Resolvent analysis of high Reynolds number turbulent boundary layers with streamwise pressure gradient histories*

Mean pressure gradient histories and associated wall-shear stress play an overarching role in turbulent flows relevant to engineering applications. The relative importance of these two parameters is captured through β and a series of wind tunnel experiments were carried out at Southampton to explore the effects of varied β histories on the structure of boundary layer. Measurements were obtained over a large domain at Re_ζ  ≈10,000, on flow over smooth and rough walls subjected to a family of favorable and adverse pressure gradients. This study extends the current state-of-the-art by exploring flows at high Reynolds numbers with novel sets of measurements for non-equilibrium boundary layers with and without surface roughness. A low-order representation of this problem is obtained by applying resolvent analysis to experimental mean-flow data. In particular, the biglobal resolvent analysis is used to capture nonparallel flow effects, while a local resolvent analysis is performed at a downstream location where β≈0. The rank-1 model of resolvent modes is shown to predict the shape of the energy spectrum, and thus accounts for history effects. The framework shows that the convective non-normality leads to the amplification of large-scale motions in the outer region and universality of very large-scale motions for non-equilibrium boundary layers at high Reynolds number.