- Email: [email protected]
Effect of transverse ridge microtopography on the surface shear stress distribution and soil wind erosion
Soil & Tillage Research 198 (2020) 104548
Contents lists available at ScienceDirect
Soil & Tillage Research journal homepage: www.elsevier.com/locate/still
Effect of transverse ridge microtopography on the surface shear stress distribution and soil wind erosion
T
Wenru Jiaa,b, Chunlai Zhanga,*, Xueyong Zoua, Liqiang Kanga a
State Key Laboratory of Earth Surface Processes and Resource Ecology, MOE Engineering Research Center of Desertification and Blown-sand Control, Faculty of Geographical Science, Beijing Normal University, No. 19 Xinjiekouwai Street, Beijing 100875, China b School of Land Resources and Urban & Rural Planning, Hebei GEO University, No. 136 East Huai’an Road, Shijiazhuang 050031, China
ARTICLE INFO
ABSTRACT
Keywords: Ridge microtopography Shear stress Spatial variation Effective shear stress Wind erosion
Through wind tunnel experiments, we measured the surface shear stress (τs) on a bed surface that contained widely but uniformly spaced non-erodible ridges. We found that when the ridge spacing is larger than 10 times the height (H), the τs between two adjacent ridges could be divided into two sections. In each section, shear stress gradually increases and then decreases. The first section appears to be produced by the reverse-flow vortex that develops close behind upwind ridges and the second appears to result from airflow recovery followed by ¯
blockage by the downwind ridge. The mean surface shear stress ( s ) of the total bed increases with increasing ridge spacing and friction velocity, and decreases with increasing ridge density. The spatial differences in τs lead to a non-uniform distribution of wind erosion between the ridges. Based on the threshold shear stress (τt) of the tested soil, we revealed a regular distribution of effective shear stress (τeff) on the sand bed, and established quantitative relationships among mean effective shear stress (
¯ eff ) ,
the threshold friction velocity (u*t) for sand entrainment:
= aL H (u*
1. Introduction The shear stress (τs) that an airflow transfers to an erodible bed surface is the direct driving force for wind erosion and sand transport (Kardous et al., 2005). The physical process of separating soil particles from the surface depends on the relative magnitudes of the surface shear stress and the resistance of the soil particles to entrainment (Chepil and Woodruff, 1963). The surface shear stress on a unit area of bed surface (τs) can be calculated as τs = ρ u*2, where ρ represents the air density and u* represents the friction velocity (Bagnold, 1941). However, when the topography fluctuates, the movement of the nearsurface airflow becomes complicated. It is difficult to determine the near-surface u* from the vertical wind profiles, which in turn makes it difficult to calculate τs. To solve this problem, Walker and Nickling (2003) used differential pressure transducers and successfully obtained the distribution of shear stress on the surface of a model dune according to the formula τs = 0.77dP0.65, where dP represents the differential pressure. Sutton and McKenna-Neumann (2008) and Walter et al. (2009) used Irwin sensors to measure τs distribution around cylindrical and rectangular blocks. Walter et al. (2012) further studied the surface shear stress distribution around plants and found that non-uniform
⁎
¯ eff
H, ridge spacing (L), friction velocity (u*), and
u*t )2 .
distribution of the shear stress significantly affected the sediment transport. Shear stress is generated by the moving air, and therefore depends on the airflow field. Liu et al. (2006a) measured the airflow velocity and calculated the stress distributions during different phases of the development of a vortex flow field in a two-dimensional channel. They used particle image velocimetry, a technology that permits dynamic measurement of the transient flow field, and obtained the distribution of shear stress in the channel and the periodic variation of mean shear stress. In a study of the effect of the airflow field on shear stress under different tillage measures, Liu et al. (2007) found that the shear stress mainly depended on the viscous friction between the adjacent airflow layers, and the shear stress caused by turbulent eddies was smaller than that caused by the smooth (non-diverted) airflow. For simplicity, most researchers investigated the shear stress on flat surfaces. However, in nature, surfaces are rarely flat, so more sophisticated models have been developed to account for the effect of roughness elements that disrupt the smooth airflow. Okin (2008) defined the influence of the distribution of roughness elements on the shear stress. For bare farmland, ridges are most important roughness elements, so ridge microtopography and the resultant roughness length
Corresponding author. E-mail address: [email protected] (C. Zhang).
https://doi.org/10.1016/j.still.2019.104548 Received 28 May 2019; Received in revised form 11 December 2019; Accepted 17 December 2019 0167-1987/ © 2019 Elsevier B.V. All rights reserved.
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al. ¯ eff
Nomenclature τs ¯ s
τt τeff
H L n u* u*t
Surface shear stress
Mean surface shear stress Threshold shear stress Effective shear stress
have been incorporated in various wind erosion prediction models, such as the wind erosion equation (Woodruff and Siddoway, 1965), modified wind erosion equation (Fryrear et al., 2001), and wind erosion prediction system (Hagen, 1991). Ridges block the airflow, thereby changing the near-surface airflow field and weakening its ability to entrain sand; they can therefore effectively reduce soil wind erosion (Chepil and Milne, 1941; Armbrust et al., 1964; Fryrear, 1984). Ridge height, spacing, and their ratio are the main factors that affect wind erosion (Hagen and Armbrust, 1992). The airflow field can be divided into five regions with different characteristics when the air passes over ridges with a sufficiently large inter-ridge spacing: a deceleration area upwind of the ridge’s windward slope, an area with rising and accelerating airflow above the windward slope, an area of acceleration above the top of the ridge, an area of sinking air and decelerating airflow on the leeward slope, and a downwind flow recovery area (Jia et al., 2019). These regions lead to large differences in wind velocity above different parts of the bed with ridges (Marlatt and Hyder, 1970). The wind velocity on the windward side of the ridge increases so that the top of the ridge has the highest wind velocity, whereas reverse-airflow vortices form at the leeward side (Armbrust et al., 1964; Hagen and Armbrust, 1992; Yassin et al., 2012). Therefore, the windward side and the top of the ridge have larger shear stress and become the main regions that undergo erosion (Zilker and Hanratty, 1979; Liu et al., 2006b). Although shear stress created by many kinds of rough elements has been studied, there has been no quantitative study of the distribution of τs above a surface with ridges in terms of the effect of ridge microtopography (i.e., variations of ridge height and spacing). To provide some of the missing information, we designed the present study to measure the variation of τs under different ridge microtopography conditions in a wind tunnel, and to establish a quantitative relationship between the mean surface shear stress and the ridge height and spacing. Based on the resulting distribution of τs, we discuss the distribution of surface wind erosion for beds with different ridge heights and spacing.
