3.3 Relationship between total sand transport rate and friction velocity
The total sand transport within 70 cm height was obtained by summing the sand transport of each layer within 0~70 cm height, and then the total sand transport rate near the surface under different combinations of ridge height and spacing was calculated. The results show that under different ridge structures, the total sand transport rate increases with the increase of friction velocity, which conforms to the power function distribution, and the correlation of most ridge structures is higher than 0.9 (Fig. 4). With the increase of ridge spacing, the total sand transport rate increases rapidly, but the change of total sand transport rate with ridge height does not show a certain regularity. Compared with no ridges, the total sand transport rate under different ridge structures is lower when the friction velocity is 0.34 m·s-1 and 0.42 m·s-1. When the friction velocity increases to 0.51 m·s-1, the total sand transport rate of a few ridge structures with large ridge spacing increases rapidly, which has exceeded the total sand transport rate without ridge. When the friction velocity continues to increase, the total sand transport rate of all ridge structures with a ridge spacing of 25H has exceeded that of no ridge.
This is because compared with the uniform bed with smooth surface, the take-off angle and saltation height of sand particles on the rough bed are significantly increased (Ding, 2010). When there is a ridge, the subducted sand particles rebound violently on the ridge, which not only increases the amount of sand transported in the upper airflow, but also the resistance to airflow decreases as the sand particles fly farther during the flight. The sand saltation height and horizontal distance are small on smooth bed surface. The sand particles are close to the ground in the transportation process, and the sand transport rate in the lower layer increases greatly, which increases the energy consumption of the airflow near the ground and weakens the transportation capacity of the airflow. Therefore, under a certain wind force, the sand transport rate on the loose bed with no ridges is smaller than that with ridge coverage. This phenomenon is also common on the Gobi surface covered with gravel (Zhang et al., 2007).
DISCUSSION
When there is no ridge, the sand transport rate decreases with the increase of height in a power function law. Under different ridge structures, the change of sand transport rate with height shows two trends. One is that the sand transport rate decreases exponentially with the increase of height. The other one shows an ”elephant nose” effect, which is similar to the drifting sand flux structure in Gobi desert, as the near surface sand transport rate increases with the increase of height, and decreases exponentially above a certain height.
When the surface friction velocity exceeds the critical friction velocity of sand movement, the sand particles are separated from the surface and enter the airflow by the lifting power of wind. The movement of sand particles in drifting sand flux is very complex, which is not only affected by the airflow field, but also by the sand particle size, sand shape, environmental humidity and temperature (Neuman and Maljaars, 1997; Wiggs et al., 2004). Among them, the velocity of sand particles reflects the kinetic energy changes of airflow field and drifting sand flux in the process of sand movement, which has an important influence on sand transport process (Sharp, 1964; Zou et al., 2001). When the friction velocity is low, the surface wind pressure is also low, only a few sand particles leave the surface and begin to move, and the movement speed of sand particles is very slow. Because the average saltation velocity of sand particles is power function distribution with the saltation height (Zou et al., 2001; Dong et al., 2004; Yang et al., 2007), when the saltation height of sand particles is very low, the sand transport rate is small, and the percentage of sand transport in the lower layer is large. When the friction velocity increases, more sand particles leave the bed and begin to move. Because the resistance of sand particles in the movement process is small, they still have considerable momentum when they falling to the bed. Therefore, not only the falling sand particles themselves may rebound and continue to move, but also part of the sand particles around the falling point can splash into the motion state under its impact, and then cause a series of chain reactions. When the saltation motion state of sand particles in the drifting sand flux is stable, the amount of sand particles initiated by the direct effect of wind can be ignored, and the sand particles in the drifting sand flux mainly taking off due to the impact collision effect (Anderson and Haff, 1991). Because the impact velocity of sand particles increases with the increase of friction velocity, the movement velocity and height of sand particles also increase with the increase of friction velocity. For the above reason, the larger the friction velocity, the larger the sand transport rate, the higher the proportion of sand transport in the higher height level. However, the sand movement mainly occurs in the limited height near the surface (Shao and Li, 1999; Kok and Renno, 2009), the proportion of sand transport in the near surface height layer is much larger than that in the higher height layer under different friction velocities.
