Study on mathematical model construction of typical gorge wind field

Wind conditions in gorges have a significant impact on the safe operation of high-speed trains, due to the lack of a unified gorge wind model and the limitations of traditional simulations that use oversimplified wind models, the complex wind speed distribution arising from the mountain surface boundary layer cannot be accurately captured. To address this, a three-dimensional, incompressible, steady calculation method is used to study wind field characteristics in a typical gorge. We propose a two-dimensional mathematical model to study the effects of gorge width on model parameters, including wind speed growth indices a(1) and a(2) in the height and horizontal directions, respectively. Our results demonstrate that the thickness of the mountain boundary layer can reach a maximum of approximately 30 metres, and the values of a(1) and a(2) range from 0.11 to 0.19 and 0.21 to 0.5, respectively. As gorge width increases, boundary layer thickness remains constant, a(1) gradually decreases, a(2 )remains unchanged above 250 m height. Our findings provide more accurate boundary conditions for numerical simulations of high-speed train operation in gorge wind conditions and offer theoretical recommendations for safe high-speed train operation through bridges, tunnels, and railways in mountainous regions.