The objective has been to study turbulent boundary layers under adverse pressure gradients (APG) through direct numerical simulation (DNS). The numerical code is based on a pseudo-spectral technique which is suitable for the simple geometry (flat plate) considered here. A large effort has been put into the optimization of the numerical code on various super computers. Five large simulations have been performed, ranging from a zero pressure gradient boundary layer to a separating flow. The simulations have revealed many features of APG turbulent boundary layers which are difficult to capture in experiments. Especially the near-wall behavior has been investigated thoroughly, both through the statistical and instantaneous flow.

Theoretical work based on the turbulent boundary layer equation has been conducted with the aim to develop near-wall laws suitable for turbulence models. The conditions for self-similarity and relations between mean flow parameters have been reviewed and applied in the DNS. The results from the simulations have confirmed the theoretical part of this work. The turbulent flows have also been investigated using turbulence models. A boundary layer under strong APG is difficult to predict correctly, and the separating boundary layer is one of the most difficult flows in this respect. The near-wall damping was improved by comparing DNS data and model predictions. The asymptotic behavior of an APG boundary layer for large Reynolds numbers has been determined through asymptotic analysis and with the aid of turbulence models.