent structures inthe turbulent state of the system. Examples from the caseof thermal convection in alayer heated from below are used to illustrate thesequence-of-bifurcations approach.