Mean effective shear stress Ridge height Ridge spacing Ridge density Friction velocity Threshold friction velocity
ridge was 100 cm long and perpendicular to the direction of the airflow with no gap from the two walls of the wind tunnel. The heights (H) of the ridge models were set as 5, 10, and 15 cm, and the ridges were spaced at 5, 10, 15, 20, and 25 times the ridge height (i.e., at 5H, 10H, 15H, 20H, and 25H, respectively). Here, the spacing refers to the distance between the centers of two adjacent ridges. The first ridge was installed 6 m downwind from the upwind edge of the wind tunnel’s experimental section. Based on the ridge heights and spacings, ridge models were established in the 10-m-long section downwind from the first ridge. Because of the effect of ridge height on the inter-ridge spacing, the number of ridges downwind from the first ridge differed among the experiments. We developed a shear stress measurement system that included 32 shear-stress sensors, 32 differential pressure transducers, and a data-acquisition system. The shearstress sensor, which is an Irwin-type sensor but is smaller compared with an actual one (Irwin, 1981), has a sensor tube and hole connected to a differential pressure transducer, whose output is transformed into a voltage signal by the data-acquisition system. The data-acquisition board used in this system has 32 input channels, and includes software (NI Labview SignalExpress 2011) and a computer for recording the signal. Details of these instruments are provided by Kang et al. (2018). The data-acquisition frequency was 100 Hz and the effective duration at each measurement point was 1 min. We used the 1-min mean values as the final measurement results in our analysis. The line of sensor positions was parallel to the axis of the wind tunnel, with which the first measurement point at a distance 10H upwind from the first ridge. The distance between adjacent measurement points was 5 cm (Fig. 1). Considering that our previous wind tunnel studies on wind erosion from a sand bed, which was covered by the same wooden ridges as used in the present study, were conducted at experimental free-stream friction velocities of 0.30, 0.36, 0.42, 0.49, and 0.58 m s−1, we used the same five free-stream friction velocities in the present wind tunnel tests. In the absence of ridges, τs for the bare wooden floor showed only minor variation along the wind direction at the five friction velocities ¯
(Fig. 2). The mean surface shear stress ( s ) for these velocities was 0.090, 0.135, 0.188, 0.248, and 0.321 Pa, respectively.
2. Research methods 2.1. Wind tunnel experiments We conducted wind tunnel experiments to measure τs at the State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University. The wind tunnel is a blowing type with a total length of 37.8 m, and the experimental section is 15.9 m long, 1 m wide, and 1 m tall. We installed roughness elements upwind of the experimental section to adjust the wind velocity profiles so they would resemble the profiles observed in the field under different free-stream wind velocities. Details are provided by Kang et al. (2018). The thickness of the boundary layer was about 35 cm in the experimental section. 2.2. Ridge microtopography and surface shear stress measurement Because existing equipment cannot measure shear stress on the soil and ridge surfaces during wind erosion, we used non-erodible smooth wooden ridge models. The bed surface between adjacent ridges was also a smooth wooden board, which supported the shear stress sensors (described later in this section). The cross-section of the ridge models was an isosceles triangle with a 90° apex and 45° slope angles. Each
Fig. 1. Illustration of the experimental equipment and setup. 2
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
3.2. Relationship between the ridge spacing, density, free-stream friction velocity and mean surface shear stress We used version 9.0 of the Origin software (https://www.originlab. com/) to graph τs as a function of the actual downwind distance of the measurement points. We then integrated the stress over this distance from the first upwind measurement point to the last point in the downwind direction. Dividing the result by the distance between these ¯
two measurement points provides the mean surface shear stress ( s ). ¯ s
At a given ridge height, increases with increasing ridge spacing (Fig. 5) following an exponential distribution that can be expressed by the function
¯ s
= a·exp(b·L). The smaller the ridge spacing, the lower ¯
the degree of airflow recovery between ridges, and the smaller the s . Ridge density is defined as the number of ridges per unit length (n, ridge m−1). The greater the ridge density, the rougher the bed and the stronger the influence of the ridges on the near-surface airflow. When ¯
the ridge density is less than 2 ridges m−1, s decreases rapidly with increasing ridge density. However, when the ridge density is greater
Fig. 2. Surface shear stress (τ0) without ridge.
¯
than 2 ridges m−1, s decreases more slowly with increasing ridge density (Fig. 6). Regression analysis showed that the relationship be-
3. Results and analysis
¯
¯
tween s and ridge density follows a power function relationship ( s = a·nb). The greater the ridge height and the greater the wind speed, the stronger the relationship.
3.1. Distribution of surface shear stress
¯
The s increases linearly with increasing friction velocity (Fig. 7). The slope and intercept of these regressions show that with increasing
The shear stress between the first and second ridges differed from that between subsequent pairs of adjacent ridges in the downwind direction. It fluctuated regularly moving downwind for all the ridge heights and spacings that we studied (Fig. 3). Between the first and second ridges, τs has the following characteristics. First, it decreases much more between the first two ridges than between adjacent ridges farther downwind. This shows that for all combinations of ridge height and spacing, the first ridge has the strongest influence on surface airflow and the downwind ridges exert a continuous weakening effect. Second, with increasing ridge spacing, the influence of an upwind ridge on the near-surface airflow tends to be relatively independent of the influence on the next downwind ridge, but each ridge reduces the surface airflow to some extent. When the ridge spacing is larger than 10H, τs between two adjacent ridges can be divided into two sections. In each section, τs gradually increases and then decreases. The first section appears to be produced by the reverse-flow vortex that forms close behind upwind ridges and the second section appears to result from airflow recovery followed by blockage by the downwind ridge (Fig. 4). The τs in front of any ridge decreases gradually as the airflow approaches the ridge. At the bottom of the windward slope of the ridges, it decreases to its lowest value, and behind the ridges it increases gradually with increasing distance downwind. As a result of the barrier effect, the near-surface airflow separates behind the ridge, leading to the formation of a vortex with reverse flow (Luo et al., 2009; Yassin et al., 2012). Within the vortex, the energy of the airflow decreases gradually in the reverse direction so that τs decreases as the airflow approaches the upwind ridge. After the airflow moves past the reverse-flow vortex, it recovers gradually and τs increases until the airflow is blocked again by the next downwind ridge. Therefore, τs between two adjacent ridges shows two fluctuation processes (except at a ridge spacing of 5H). The changes in the upwind part of the between-ridge area is controlled by the reverse-flow vortex, whose strength increases with increasing ridge height, whereas in the downwind part, the process is characterized by the gradual recovery of the shear stress. At large ridge spacings (20H and 25H), τs in the downwind part of the between-ridge area is higher than that in the upwind part. At the smaller ridge spacings (10H and 15H), τs in the upwind part of the between-ridge area is greater than that in the downwind part. At the smallest ridge spacing (5H), the two parts merge.
¯
ridge height and spacing, the s increases faster, and the increase is also faster with increasing wind velocity. 3.3. Mean effective shear stress Wind is not sufficiently strong to entrain sand until τs is greater than a certain threshold value (τt), at which erosion begins to occur. We denoted the part of the surface shear stress that exceeds the threshold as the effective shear stress (τeff), which is expressed as: τeff = τs – τt
(1)
Here, τs is the value measured in our wind tunnel experiments and τt is
Fig. 3. The distribution of the surface shear stress (τs) between the ridges at different ridge spacings (L, expressed as a multiple of H, the ridge height) and friction velocities. Data are for a ridge height (H) of 10 cm. The dashed horizontal line represents the threshold at which erosion begins. The distribution of surface shear stress for ridges with H = 5 and 15 cm but with different spacing are presented as Supplemental Figure S1. 3
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
Fig. 4. Illustration of the airflow variation around a ridge.
Fig. 5. Relationships between the mean surface shear stress (τs) and the ridge spacings (L, expressed as a multiple of H, the ridge height). All regressions were statistically significant (P < 0.05).
