CFD-compatible amplification factor transport transition model for water-medium boundary layers

In the field of boundary-layer transition prediction, the e^N method based on the linear stability theory (LST) remains among the most reliable classical methods. To broaden the applicability of this method and achieve convenient and efficient transition prediction over complex geometries, Coder et al. developed a disturbance amplification factor transport model based on stability analysis data from laminar similarity solutions. This model has demonstrated high predictive accuracy across numerous wind-tunnel benchmark cases for aerodynamic applications in air. However, in hydrodynamic boundary layers, the traditional transport model yields significant prediction deviations. This discrepancy arises from the fundamental difference in the temperature dependence of fluid viscosity between water and air, and it becomes particularly pronounced in the presence of temperature gradients. To address this issue, the present study conducts extensive linear stability analyses on laminar similarity solutions for water boundary layers and reconstructs a transport equation for the disturbance amplification factor tailored to water flows. The proposed model is validated under various geometric configurations and flow conditions. Results indicate that the model accurately captures and predicts transition phenomena induced by Tollmien-Schlichting (T-S) instabilities in water boundary layers, thereby demonstrating its physical validity and reliability.