Analysis of space-time correlations for the two-dimensional periodic hill problem to support the development of wall models

Most wall models used for Large Eddy Simulation (LES) assume that the boundary layer is fully turbulent, at equilibrium and attached. These models have also been successfully applied to turbulent boundary layers under moderated adverse pressure gradients. Once the adverse pressure gradient becomes too strong, and in particular if the boundary layer separates, equilibrium wall models are no longer applicable. Another difficulty is that in any practical applications transition may play a very important role. In view of elaborating more general wall models, the relations between the instantaneous wall shear stress , the instantaneous velocity field v and the instantaneous pressure gradients near the surface are investigated, by means of space-time correlations extracted from a wall-resolved LES (wrLES) of the two-dimensional periodic hill at a bulk Reynolds number of 10595. This work constitutes a first step towards a local wall model for flows featuring separation based on deep neural networks, by determining an adequate set of network inputs.