Fig. 6. Relationship between mean surface shear stress (τs) and ridge density. All regressions were statistically significant (P < 0.05).
the threshold shear stress for wind erosion to occur using an actual sand. Using the soil samples that our research group studied in previous wind tunnel experiments (sand with a mean particle size of 237.5 μm), we determined that the threshold wind velocity for a flat sand bed with no ridges was u*t =0.235 m s−1 (Li, 2015; Jia et al., 2019). Using the equation τt = ρ u*t2, the threshold shear stress was 0.066 Pa. is: ¯ eff
The mean effective shear stress (
¯ eff )
results for our combinations of ridge height and spacing. ¯ eff
is related to ridge height (H), ridge spacing (L), and friction velocity (u*) of the free-stream, which can be expressed as follows: ¯ eff
(3)
= f (H , L , u * ) Fitting showed that f (H , L, u *) can be expressed as follows:
per unit area of the whole bed
f (H , L, u *) = aL H (u *
1 = l
eff(i)
li
(4)
u *t )2
where a = 0.177. Therefore:
(2)
¯ eff
where l is the length of the bed and i is the i-th measurement point along ¯
= aL H (u *
According to Eqn. (5), we predicted the values of
the wind direction. The eff for the surfaces with different ridge height and spacing was calculated using Eqn. (2). Table 1 summarizes the
(5)
u*t ) 2 ¯ eff
for the dif-
ferent combinations of ridge height and spacing, and calculated 4
¯ eff
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
Fig. 7. Relationship between the mean surface shear stress (τs) and friction velocity. All regressions were statistically significant (P < 0.05).
from the measured shear stress to validate the prediction equation. We evaluated the accuracy of the equation using the root-mean-square error (RMSE), the mean absolute error (MAE), and the coefficient of determination (R2) of the regression. Fig. 8 shows that the predictions fell close to the 1:1 line, with a low RMSE (0.0161) and MAE (0.0119) and a strong and significant positive relationship (R2 = 0.893, P＜ 0.05). In addition, the predicted and calculated values show a sign¯
ificant linear relationship. Thus, Eqn. (5) predicted eff very well despite the large differences in ridge structure and friction velocity. 4. Discussion
When τs＞τt, the surface undergoes wind erosion. However, the distribution of τs between ridges is non-uniform, indicating that wind erosion between the ridges will also be non-uniform. Based on τs data and τt for a sand bed measured in the wind tunnel, we predicted the distribution of wind erosion throughout a bed that contained ridges with different heights and spacings at the five experimental free-stream wind velocities (Fig. 9). Wind erosion will not occur in the areas below the dotted line that represents τs = τt, but will occur above the dotted line. When wind velocity is small, the area between the ridges where wind erosion will occur is very small, and the erosion is weak. With increasing wind velocity, the erosion area gradually increases from one section to two sections between adjacent ridges except at a ridge Table 1 The mean effective shear stress ( Ridge height (H)
5 cm
10 cm
15 cm
¯ eff )
Ridge spacing
5H 10H 15H 20H 25H 5H 10H 15H 20H 25H 5H 10H 15H 20H 25H
¯
Fig. 8. Comparison between the mean effective shear stress ( eff ) on the bed surface predicted using Equ. (5) and calculated using the measured shear stress values. The regression was statistically significant (P < 0.05).
spacing of 5H. The first wind erosion area is caused by the reverse-flow vortex that develops behind the upwind ridge, and the second is caused by airflow recovery. As the wind velocity increased, the two wind
on the bed surface for the different combinations of ridge height (H) and spacing (L, as a multiple of H). Ridge density (ridge m−1)
4.00 2.00 1.33 1.00 0.80 2.00 1.00 0.67 0.50 0.40 1.33 0.67 0.44 0.33 0.27
¯ eff
(Pa) for the five friction velocities (m s−1)
0.30
0.36
0.42
0.49
0.58
0 0 0 0 0 0 0 0 0.0045 0.0090 0.0025 0 0 0 0.0112
0.0006 0 0 0.0036 0.0160 0.0014 0.0034 0.0012 0.0181 0.0473 0.0082 0.0050 0.0053 0.0227 0.0552
0.0007 0.0038 0.0047 0.0245 0.0415 0.0061 0.0077 0.0187 0.0518 0.0811 0.0222 0.0229 0.0353 0.0602 0.0919
0.0184 0.0166 0.0306 0.0627 0.0775 0.0265 0.0288 0.0524 0.0897 0.1166 0.0466 0.0451 0.0740 0.0944 0.1321
0.0516 0.0478 0.0682 0.0941 0.1093 0.0650 0.0683 0.0896 0.1177 0.1517 0.0848 0.0824 0.1003 0.1258 0.1688
5
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
deposit near the leeward side of the ridge or even climb the lee slope. However, the reverse airflow is not always sufficiently strong to cause this movement, and as a result, deposition on the lee side of the ridges is less than that on the upwind side (Fig. 10). The distribution of wind erosion areas on the bed surface in the presence of ridges with different structures depends on the friction velocity. When the wind velocity and ridge spacing are both small, the erosion area is mainly located between the first and second ridges. With increasing wind velocity and ridge spacing, wind erosion begins to appear between the pairs of ridges that lie farther downwind. However, with increasing ridge spacing, the erosion area created by the reverseflow vortex that forms behind the ridges did not continue to increase, whereas the erosion areas created by the airflow recovery increased rapidly. Therefore, as the ridge spacing becomes increasingly large, the erosion area that develops in front of the downwind ridges also becomes increasingly large. The larger the ridge spacing or the smaller the ridge density, the larger the range (length parallel to the wind) of the erosion area between adjacent ridges and the stronger the wind erosion. ¯
If we also consider the relationships between ridge density and s , then efforts to reduce erosion in the field should aim for a ridge density of more than 1 ridge m−1. When ridge density is less than 1 row m−1, wind erosion increases rapidly, but when the ridge density becomes greater than 2 ridges m−1, there is little improvement in the ability of the ridges to control erosion. Two-dimensional analysis of flow fields shows that wind erosion behind ridges is mainly caused by airflow recovery (Jia et al., 2019). However, the two-dimensional flow fields revealed by using pitot tubes, the most common way to measure these fields, is incomplete because the pitot tubes cannot measure the velocity of the reverse flow. This problem can be solved using techniques such as particle image velocimetry, but the equipment and expertise to use this technique are not yet common. Comparatively, the distribution of surface shear stress measured using Irwin-type sensors demonstrates the distribution of wind erosion more accurately than the airflow field measured using pitot tubes especially in the lee side of the ridges.
Fig. 9. Locations of the areas where wind erosion is predicted to occur because the shear stress is greater than the threshold stress at which sand entrainment begins (i.e., τs > τt, represented by the dashed horizontal line) for a sand bed that contains ridges. The graph shows the results for an example with a ridge height (H) of 10 cm and a between-ridge distance (L) expressed as a multiple of H. The distribution of wind erosion regions for ridges with a spacing (L) of 15H to 25H are presented as Supplemental Fig. S2.
