Boundary-layer transition in the age of data: from a comprehensive dataset to fine-grained prediction

Abstract

The laminar-to-turbulent transition remains a fundamental and enduring challenge in fluid mechanics. Its complexity arises from the intrinsic nonlinearity and extreme sensitivity to external disturbances. This transition is critical in a wide range of applications, including aerospace, marine engineering, geophysical flows, and energy systems. While the governing physics can be well described by the Navier-Stokes equations, practical prediction efforts often fall short due to the lack of comprehensive models for perturbation initialization and turbulence generation in numerical simulations. To address the uncertainty introduced by unforeseeable environmental perturbations, we propose a fine-grained predictive framework that accurately predicts the transition location. The framework generates an extensive dataset using nonlinear parabolized stability equations (NPSE). NPSE simulations are performed over a wide range of randomly prescribed initial conditions for the generic zero-pressure-gradient flat-plate boundary-layer flow, resulting in a large dataset that captures the nonlinear evolution of instability waves across three canonical transition pathways (Type-K, -H, and -O). From a database of 3000 simulation cases, we extract diagnostic quantities (e.g., wall pressure signals and skin-friction coefficients) from each simulation to construct a feature set that links pre-transition flow characteristics to transition onset locations. Machine learning models are systematically evaluated, with ensemble methods-particularly XGBoost-demonstrating exceptional predictive accuracy (mean relative error of approximately 0.001). Compared to methods currently available (e.g., N-factor, transitional turbulence model), this approach accounts for the physical process and achieves transition prediction without relying on any empirical parameters.