## 3 Results  
### Flow Field Characteristics of Railway Culvert  
The airflow is the power source of the sand movement and significantly influences the initiation of the sand, sand transport, and sand sedimentation. Figure 4 shows the flow field distribution on the axial plane (_xy_) of the culvert at an inflow velocity of \(v=15\) m/s. Figure 4: Flow field distribution of railway culvert. (**a**) Streamline diagram and (**b**) velocity cloud diagram of axial plane in the culvert. Figure 3: Comparison of horizontal wind speeds around wind-break wall [27]. Figure 4a shows that the airflow velocity on the windward side of the subgrade significantly decreases, creating a deceleration zone. The airflow was separated at the culvert inlet; one part moved upward along the windward side of the subgrade slope (the former), and the other part flowed into the culvert (the latter). The former converged on the windward side of the subgrade. The pressure increased, and the airflow passed rapidly over the railway track at the shoulder, forming an acceleration zone above the track. The pressure dropped, and a recovery zone formed in the far field as the airflow moved to the leeward side of the subgrade. Simultaneously, the airflow moved toward the ground due to gravity. The low-velocity airflow flowed towards the culvert outlet, creating a vortex due to the strong pressure resistance of the upper airflow. The latter was squeezed by the top surface of the culvert body, forming a local low-speed zone and then flowed through the culvert close to the ground. At this time, the airflow from the culvert outlet lifted the vortex away from the ground and reduced its intensity. However, a small vortex zone was formed because the low-velocity and low-pressure of the latter were not enough to resist the high-velocity and high-pressure of the former. The velocity cloud diagram of the axial plane in the culvert is shown in Figure 4b. To make certain the horizontal wind velocity distribution and variation law of the vertical wind direction cross-section (3 m \(\times\) 3 m) inside the culvert, Figure 5 shows the wind velocity cloud diagram at different positions of the culvert body in the \(x\) direction. It can be seen from Figure 5 that when \(x\leq\) 54 m, the horizontal velocity had obvious stratification characteristics, and as the height increased, the velocity in the culvert body increased first and then decreased. The sequence is the airflow sub high speed zone, high speed zone, and low speed zone. The above phenomenon was fully consistent with the fluid boundary layer theory, that is, the viscous force of the airflow away from the culvert wall gradually decreased, the airflow velocity increased continuously, and finally the maximum velocity was reached in the middle of the hole. In addition, it was also found that as the position of the cross-section inside the culvert continuously shifted to the right, that is, the depth of the culvert body continued to increased, and the high-speed area of the airflow gradually moved up. When \(x\) = 58.2 m, the horizontal velocity at the culvert outlet was not stratified, and the airflow velocity was significantly lower than that of \(x\) = 54 m section. The main reason was that the wing walls structure of the culvert outlet increased the cross-sectional area, resulting in rapid decreased in airflow pressure and wind velocity. Figure 6 shows the change in the horizontal wind speed from the windward side to the leeward side of the subgrade. The wind speed in the culvert had a range of 30-110 m at heights above the ground of \(y\) = 0.2, 1, and 2 m.  
Figure 5: Wind velocity cloud maps of different cross-sections from culvert inlet to outlet. The curve of the horizontal wind speed along the culvert axis has a W shape, consistent with the results in Ref. [22]. At the height \(y=0.2\) m, the wind speed at the foot of the slope on the windward side decreased in the wind direction, increased after entering the culvert, and decreased at the culvert outlet.