Modelling of near-wall turbulence with large-eddy velocity modes

In the paper, low-order modelling of the turbulent velocity field in the near-wall region is performed using the Proper Orthogonal Decomposition (POD) approach. First, an empirical eigenfunction basis is computed, basing on two-point velocity correlations. Next, the Galerkin projection of the Navier-Stokes equations on the truncated basis is performed. This results in a system of Ordinary Differential Equations (ODEs) for time-dependent coefficients. Evolution of the largest vortical structures in the near-wall zone is then obtained from the time dependent coefficients and eigenfunctions. The system applied in the present work consists of 20 ODEs, the reconstructed velocity field is two-dimensional in the plane perpendicular to the main flow direction. Moreover, the filtering procedure associated with the POD method is discussed, the POD filter is derived and compared with LES filters.