Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation
The statistical properties are presented for the direct numerical simulation (DNS) of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness based Reynolds number range from $Re_{δ_2}=570$ to $13800$, with a self-similar region from $Re_{δ_2} = 10000$ to $12300$. Within this domain the average non-dimensional pressure gradient parameter $β=39$, where for a unit density $β=δ_1 P_e^\prime / τ_w$, with $δ_1$ the displacement thickness, $τ_w$ the mean shear stress at the wall, and $P_e^\prime$ the farfield pressure gradient. This flow is compared to previous zero pressure gradient (ZPG) and mild APG TBL ($β=1$) results of similar Reynolds number. All flows are generated via the DNS of a TBL on a flat surface with farfield boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases the flow has properties less like a ZPG TBL and more akin to a free shear layer.