Direct numerical simulation of adverse pressure gradient turbulent boundary layer up to ≃ 8000

A direct numerical simulation of a moderate adverse pressure gradient turbulent boundary layer flow on a flat plate was performed on a fairly long domain with a Reynolds number from ������������������& SIME; 2000 to ������������������& SIME; 8000. The mean streamwise velocity profile does not exhibit a clear log region even at the highest Reynolds number. The Reynolds stresses exhibit a well defined peak in the outer region which moves away from the wall before to stabilise at a wall distance ������of 0.45 boundary layer thickness after evolving over 20 local boundary layer thicknesses. These outer peaks are the consequences of an excess of production over dissipation and they all scale with the shear stress velocity for wall distance 0.2 ������ < ������ < 0.85 ������. The different terms of the Reynolds stresses equations are analysed in the outer region and the analysis confirms that the leading terms are the same as for a zero pressure gradient turbulent boundary layer except that the production and dissipation are not negligible in the outer region. The most significant contribution of scales smaller than two Taylor scales is on the pressure strain term of the shear stress equation. The probability of the occurrence of small scale vortices conditioned by the presence of an ejection or a sweep shows that the shear stress contained in ejections is associated with the production and transport of near wall vortices away from the wall. The local mean shear generated by the sweeps increases the production of near wall vortices. Lastly, the large scale structures analysed by means of two point correlations of the streamwise fluctuating velocity are shown to be strongly modified by the adverse pressure gradient. The correlation reveals a decoupling between the near wall streaks and the large scale streamwise structures enhanced by the adverse pressure gradient.