5. Conclusions Using wind tunnel experiments, we measured the surface shear stress between pairs of non-erodible ridges with different combinations of ridge height and spacing. We found regular fluctuation of τs moving downwind. τs between the upwind first ridge and the second ridge decreases more than the decrease between pairs of ridges farther downwind. Between adjacent ridges, the area can be divided into two sections (except at a ridge spacing of 5H): one behind the upwind ridge and one in front of the downwind ridge. Surface shear stress in both sections first increases and then decreases along the wind direction. The
erosion areas gradually merged and their range (i.e., their length parallel to the wind direction) increased. No wind erosion would occur outside these areas, and it is possible that deposition would instead occur at a given wind velocity especially when the ridges are close together. In general, saltating particles in the lower layer of the sand flow are deposited at the bottom of the windward slope of a ridge as a result of the barrier effect. On the leeward side of the ridge, the reverseflow vortices might cause the moving particles to move upwind and
¯
mean surface shear stress ( s ) increases with increasing ridge spacing and friction velocity, but decreases with increasing ridge density. The spatial distribution of τeff (i.e., the proportion of the shear stress that
Fig. 10. Two examples of the distribution of wind erosion and accumulation between ridges on the bed surface for an example with a ridge height of 10 cm and a ridge spacing of 100 cm. 6
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
leads to sand entrainment according to the threshold shear stress measured for a sand sample used in our previous research) between ridges demonstrates a non-uniform distribution of the areas where wind erosion would occur and variations in the intensity of erosion through the surface. As the ridge spacing increases from 5H to 25H, the erosion areas between adjacent ridges change from one section to two sections, the upwind section of which is created by the reverse-flow vortex that forms behind the upwind ridge and the downwind section is created by the airflow recovery that occurs downwind of the vortex. The mean
Conserv. 46 (2), 106–111. Hagen, L.J., Armbrust, D.V., 1992. Aerodynamic roughness and saltation trapping efficiency of tillage ridges. Trans. ASAE 35 (4), 1179–1184. Irwin, H.P.A.H., 1981. A simple omnidirectional sensor for wind-tunnel studies of pedestrian-level winds. J. Wind Eng. Ind. Aerodyn. 7 (3), 219–239. Jia, W.R., Zhang, C.L., Zou, X.Y., Cheng, H., Kang, L.Q., Liu, B., Li, J.F., Shen, Y.P., Liu, W., Fang, Y., Li, H.R., 2019. Effects of ridge height and spacing on near-surface airflow field and wind erosion of a sandy soil: results of a wind tunnel study. Soil Till. Res. 186 (3), 94–104. Kang, L.Q., Zhang, J.J., Yang, Z.C., Zou, X.Y., Cheng, H., Zhang, C.L., 2018. Experimental investigation on shear-stress partitioning for flexible plants with approximately zero basal-to-frontal area ratio in a wind tunnel. Bound-Lay. Meteorol. 169 (2), 251–273. Kardous, M., Bergametti, G., Marticorena, B., 2005. Aerodynamic roughness length related to non-aggregated tillage ridges. Ann. Geophys-Germany 23 (10), 3187–3193. Li, J.F., 2015. A Study on Shear Strength and Wind Erosion-antierodibility of Sieved Soils. Ph.D. Thesis. Beijing Normal University (in Chinese with English abstract). Liu, F.X., Liu, Z.J., Wang, L., Shi, Q.C., Zhou, J.T., 2006a. On the measurement of velocities and stress in vortex wave field with particle image velocimetry. J. Exp. Mech. 21 (3), 278–284 (in Chinese with English abstract). Liu, M.X., Liu, L.Y., Wang, J.A., Yan, P., Yang, X.C., Qi, X.F., Song, Y., Hu, Y., 2007. Windbreaking effect of various conservation tillage measures during fallow period of cropland. J. Desert Res. 27 (1), 46–51 (in Chinese with English abstract). Liu, M.X., Wang, J.A., Yan, P., Liu, L.Y., Ge, Y.Q., Li, X.Y., Hu, X., Song, Y., Wang, L., 2006b. Wind tunnel simulation of ridge-tillage effects on soil erosion from cropland. Soil Till. Res. 90 (1), 242–249. Luo, W.Y., Dong, Z.B., Qian, G.Q., Wang, H.T., Yuan, W.L., 2009. Wind tunnel simulation on the flow characteristics around upright fences. J. Desert Res. 29 (2), 200–205 (in Chinese with English abstract). Marlatt, W.E., Hyder, D.N., 1970. Soil ridging for reduction of wind erosion from grass seedbeds. J. Range Manage. 23 (3), 170. Okin, G.S., 2008. A new model of wind erosion in the presence of vegetation. J. Geophys. Res. Earth Surf. 113 (F2). Sutton, S.L.F., McKenna-Neumann, C., 2008. Variation in bed level shear-stress on surfaces sheltered by nonerodible roughness elements. J. Geophys. Res. Earth Surf. 113 (F3), F03016. Walker, I.J., Nickling, W.G., 2003. Simulation and measurement of surface shear stress over isolated and closely spaced transverse dunes in a wind tunnel. Earth Surf. Proc. Land. 28 (10), 1111–1124. Walter, B., Gromke, C., Lehning, M., 2009. The SLF boundary layer wind tunnel—an experimental facility for aerodynamical investigations of living plants. In: 2nd International Conference on Wind Effects on Trees. Freiburg, Germany. pp. 31–37. Walter, B., Gromke, C., Leonard, K.C., Manes, C., Lehning, M., 2012. Spatio-temporal surface shear-stress variability in live plant canopies and cube arrays. Bound-Lay. Meteorol. 143 (2), 337–356. Woodruff, N.P., Siddoway, F.H., 1965. A wind erosion equation. Soil Sci. Soc. Am. J. 29 (5), 602–608. Yassin, M.F., Takahashi, T., Kato, S., 2012. Experimental simulation of wind flow over the ridge topography. Air Qual. Atmos. Health 5 (3), 293–301. Zilker, D.P., Hanratty, T.J., 1979. Influence of the amplitude of a solid wavy wall on a turbulent flow. J. Fluid Mech. 90 (2), 257–271.
