Physics-based distinction of nonequilibrium effects in near-wall modeling of turbulent separation bubble with and without sweep

Three-dimensional turbulent boundary layers subject to pressure gradients and undergoing separation remain a key challenge for wall modeling. Using DNS datasets of swept and unswept separation bubbles, this study employs the Renard--Deck skin-friction decomposition to isolate and analyze nonequilibrium contributions critical to near-wall modeling. Wall-modeled LES demonstrates that only wall models capturing the spatial growth term accurately reproduce the true energy balance in nonequilibrium zones. The analysis highlights when and why nonequilibrium effects must be incorporated, providing physics-based guidance for improving wall model predictions in practical flows.