Restricted Nonlinear Simulations of Boundary Layers Developing Over Decelerating Walls

Temporally-developing boundary layers (BLs) yield statistics and structural flow features comparable to spatially-developing BLs with reduced computational burden. Further tractability can be achieved using a reduced order model, such as the restricted nonlinear (RNL) model, which is well-suited to temporally developing flows. BL development over a time-horizon is natural in the RNL system as the model lacks a physical streamwise coordinate due to its decomposition of the flow field into a streamwise constant mean (large-scale) and a small subset of perturbations about that mean (small-scales). This representation sustains turbulence with accurate low-order statistics and reproduces statistical features of temporally developing BLs. In this work, we conduct RNL wall-resolved large eddy simulations (WRLES) of temporally-developing BLs with prescribed wall decelerations designed to mimic adverse pressure gradient (APG) conditions in spatially developing BLs. Despite order truncation, RNL simulations reproduce mean velocity profiles with growing wake regions and Reynolds stress trends commensurate with prior direct numerical simulation (DNS) studies of developing BLs under decelerating wall conditions, analogous to increasing APGs. Spanwise pre-multiplied energy spectra also reveal an emerging outer-layer peak as wall deceleration increases. Therefore, nonlinear interactions in the RNL model are appropriate to study mechanisms associated with the effects of wall decelerations.