Data-driven perspectives on linear stability theory: Dataset support and pattern-based <i>N</i>-factor evaluation

Boundary-layer instability acts as the precursor to the laminar–turbulent transition, influencing both its initiation and spatiotemporal characteristics. In the linear regime, linear stability theory (LST) has proven effective in identifying neutral curves and predicting transition via the N-factor. However, a clear connection between data in Fourier space and physical space has yet to be fully established—despite the latter offering an agreeable dataset that could address the increasing complexity of flow conditions in real-world applications. To investigate this link, we apply LST in the Fourier domain to two representative cases: an incompressible flat-plate boundary layer and its hypersonic counterpart (Ma=4.8), producing baseline data. We then reconstruct the perturbation fields in physical space and introduce various initial disturbances. The evolution and spatial distribution of modal perturbations are visualized across different planes. Next, we utilize a convolutional neural network (CNN) to predict the N-factor based on these visualized perturbation fields. Our results demonstrate that the majority of the absolute errors between CNN predictions and LST calculations remain within ±0.2. Moreover, by employing more advanced neural network architectures, we reduce the median prediction error to ±0.03, indicating a minimal error for the N-factor. These results highlight the potential of leveraging upstream perturbation amplitude measurements in conjunction with data-driven models to enable real-time prediction of transition onset—with performance and coverage expected to improve further as larger datasets become available.