Coherent structures of turbulence: Methods of education and results

In this paper the issue of the coherent structures of turbulence developing in wall-bounded flows is addressed. After a short historical synthesis, some basic concepts are reviewed and the idea of coherent structure is introduced. The phenomena occurring in the inner and outer regions of the turbulent boundary layer in conjunction with the most widely used event-detection techniques are considered, with reference to the large amount of mainly experimental results existing on the subject. The flow phenomena are described in terms of events occurring in the inner region, large-scale motions developing in the outer layer and dynamics of vortical structures. In the second part of the paper methods for the eduction of the coherent structures of turbulence from the background flow and results obtained in the framework of each method are presented. The techniques involving the invariants of the velocity gradient tensor, the analysis of the Hessian of the pressure and the proper orthogonal decomposition are considered. Each procedure involves a particular definition of coherent structure that is supported by an appropriate mathematical framework and permits the analysis of a turbulent-flow, database in terms of dynamics of coherent structures. This work may contribute to the dissemination of the most recent concepts and techniques now in use in turbulence research among fluid dynamicists.