Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer

Abstract

Abstract The statistical properties of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) are presented. The flow is generated via the direct numerical simulation of a TBL on a flat surface with a farfield boundary condition designed to apply the desired pressure gradient. The conditions for self-similarity and appropriate scaling are derived, with the mean profiles, Reynolds stress profiles, and turbulent kinetic energy budgets non-dimensionalised using this scaling. The APG TBL has a momentum thickness based Reynolds number range from R e δ 2 = 300 to 6000, with a self-similar region spanning a Reynolds number range from R e δ 2 = 3500 to 4800. Within this range the non-dimensional pressure gradient parameter β = 1 . Two-point correlations of each of the velocity components in the streamwise/wall-normal plane are also presented, which illustrate the statistical imprint of the structures in this plane for the APG TBL.