Special Issue: data-driven and physics-based modelling of coherent structures in turbulent shear flow

The concept of coherent structures in turbulent shear flows has profoundly shaped our understanding of turbulence over the last five decades.The seminal work of Brown and Roshko in the 1970s first revealed that turbulence is not merely random, but often organized around coherent, dynamically significant structures embedded within the chaotic background (see Fig. 1a).Their discoveries opened the door to a new paradigm in turbulence research, one that seeks order within disorder.The discovery of coherent structures gave rise to a new line of research focused on leveraging flowinherent instabilities as a means of control.By deliberately triggering these instabilities, it became possible to manipulate the generation and dynamics of coherent structures in a targeted way.This approach enabled a highly efficient enhancement of momentum transfer and entrainment with minimal energy input, an insight that proved especially powerful for controlling flow separation in aerodynamic applications.The work by Greenblatt and Wygnanski [4] exemplified this principle, showing how excitation of inherent instabilities could dramatically improve performance with remarkably low actuation effort.In parallel, efforts to model coherent structures gained traction.A pivotal contribution came from Reynolds and Hussain, who introduced the concept of triple decomposition, separating a turbulent signal into mean, coherent, and stochastic components [5].This framework formed the basis for physics-based modeling using linearized methods such as global linear stability analysis [6] and resolvent analysis [7] and simultaneously emphasized the need for effective turbulence closure models [8][9][10][11][12][13] ultimately motivating the integration of data assimilation techniques [14].With the advent of time-resolved particle image velocimetry (PIV) and high-fidelity numerical simulations, empirical data-driven techniques like Proper Orthogonal Decomposition [15] and its spectral variants [16,17] became increasingly popular.These tools enable the identification of dominant flow structures and have proven instrumental when combined with linearized analysis.They help uncover the physical mechanisms underlying