Low-dimensional representation of near-wall dynamics in shear flows, with implications to wall-models

The dynamics of coherent structures near the wall of a turbulent boundary layer is investigated with the aim of a low-dimensional representation of its essential features. Based on a triple decomposition into mean, coherent and incoherent motion and a dynamic mode decomposition to recover statistical information about the incoherent part of the flow field, a driven linear system coupling first- and second-order moments of the coherent structures is derived and analysed. The transfer function for this system, evaluated for a wall-parallel plane, confirms a strong bias towards streamwise elongated structures, and is proposed as an ‘impedance’ boundary condition which replaces the bulk of the transport between the coherent velocity field and the coherent Reynolds stresses, thus acting as a wall model for large-eddy simulations (LES). It is interesting to note that the boundary condition is non-local in space and time. The extracted model is capable of reproducing the principal Reynolds stress components for the pretransitional, transitional and fully turbulent boundary layer. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.