¯
effective surface shear stress ( eff ) can be predicted using a model that contains ridge height, spacing and u* of free-stream. Declaration of Competing Interest
The authors declare that there is no conflict of interest to this work. Acknowledgments We thank postgraduate students Xuesong WANG, Junjie ZHANG, and Zhicheng YANG of Beijing Normal University for their assistance during the wind tunnel experiments. This study was supported by the National Natural Science Foundation of China (Nos. 41630747 and 41330746). Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.still.2019.104548. References Armbrust, D.V., Chepil, W.S., Siddoway, F.H., 1964. Effects of ridges on erosion of soil by wind. Soil Sci. Soc. Am. J. 28 (4), 557–560. Bagnold, R.A., 1941. The Physics of Blown Sand and Desert Dunes. Methuen, London. Chepil, W.S., Milne, R.A., 1941. Wind erosion of soil in relation to roughness of surface. Soil Sci. 52 (6), 417–434. Chepil, W.S., Woodruff, N.P., 1963. The physics of wind erosion and its control. Adv. Agron. 15, 211–302. Fryrear, D.W., 1984. Soil ridges-clods and wind erosion. Trans. ASAE 27 (2), 445–448. Fryrear, D.W., Chen, W.N., Lester, C., 2001. Revised wind erosion equation. Ann. Arid Zone 40 (3), 265–279. Hagen, L.J., 1991. A wind erosion prediction system to meet user needs. J. Soil Water
7
Contents lists available at ScienceDirect
Soil & Tillage Research journal homepage: www.elsevier.com/locate/still
Effect of transverse ridge microtopography on the surface shear stress distribution and soil wind erosion
T
Wenru Jiaa,b, Chunlai Zhanga,*, Xueyong Zoua, Liqiang Kanga a
State Key Laboratory of Earth Surface Processes and Resource Ecology, MOE Engineering Research Center of Desertification and Blown-sand Control, Faculty of Geographical Science, Beijing Normal University, No. 19 Xinjiekouwai Street, Beijing 100875, China b School of Land Resources and Urban & Rural Planning, Hebei GEO University, No. 136 East Huai’an Road, Shijiazhuang 050031, China
ARTICLE INFO
ABSTRACT
Keywords: Ridge microtopography Shear stress Spatial variation Effective shear stress Wind erosion
Through wind tunnel experiments, we measured the surface shear stress (τs) on a bed surface that contained widely but uniformly spaced non-erodible ridges. We found that when the ridge spacing is larger than 10 times the height (H), the τs between two adjacent ridges could be divided into two sections. In each section, shear stress gradually increases and then decreases. The first section appears to be produced by the reverse-flow vortex that develops close behind upwind ridges and the second appears to result from airflow recovery followed by ¯
blockage by the downwind ridge. The mean surface shear stress ( s ) of the total bed increases with increasing ridge spacing and friction velocity, and decreases with increasing ridge density. The spatial differences in τs lead to a non-uniform distribution of wind erosion between the ridges. Based on the threshold shear stress (τt) of the tested soil, we revealed a regular distribution of effective shear stress (τeff) on the sand bed, and established quantitative relationships among mean effective shear stress (
¯ eff ) ,
the threshold friction velocity (u*t) for sand entrainment:
= aL H (u*
1. Introduction The shear stress (τs) that an airflow transfers to an erodible bed surface is the direct driving force for wind erosion and sand transport (Kardous et al., 2005). The physical process of separating soil particles from the surface depends on the relative magnitudes of the surface shear stress and the resistance of the soil particles to entrainment (Chepil and Woodruff, 1963). The surface shear stress on a unit area of bed surface (τs) can be calculated as τs = ρ u*2, where ρ represents the air density and u* represents the friction velocity (Bagnold, 1941). However, when the topography fluctuates, the movement of the nearsurface airflow becomes complicated. It is difficult to determine the near-surface u* from the vertical wind profiles, which in turn makes it difficult to calculate τs. To solve this problem, Walker and Nickling (2003) used differential pressure transducers and successfully obtained the distribution of shear stress on the surface of a model dune according to the formula τs = 0.77dP0.65, where dP represents the differential pressure. Sutton and McKenna-Neumann (2008) and Walter et al. (2009) used Irwin sensors to measure τs distribution around cylindrical and rectangular blocks. Walter et al. (2012) further studied the surface shear stress distribution around plants and found that non-uniform
⁎
¯ eff
H, ridge spacing (L), friction velocity (u*), and
u*t )2 .
distribution of the shear stress significantly affected the sediment transport. Shear stress is generated by the moving air, and therefore depends on the airflow field. Liu et al. (2006a) measured the airflow velocity and calculated the stress distributions during different phases of the development of a vortex flow field in a two-dimensional channel. They used particle image velocimetry, a technology that permits dynamic measurement of the transient flow field, and obtained the distribution of shear stress in the channel and the periodic variation of mean shear stress. In a study of the effect of the airflow field on shear stress under different tillage measures, Liu et al. (2007) found that the shear stress mainly depended on the viscous friction between the adjacent airflow layers, and the shear stress caused by turbulent eddies was smaller than that caused by the smooth (non-diverted) airflow. For simplicity, most researchers investigated the shear stress on flat surfaces. However, in nature, surfaces are rarely flat, so more sophisticated models have been developed to account for the effect of roughness elements that disrupt the smooth airflow. Okin (2008) defined the influence of the distribution of roughness elements on the shear stress. For bare farmland, ridges are most important roughness elements, so ridge microtopography and the resultant roughness length
Corresponding author. E-mail address: [email protected] (C. Zhang).
https://doi.org/10.1016/j.still.2019.104548 Received 28 May 2019; Received in revised form 11 December 2019; Accepted 17 December 2019 0167-1987/ © 2019 Elsevier B.V. All rights reserved.
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al. ¯ eff
Nomenclature τs ¯ s
τt τeff
H L n u* u*t
Surface shear stress
Mean surface shear stress Threshold shear stress Effective shear stress
have been incorporated in various wind erosion prediction models, such as the wind erosion equation (Woodruff and Siddoway, 1965), modified wind erosion equation (Fryrear et al., 2001), and wind erosion prediction system (Hagen, 1991). Ridges block the airflow, thereby changing the near-surface airflow field and weakening its ability to entrain sand; they can therefore effectively reduce soil wind erosion (Chepil and Milne, 1941; Armbrust et al., 1964; Fryrear, 1984). Ridge height, spacing, and their ratio are the main factors that affect wind erosion (Hagen and Armbrust, 1992). The airflow field can be divided into five regions with different characteristics when the air passes over ridges with a sufficiently large inter-ridge spacing: a deceleration area upwind of the ridge’s windward slope, an area with rising and accelerating airflow above the windward slope, an area of acceleration above the top of the ridge, an area of sinking air and decelerating airflow on the leeward slope, and a downwind flow recovery area (Jia et al., 2019). These regions lead to large differences in wind velocity above different parts of the bed with ridges (Marlatt and Hyder, 1970). The wind velocity on the windward side of the ridge increases so that the top of the ridge has the highest wind velocity, whereas reverse-airflow vortices form at the leeward side (Armbrust et al., 1964; Hagen and Armbrust, 1992; Yassin et al., 2012). Therefore, the windward side and the top of the ridge have larger shear stress and become the main regions that undergo erosion (Zilker and Hanratty, 1979; Liu et al., 2006b). Although shear stress created by many kinds of rough elements has been studied, there has been no quantitative study of the distribution of τs above a surface with ridges in terms of the effect of ridge microtopography (i.e., variations of ridge height and spacing). To provide some of the missing information, we designed the present study to measure the variation of τs under different ridge microtopography conditions in a wind tunnel, and to establish a quantitative relationship between the mean surface shear stress and the ridge height and spacing. Based on the resulting distribution of τs, we discuss the distribution of surface wind erosion for beds with different ridge heights and spacing.
