Coherent structures and dynamical systems

Any flow of a viscous fluid has a finite number of degrees of freedom, and can therefore be seen as a dynamical system. A coherent structure can be thought of as a lower dimensional manifold in whose neighborhood the dynamical system spends a substantial fraction of its time. If such a manifold exists, and if its dimensionality is substantially lower that that of the full flow, it is conceivable that the flow could be described in terms of the reduced set of degrees of freedom, and that such a description would be simpler than one in which the existence of structure was not recognized. Several examples are briefly summarized.