Space-selective nonlinear reduced-order models for turbulent boundary layer drag reduction

Reduced-Order Models (ROMs) for 3D-turbulent flows based on Galerkin projection usually suffer from a large number of necessary basis functions to capture the relevant system dynamics. In this paper a new method to build a ROM for turbulent boundary layers is presented. Therefore the authors combine the Laplacian Eigenmaps as nonlinear dimensionality reduction method with the Galerkin projection. The neighborhood appearing in the Laplacian Eigenmaps is defined by a space-selective weighting approach, which moves the focus to the wall-near structures and thus enables to catch the control-relevant dynamics. As example turbulent boundary layer drag reduction by spanwise traveling waves is investigated using high-resolved CFD simulations.