Mean effective shear stress Ridge height Ridge spacing Ridge density Friction velocity Threshold friction velocity
ridge was 100 cm long and perpendicular to the direction of the airflow with no gap from the two walls of the wind tunnel. The heights (H) of the ridge models were set as 5, 10, and 15 cm, and the ridges were spaced at 5, 10, 15, 20, and 25 times the ridge height (i.e., at 5H, 10H, 15H, 20H, and 25H, respectively). Here, the spacing refers to the distance between the centers of two adjacent ridges. The first ridge was installed 6 m downwind from the upwind edge of the wind tunnel’s experimental section. Based on the ridge heights and spacings, ridge models were established in the 10-m-long section downwind from the first ridge. Because of the effect of ridge height on the inter-ridge spacing, the number of ridges downwind from the first ridge differed among the experiments. We developed a shear stress measurement system that included 32 shear-stress sensors, 32 differential pressure transducers, and a data-acquisition system. The shearstress sensor, which is an Irwin-type sensor but is smaller compared with an actual one (Irwin, 1981), has a sensor tube and hole connected to a differential pressure transducer, whose output is transformed into a voltage signal by the data-acquisition system. The data-acquisition board used in this system has 32 input channels, and includes software (NI Labview SignalExpress 2011) and a computer for recording the signal. Details of these instruments are provided by Kang et al. (2018). The data-acquisition frequency was 100 Hz and the effective duration at each measurement point was 1 min. We used the 1-min mean values as the final measurement results in our analysis. The line of sensor positions was parallel to the axis of the wind tunnel, with which the first measurement point at a distance 10H upwind from the first ridge. The distance between adjacent measurement points was 5 cm (Fig. 1). Considering that our previous wind tunnel studies on wind erosion from a sand bed, which was covered by the same wooden ridges as used in the present study, were conducted at experimental free-stream friction velocities of 0.30, 0.36, 0.42, 0.49, and 0.58 m s−1, we used the same five free-stream friction velocities in the present wind tunnel tests. In the absence of ridges, τs for the bare wooden floor showed only minor variation along the wind direction at the five friction velocities ¯
(Fig. 2). The mean surface shear stress ( s ) for these velocities was 0.090, 0.135, 0.188, 0.248, and 0.321 Pa, respectively.
2. Research methods 2.1. Wind tunnel experiments We conducted wind tunnel experiments to measure τs at the State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University. The wind tunnel is a blowing type with a total length of 37.8 m, and the experimental section is 15.9 m long, 1 m wide, and 1 m tall. We installed roughness elements upwind of the experimental section to adjust the wind velocity profiles so they would resemble the profiles observed in the field under different free-stream wind velocities. Details are provided by Kang et al. (2018). The thickness of the boundary layer was about 35 cm in the experimental section. 2.2. Ridge microtopography and surface shear stress measurement Because existing equipment cannot measure shear stress on the soil and ridge surfaces during wind erosion, we used non-erodible smooth wooden ridge models. The bed surface between adjacent ridges was also a smooth wooden board, which supported the shear stress sensors (described later in this section). The cross-section of the ridge models was an isosceles triangle with a 90° apex and 45° slope angles. Each
Fig. 1. Illustration of the experimental equipment and setup. 2
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
3.2. Relationship between the ridge spacing, density, free-stream friction velocity and mean surface shear stress We used version 9.0 of the Origin software (https://www.originlab. com/) to graph τs as a function of the actual downwind distance of the measurement points. We then integrated the stress over this distance from the first upwind measurement point to the last point in the downwind direction. Dividing the result by the distance between these ¯
two measurement points provides the mean surface shear stress ( s ). ¯ s
At a given ridge height, increases with increasing ridge spacing (Fig. 5) following an exponential distribution that can be expressed by the function
¯ s
= a·exp(b·L). The smaller the ridge spacing, the lower ¯
the degree of airflow recovery between ridges, and the smaller the s . Ridge density is defined as the number of ridges per unit length (n, ridge m−1). The greater the ridge density, the rougher the bed and the stronger the influence of the ridges on the near-surface airflow. When ¯
the ridge density is less than 2 ridges m−1, s decreases rapidly with increasing ridge density. However, when the ridge density is greater
Fig. 2. Surface shear stress (τ0) without ridge.
¯
than 2 ridges m−1, s decreases more slowly with increasing ridge density (Fig. 6). Regression analysis showed that the relationship be-
3. Results and analysis
¯
¯
tween s and ridge density follows a power function relationship ( s = a·nb). The greater the ridge height and the greater the wind speed, the stronger the relationship.
3.1. Distribution of surface shear stress
¯
The s increases linearly with increasing friction velocity (Fig. 7). The slope and intercept of these regressions show that with increasing
The shear stress between the first and second ridges differed from that between subsequent pairs of adjacent ridges in the downwind direction. It fluctuated regularly moving downwind for all the ridge heights and spacings that we studied (Fig. 3). Between the first and second ridges, τs has the following characteristics. First, it decreases much more between the first two ridges than between adjacent ridges farther downwind. This shows that for all combinations of ridge height and spacing, the first ridge has the strongest influence on surface airflow and the downwind ridges exert a continuous weakening effect. Second, with increasing ridge spacing, the influence of an upwind ridge on the near-surface airflow tends to be relatively independent of the influence on the next downwind ridge, but each ridge reduces the surface airflow to some extent. When the ridge spacing is larger than 10H, τs between two adjacent ridges can be divided into two sections. In each section, τs gradually increases and then decreases. The first section appears to be produced by the reverse-flow vortex that forms close behind upwind ridges and the second section appears to result from airflow recovery followed by blockage by the downwind ridge (Fig. 4). The τs in front of any ridge decreases gradually as the airflow approaches the ridge. At the bottom of the windward slope of the ridges, it decreases to its lowest value, and behind the ridges it increases gradually with increasing distance downwind. As a result of the barrier effect, the near-surface airflow separates behind the ridge, leading to the formation of a vortex with reverse flow (Luo et al., 2009; Yassin et al., 2012). Within the vortex, the energy of the airflow decreases gradually in the reverse direction so that τs decreases as the airflow approaches the upwind ridge. After the airflow moves past the reverse-flow vortex, it recovers gradually and τs increases until the airflow is blocked again by the next downwind ridge. Therefore, τs between two adjacent ridges shows two fluctuation processes (except at a ridge spacing of 5H). The changes in the upwind part of the between-ridge area is controlled by the reverse-flow vortex, whose strength increases with increasing ridge height, whereas in the downwind part, the process is characterized by the gradual recovery of the shear stress. At large ridge spacings (20H and 25H), τs in the downwind part of the between-ridge area is higher than that in the upwind part. At the smaller ridge spacings (10H and 15H), τs in the upwind part of the between-ridge area is greater than that in the downwind part. At the smallest ridge spacing (5H), the two parts merge.
¯
ridge height and spacing, the s increases faster, and the increase is also faster with increasing wind velocity. 3.3. Mean effective shear stress Wind is not sufficiently strong to entrain sand until τs is greater than a certain threshold value (τt), at which erosion begins to occur. We denoted the part of the surface shear stress that exceeds the threshold as the effective shear stress (τeff), which is expressed as: τeff = τs – τt
(1)
Here, τs is the value measured in our wind tunnel experiments and τt is
Fig. 3. The distribution of the surface shear stress (τs) between the ridges at different ridge spacings (L, expressed as a multiple of H, the ridge height) and friction velocities. Data are for a ridge height (H) of 10 cm. The dashed horizontal line represents the threshold at which erosion begins. The distribution of surface shear stress for ridges with H = 5 and 15 cm but with different spacing are presented as Supplemental Figure S1. 3
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
Fig. 4. Illustration of the airflow variation around a ridge.
Fig. 5. Relationships between the mean surface shear stress (τs) and the ridge spacings (L, expressed as a multiple of H, the ridge height). All regressions were statistically significant (P < 0.05).
