Velocity-dependent turbulent boundary layer dynamics on multi-unit high-speed trains: Instability analysis and normalized characterization

In this study, three-dimensional numerical simulations of multi-unit high-speed trains (HSTs) were conducted under various inflow velocities using the improved delayed detached eddy simulation method. Key boundary layer parameters were normalized and curve-fitted to examine their evolution. The results show that drag proportions remain largely stable across speeds, with skin friction contributing about 40% of total drag, while overall drag rises significantly, with friction drag increasing by over 70% from 300 to 400 km/h. The streamwise distribution of the skin friction coefficient remains similar across different speeds, but the transition point on the top surface shifts downstream at higher velocities. The roof surface wall shear stress is highly non-uniform, characterized by “Y”-shaped low-stress streaks and Görtler-type vortical structures generated by the streamlined nose and curved shoulder geometry. At lower speeds, the stronger adverse pressure gradient promotes the amplification of boundary-layer disturbances, resulting in a broader spanwise distribution of transverse velocity disturbances. Quadrant analysis of Reynolds shear stress indicates that high inflow velocities mainly intensify near-wall ejection (Q2) and sweep (Q4) events, while the inner layer of the boundary layer under low-speed conditions is more influenced by disturbances originating from the outer layer. Finally, normalization and curve-fitting analyses indicate that the evolution of boundary-layer parameters and velocity profiles is closely related to both inflow velocity and streamwise position. This study illustrates how inflow velocity influences turbulent boundary layer behavior over HST surfaces, providing an important theoretical basis for boundary-layer modeling and the development of friction-reduction technologies for HSTs.