Scaling-Learning in Non-Equilibrium Turbulent Boundary Layers

Turbulent boundary layers (TBLs) under pressure gradient effects are ubiquitous in many engineering applications. While zero-pressure-gradient TBLs are relatively well understood and admit well-established scaling laws, TBLs subjected to non-equilibrium conditions such as adverse and favorable pressure gradients (APG and FPG) still lack a unified framework to characterize their behavior across Reynolds numbers and flow conditions. This challenge arises primarily from the influence of pressure gradient history, which introduces strong non-local effects and breaks the self-similarity assumptions that underpin traditional scaling arguments. In this work, we apply IT-π, a data-driven, information-theoretic framework, to identify scaling laws for TBLs under varying pressure gradients. We focus on the scaling of the mean velocity and Reynolds stress profiles, as well as the wall pressure and skin friction coefficients. Rather than assuming a fixed set of scaling parameters, the proposed framework aims to maximize the shared information between candidate scaling variables and the aforementioned flow quantities in the dataset. The data used are obtained from high-fidelity numerical simulations of turbulent boundary layers subjected to streamwise-varying pressure gradients generated by a smooth ramp geometry. By varying the ramp angle, we explore a wide range of flow conditions, from strongly FPG to APG cases, including flow separation.