Fig. 6. Relationship between mean surface shear stress (τs) and ridge density. All regressions were statistically significant (P < 0.05).
the threshold shear stress for wind erosion to occur using an actual sand. Using the soil samples that our research group studied in previous wind tunnel experiments (sand with a mean particle size of 237.5 μm), we determined that the threshold wind velocity for a flat sand bed with no ridges was u*t =0.235 m s−1 (Li, 2015; Jia et al., 2019). Using the equation τt = ρ u*t2, the threshold shear stress was 0.066 Pa. is: ¯ eff
The mean effective shear stress (
¯ eff )
results for our combinations of ridge height and spacing. ¯ eff
is related to ridge height (H), ridge spacing (L), and friction velocity (u*) of the free-stream, which can be expressed as follows: ¯ eff
(3)
= f (H , L , u * ) Fitting showed that f (H , L, u *) can be expressed as follows:
per unit area of the whole bed
f (H , L, u *) = aL H (u *
1 = l
eff(i)
li
(4)
u *t )2
where a = 0.177. Therefore:
(2)
¯ eff
where l is the length of the bed and i is the i-th measurement point along ¯
= aL H (u *
According to Eqn. (5), we predicted the values of
the wind direction. The eff for the surfaces with different ridge height and spacing was calculated using Eqn. (2). Table 1 summarizes the
(5)
u*t ) 2 ¯ eff
for the dif-
ferent combinations of ridge height and spacing, and calculated 4
¯ eff
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
Fig. 7. Relationship between the mean surface shear stress (τs) and friction velocity. All regressions were statistically significant (P < 0.05).
from the measured shear stress to validate the prediction equation. We evaluated the accuracy of the equation using the root-mean-square error (RMSE), the mean absolute error (MAE), and the coefficient of determination (R2) of the regression. Fig. 8 shows that the predictions fell close to the 1:1 line, with a low RMSE (0.0161) and MAE (0.0119) and a strong and significant positive relationship (R2 = 0.893, P＜ 0.05). In addition, the predicted and calculated values show a sign¯
ificant linear relationship. Thus, Eqn. (5) predicted eff very well despite the large differences in ridge structure and friction velocity. 4. Discussion
When τs＞τt, the surface undergoes wind erosion. However, the distribution of τs between ridges is non-uniform, indicating that wind erosion between the ridges will also be non-uniform. Based on τs data and τt for a sand bed measured in the wind tunnel, we predicted the distribution of wind erosion throughout a bed that contained ridges with different heights and spacings at the five experimental free-stream wind velocities (Fig. 9). Wind erosion will not occur in the areas below the dotted line that represents τs = τt, but will occur above the dotted line. When wind velocity is small, the area between the ridges where wind erosion will occur is very small, and the erosion is weak. With increasing wind velocity, the erosion area gradually increases from one section to two sections between adjacent ridges except at a ridge Table 1 The mean effective shear stress ( Ridge height (H)
5 cm
10 cm
15 cm
¯ eff )
Ridge spacing
5H 10H 15H 20H 25H 5H 10H 15H 20H 25H 5H 10H 15H 20H 25H
¯
Fig. 8. Comparison between the mean effective shear stress ( eff ) on the bed surface predicted using Equ. (5) and calculated using the measured shear stress values. The regression was statistically significant (P < 0.05).
spacing of 5H. The first wind erosion area is caused by the reverse-flow vortex that develops behind the upwind ridge, and the second is caused by airflow recovery. As the wind velocity increased, the two wind
on the bed surface for the different combinations of ridge height (H) and spacing (L, as a multiple of H). Ridge density (ridge m−1)
4.00 2.00 1.33 1.00 0.80 2.00 1.00 0.67 0.50 0.40 1.33 0.67 0.44 0.33 0.27
¯ eff
(Pa) for the five friction velocities (m s−1)
0.30
0.36
0.42
0.49
0.58
0 0 0 0 0 0 0 0 0.0045 0.0090 0.0025 0 0 0 0.0112
0.0006 0 0 0.0036 0.0160 0.0014 0.0034 0.0012 0.0181 0.0473 0.0082 0.0050 0.0053 0.0227 0.0552
0.0007 0.0038 0.0047 0.0245 0.0415 0.0061 0.0077 0.0187 0.0518 0.0811 0.0222 0.0229 0.0353 0.0602 0.0919
0.0184 0.0166 0.0306 0.0627 0.0775 0.0265 0.0288 0.0524 0.0897 0.1166 0.0466 0.0451 0.0740 0.0944 0.1321
0.0516 0.0478 0.0682 0.0941 0.1093 0.0650 0.0683 0.0896 0.1177 0.1517 0.0848 0.0824 0.1003 0.1258 0.1688
5
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
deposit near the leeward side of the ridge or even climb the lee slope. However, the reverse airflow is not always sufficiently strong to cause this movement, and as a result, deposition on the lee side of the ridges is less than that on the upwind side (Fig. 10). The distribution of wind erosion areas on the bed surface in the presence of ridges with different structures depends on the friction velocity. When the wind velocity and ridge spacing are both small, the erosion area is mainly located between the first and second ridges. With increasing wind velocity and ridge spacing, wind erosion begins to appear between the pairs of ridges that lie farther downwind. However, with increasing ridge spacing, the erosion area created by the reverseflow vortex that forms behind the ridges did not continue to increase, whereas the erosion areas created by the airflow recovery increased rapidly. Therefore, as the ridge spacing becomes increasingly large, the erosion area that develops in front of the downwind ridges also becomes increasingly large. The larger the ridge spacing or the smaller the ridge density, the larger the range (length parallel to the wind) of the erosion area between adjacent ridges and the stronger the wind erosion. ¯
If we also consider the relationships between ridge density and s , then efforts to reduce erosion in the field should aim for a ridge density of more than 1 ridge m−1. When ridge density is less than 1 row m−1, wind erosion increases rapidly, but when the ridge density becomes greater than 2 ridges m−1, there is little improvement in the ability of the ridges to control erosion. Two-dimensional analysis of flow fields shows that wind erosion behind ridges is mainly caused by airflow recovery (Jia et al., 2019). However, the two-dimensional flow fields revealed by using pitot tubes, the most common way to measure these fields, is incomplete because the pitot tubes cannot measure the velocity of the reverse flow. This problem can be solved using techniques such as particle image velocimetry, but the equipment and expertise to use this technique are not yet common. Comparatively, the distribution of surface shear stress measured using Irwin-type sensors demonstrates the distribution of wind erosion more accurately than the airflow field measured using pitot tubes especially in the lee side of the ridges.
Fig. 9. Locations of the areas where wind erosion is predicted to occur because the shear stress is greater than the threshold stress at which sand entrainment begins (i.e., τs > τt, represented by the dashed horizontal line) for a sand bed that contains ridges. The graph shows the results for an example with a ridge height (H) of 10 cm and a between-ridge distance (L) expressed as a multiple of H. The distribution of wind erosion regions for ridges with a spacing (L) of 15H to 25H are presented as Supplemental Fig. S2.
