Data-driven and operator-based tools for the analysis of turbulent flows

Coherent structures-defined as organized fluid elements of significant life-time and scale-have been the focus of many studies of turbulent flows. The extraction, tracking and interpretation of these structures has become a key endeavor in the analysis and understanding of momentum and energy transfer processes when turbulence is a central feature. In this chapter, we review common techniques for the detection of coherent structures from data sequences or their inference from governing equations. Starting with general decompositions of data sequences, we motivate the use of orthogonal and single-frequential decompositions. Operator-based resolvent analysis is covered, as are algorithmic steps for the efficient and robust computation of the modal decompositions. Less common techniques that address special flow features and a brief outlook towards recent developments conclude this exposition.