On the dynamical role of coherent structures in turbulence

The notion of coherent structures in fluid mechanics – distinguishable regions of the flow field that share common properties and are correlated in space and time – has played a significant role in characterizing and modeling turbulent flows. They have not yet, however, truly become predictive tools, in part because there is no universally accepted way of extracting coherent structures from the flow field. A wide range of types of structures have been suggested, but there has been comparatively little work done to determine their role in the flow dynamics, and therefore to discern which structures are useful for more than flow visualization. Here, I review several common types of coherent structures, both Eulerian and Lagrangian, with a focus on two-dimensional turbulence far from boundaries. I also discuss a framework for pinpointing the dynamical role of coherent structures based on spatial localization of the spectral properties of the flow. Future work on coherent structures should focus on defining structures that play clear roles in the turbulence dynamics.