Due to the influence of ridge, the wind velocity near surface decreases, the total sand transport decreases, the sand transport in the lower layer decreases as a whole, while the sediment concentration in the upper layer changes relatively little, and the surface sand transport rate decreases exponentially with the increase of height. This is due to the variation of drifting sand flux structure caused by the influence of underlying surface (Ma, 1988). Taking a ridge height of 5 cm as an example, the drifting sand flux structure of five ridge spacings under different experimental wind velocities conforms exponential distribution, which can be expressed by the formulaq =A exp(-Bh ). Haas et al. (2004) pointed out in the study on the vertical distribution of surface sand transport rate of dunes in Tengger desert that the fitting coefficient A refers to the near surface sand transport, and B refers to the decreasing rate of surface sand transport rate with height. It can be seen that with the increase of wind velocity the value of A increases continuously, and the change of B value is not obvious. When the ridge spacing is 5H, the friction velocity increases from 0.42 m·s-1 to 0.68 m·s-1, the value ofA increases from 0.003 to 0.056, and the value of B first increases and then decreases. This shows that the sand transport rate increases continuously within the height of 0~10 cm on the surface, and the decreasing rate of sand transport rate with height increases first and then decreases. When the friction velocity is 0.68 m·s-1, the ridge spacing increases from 5H to 25H, the value of A increases from 0.056 to 6.696, and the value ofB changes little. That is, when the ridge height is 5 cm, the sand transport rate within the height of 0~10 cm increases with the increase of ridge spacing, and the decrease rate of sand transport rate among the five ridge spacings with height does not change significantly.
There are two reasons why the surface drifting sand flux structure covered by ridges has the ”elephant nose” effect which is similar to that on Gobi surface. One reason is that, the sand transport in the low height layer is greatly affected by the ridge, especially for the structure of the last row ridge in the downwind direction which is close to the sand sampler. Due to the barrier action of ridges, the sand particles with low saltation height between ridges can not reach the end of the sample trough, so the sand transport in the low height layer mainly comes from the wind erosion of the bed surface behind the last row of ridges. With the increase of height, the mean diameter of wind erosion sediment decreases. Compared with coarse particles, fine particles have long transport distance and large transport height (Arens et al., 2002). Therefore, a large number of saltation fine particles from upwind ridges can reach the end of the sample trough, which increases the sand transport rate of the middle height layer of the sand sampler. The second reason is that, the collision properties between sand and ridge is different from that between sand and bare soil. Qu et al. (2005) considered that the ”elephant nose” effect of the drifting sand flux structure on the Gobi surface is because the Gobi surface is mainly composed of gravel with large compactness, and the collision between moving particles and the surface is similar to elastic collision, resulting in large take-off angle and initial velocity of sand particles. When sand particles move to a higher space, they can make more use of the energy of high-level air flow, while the collision between sand particles and bare soil is opposite. Through field observation, Bagnold (1941) found that the maximum saltation height of sand particles can reach 2 m in gravel area, while the maximum saltation height of sand is 9 cm on the sandy surface. There is a certain similarity between the surface of ridge cover and the surface of Gobi. The ridge model is a rigid barrier, and the saltation particles are elastic collision when they collide with it. After the collision, the sand particles can rebound higher and farther, and make full use of the energy of the high-level air flow, resulting in the drifting sand flux mainly concentrated near the ridge height, which is similar to the ”elephant nose” effect of the Gobi surface.
Compared with no ridges, the transport height of sand particles increased. Under most ridge structures, the sand transport height reached a height layer of 60~70 cm. Since more than 90% of the saltation sand particles transport within the height of 30 cm near the surface (Ding, 2010), the sand particles in the higher layer are mainly suspended. This also proves the conclusion of Fryear and Saleh (1993) that the variation of saltation sand transport with height follows a power function distribution law, while the suspension follows an exponential function distribution.
CONCLUSIONS
Using wind tunnel experiments, we measured the near-surface drifting sand flux structure and sand transport rate with different combinations of height and spacing for non-erodible ridges. The results show that: (1) Under the condition of no ridges, the sand transport rate within the height of 0~70 cm above the sand bed decreases with the increase of height, but the decline rate between each height layer is becoming smaller and smaller. With the increase of friction velocity, the sand transport rate continues to increase, and the proportion of sand transported in the drifting sand flux layer near the bed decreases relatively, and the proportion of sand transported in the upper layer increases accordingly. More than 97% of the sand transport is concentrated in the height of 0~10 cm, the sand transport rate decreases with the increase of height in a power function. (2) The sand transport rate at 0~70 cm height with different ridge structure increases continuously with the increase of friction velocity, while the change of sand transport rate with height can be divided into two cases. One is that the sand transport rate decreases with the increase of height, and the fitting relationship between surface sand transport rate and height deviates from the power function law with no ridges, but mostly conforms the exponential function law of particle distribution of reaction saltation. The second one is that the sand transport rate increases with the increase of height below a certain height, and decreases with the increase of height above the certain height, showing the ”elephant nose” effect similar to the drifting sand flux structure in Gobi desert. (3) The total sand transport rate in 0~70 cm height increases with the increase of friction velocity, which conforms to the power function distribution. With the increase of ridge spacing, the total sand transport rate increases rapidly, but the change of total sand transport rate with ridge height does not show a certain regularity. When the friction velocity is low, the total sand transport rate under different ridge structures is lower than that with no ridges, but when the friction velocity and ridge spacing are high, the total sand transport rate of some ridge structures exceeds that with no ridges.