5. Conclusions Using wind tunnel experiments, we measured the surface shear stress between pairs of non-erodible ridges with different combinations of ridge height and spacing. We found regular fluctuation of τs moving downwind. τs between the upwind first ridge and the second ridge decreases more than the decrease between pairs of ridges farther downwind. Between adjacent ridges, the area can be divided into two sections (except at a ridge spacing of 5H): one behind the upwind ridge and one in front of the downwind ridge. Surface shear stress in both sections first increases and then decreases along the wind direction. The
erosion areas gradually merged and their range (i.e., their length parallel to the wind direction) increased. No wind erosion would occur outside these areas, and it is possible that deposition would instead occur at a given wind velocity especially when the ridges are close together. In general, saltating particles in the lower layer of the sand flow are deposited at the bottom of the windward slope of a ridge as a result of the barrier effect. On the leeward side of the ridge, the reverseflow vortices might cause the moving particles to move upwind and
¯
mean surface shear stress ( s ) increases with increasing ridge spacing and friction velocity, but decreases with increasing ridge density. The spatial distribution of τeff (i.e., the proportion of the shear stress that
Fig. 10. Two examples of the distribution of wind erosion and accumulation between ridges on the bed surface for an example with a ridge height of 10 cm and a ridge spacing of 100 cm. 6
Soil & Tillage Research 198 (2020) 104548
W. Jia, et al.
leads to sand entrainment according to the threshold shear stress measured for a sand sample used in our previous research) between ridges demonstrates a non-uniform distribution of the areas where wind erosion would occur and variations in the intensity of erosion through the surface. As the ridge spacing increases from 5H to 25H, the erosion areas between adjacent ridges change from one section to two sections, the upwind section of which is created by the reverse-flow vortex that forms behind the upwind ridge and the downwind section is created by the airflow recovery that occurs downwind of the vortex. The mean
Conserv. 46 (2), 106–111. Hagen, L.J., Armbrust, D.V., 1992. Aerodynamic roughness and saltation trapping efficiency of tillage ridges. Trans. ASAE 35 (4), 1179–1184. Irwin, H.P.A.H., 1981. A simple omnidirectional sensor for wind-tunnel studies of pedestrian-level winds. J. Wind Eng. Ind. Aerodyn. 7 (3), 219–239. Jia, W.R., Zhang, C.L., Zou, X.Y., Cheng, H., Kang, L.Q., Liu, B., Li, J.F., Shen, Y.P., Liu, W., Fang, Y., Li, H.R., 2019. Effects of ridge height and spacing on near-surface airflow field and wind erosion of a sandy soil: results of a wind tunnel study. Soil Till. Res. 186 (3), 94–104. Kang, L.Q., Zhang, J.J., Yang, Z.C., Zou, X.Y., Cheng, H., Zhang, C.L., 2018. Experimental investigation on shear-stress partitioning for flexible plants with approximately zero basal-to-frontal area ratio in a wind tunnel. Bound-Lay. Meteorol. 169 (2), 251–273. Kardous, M., Bergametti, G., Marticorena, B., 2005. Aerodynamic roughness length related to non-aggregated tillage ridges. Ann. Geophys-Germany 23 (10), 3187–3193. Li, J.F., 2015. A Study on Shear Strength and Wind Erosion-antierodibility of Sieved Soils. Ph.D. Thesis. Beijing Normal University (in Chinese with English abstract). Liu, F.X., Liu, Z.J., Wang, L., Shi, Q.C., Zhou, J.T., 2006a. On the measurement of velocities and stress in vortex wave field with particle image velocimetry. J. Exp. Mech. 21 (3), 278–284 (in Chinese with English abstract). Liu, M.X., Liu, L.Y., Wang, J.A., Yan, P., Yang, X.C., Qi, X.F., Song, Y., Hu, Y., 2007. Windbreaking effect of various conservation tillage measures during fallow period of cropland. J. Desert Res. 27 (1), 46–51 (in Chinese with English abstract). Liu, M.X., Wang, J.A., Yan, P., Liu, L.Y., Ge, Y.Q., Li, X.Y., Hu, X., Song, Y., Wang, L., 2006b. Wind tunnel simulation of ridge-tillage effects on soil erosion from cropland. Soil Till. Res. 90 (1), 242–249. Luo, W.Y., Dong, Z.B., Qian, G.Q., Wang, H.T., Yuan, W.L., 2009. Wind tunnel simulation on the flow characteristics around upright fences. J. Desert Res. 29 (2), 200–205 (in Chinese with English abstract). Marlatt, W.E., Hyder, D.N., 1970. Soil ridging for reduction of wind erosion from grass seedbeds. J. Range Manage. 23 (3), 170. Okin, G.S., 2008. A new model of wind erosion in the presence of vegetation. J. Geophys. Res. Earth Surf. 113 (F2). Sutton, S.L.F., McKenna-Neumann, C., 2008. Variation in bed level shear-stress on surfaces sheltered by nonerodible roughness elements. J. Geophys. Res. Earth Surf. 113 (F3), F03016. Walker, I.J., Nickling, W.G., 2003. Simulation and measurement of surface shear stress over isolated and closely spaced transverse dunes in a wind tunnel. Earth Surf. Proc. Land. 28 (10), 1111–1124. Walter, B., Gromke, C., Lehning, M., 2009. The SLF boundary layer wind tunnel—an experimental facility for aerodynamical investigations of living plants. In: 2nd International Conference on Wind Effects on Trees. Freiburg, Germany. pp. 31–37. Walter, B., Gromke, C., Leonard, K.C., Manes, C., Lehning, M., 2012. Spatio-temporal surface shear-stress variability in live plant canopies and cube arrays. Bound-Lay. Meteorol. 143 (2), 337–356. Woodruff, N.P., Siddoway, F.H., 1965. A wind erosion equation. Soil Sci. Soc. Am. J. 29 (5), 602–608. Yassin, M.F., Takahashi, T., Kato, S., 2012. Experimental simulation of wind flow over the ridge topography. Air Qual. Atmos. Health 5 (3), 293–301. Zilker, D.P., Hanratty, T.J., 1979. Influence of the amplitude of a solid wavy wall on a turbulent flow. J. Fluid Mech. 90 (2), 257–271.
¯
effective surface shear stress ( eff ) can be predicted using a model that contains ridge height, spacing and u* of free-stream. Declaration of Competing Interest
The authors declare that there is no conflict of interest to this work. Acknowledgments We thank postgraduate students Xuesong WANG, Junjie ZHANG, and Zhicheng YANG of Beijing Normal University for their assistance during the wind tunnel experiments. This study was supported by the National Natural Science Foundation of China (Nos. 41630747 and 41330746). Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.still.2019.104548. References Armbrust, D.V., Chepil, W.S., Siddoway, F.H., 1964. Effects of ridges on erosion of soil by wind. Soil Sci. Soc. Am. J. 28 (4), 557–560. Bagnold, R.A., 1941. The Physics of Blown Sand and Desert Dunes. Methuen, London. Chepil, W.S., Milne, R.A., 1941. Wind erosion of soil in relation to roughness of surface. Soil Sci. 52 (6), 417–434. Chepil, W.S., Woodruff, N.P., 1963. The physics of wind erosion and its control. Adv. Agron. 15, 211–302. Fryrear, D.W., 1984. Soil ridges-clods and wind erosion. Trans. ASAE 27 (2), 445–448. Fryrear, D.W., Chen, W.N., Lester, C., 2001. Revised wind erosion equation. Ann. Arid Zone 40 (3), 265–279. Hagen, L.J., 1991. A wind erosion prediction system to meet user needs. J. Soil Water
7