The field experiment was conducted from Dec. 2017 to Mar. 2018 on a dry, flat beach (25°25′32.48′′N, 119°45′0.01′′E) at the Yuandang Bay, Pingtan, China (Fig. 1), with NNE–NE in prevailing wind direction and active sand transport in winter (He et al., 2022). The nearshore has an annual wave height of 1.1 m and a typical tidal range of 5 m and the sand is well-sorted with median grain size of 0.25–0.45 mm (He et al., 2022).

Ning et al. (2020) observed two stages of dune development around fences. In Stage I, the dune grows vertically to reach the maximum height, and in Stage II the dune grows horizontally to expand the dune crest. For Experiments 1 and 2, we only observe the dune development in Stage I (c.f. Figs 4a–d) due to limited sand supply. However, for Experiments 3 and 4, dunes had entered Stage II and even stopped growing after their last measurements (c.f. Figs 4e–h), indicating they reached an equilibrium status.

As shown in Fig. 4, for all cases, there emerged two dunes on windward and leeward sides of each fence, respectively, after sand started to move. All windward dunes were much smaller than the leeward dunes. For each fence, there is a distinct trough between these two dunes except for the cases of MG and SG, when erosion pins were used, maybe because of the lack of erosion pin deployment at the fences. The trough is deeper for HS and UD than their counterparts VS and LD, respectively. For all fences, the profile patterns of windward dunes were very similar to each other and their occurrence locations are quite close while for the leeward dunes, their profiles varied both in location and geometry. These two dunes start to merge during Stage II and finally only a small trough was observed at LD fence while no observable trough for UD fence.

As shown in Fig. 4, although the general patterns of the dune development is similar between fences, the specific dune crest locations can be very different. To explore this, we have plotted the peak locations with distance to fence as x and height as y in Stage I (Fig. 5). As shown in the Fig. 5a, most of windward dune peaks are located between −1 m and 0 m, with distance almost as a constant for most of fences except HS, MG and SG, demonstrating almost the vertical growth in Stage I. The sudden increase of peak distance may be due to the scanning error induced abrupt local topography change as shown in Fig. 4d. For MG and SG fences, as mentioned before, their peaks may not be correctly identified due to the low spatial resolution of erosion pins. The UD fence also has the longest distances compared to other fences.

As shown in Fig. 5b, after some initial adjustments, the most leeward dunes have slight tendency to move downwind with increase of dune height except for UD fence which has the opposite trend. Moreover, peak distance has more variability than windward cases. For example, UD fence has the longest distances and LD fence has the shortest distance. SG fence has longer distance than LD but smaller than other fences. For most heights, there are insignificant differences in distance among LG, RLG, HS, VS, and MG.

With the development of the dune, the windward dune and leeward dune are prone to merge into one large dune during the Stage II. Figure 6 demonstrates the last profiles for MG, SG, UD and LD fences. MG and LD fences have flatter crest with more downwind peak locations than SG and UD. The peak height has the order of UD > MG > SG > LD, same as the order of the cross-sectional areas, indicating UD and MG has larger trapping capacity.

The accumulated deposition volumes V_t in Stage I is plotted against accumulated incoming sand flux F_t at time t (c.f. Fig. 7). Statistical analysis shows that there are linear relationships between them for all fences at 95% confidence level. The slope of these curves represents the ratio of deposited sand to incoming sand, therefore, it can be used to as a proxy to represent the trapping efficiency. As shown in the subplot of Fig. 7, the trapping efficiency has the order of UD > LD > SG > MG > VS > LG and RLG, showing fences with small, non-uniform porosity have higher trapping efficiency than fences with large, uniform porosity.

Here we propose a framework to demonstrate the interactions between wind, fence, sand, and dunes based on previous relevant aerodynamic works (Plate, 1971; Judd et al., 1996; Dong et al., 2006). As shown in Fig. 8, at the beginning of Stage I, the incoming sand-laden flow slows down its speed once it approaches the fence, where sand starts to deposit. However, when the flow passes through the fence openings, it is split and accelerated into numerous jets and thus almost no sand deposition at the fence. However, as the air behind the solid area of the fences is still, the spatially averaged wind speed in the near lee is low, leading to sand deposition where the jets are merged downwind. There is a flow separation at the fence top, generating a strong shear flow downwind, and this flow reattaches ground and stops sand deposition in the farther lee. The two deposition zones result in the formation and growth of the two dunes with a trough area in between. As the vertical growth of windward dune, the wind shadow area becomes larger and larger, thus weakening the jet flows, especially near the ground. This leads to more deposition in the trough area, and the two dunes start to merge. At the end of Stage I, the vertical growth of leeward dune stops due to the strong shear flow at the fence top level while the windward dune continues to grow vertically, which keeps enlarging the wind shadow area, resulting the continuous sand filling in the trough. Finally, the two dunes completely merge at the fence and form an equilibrium dune profile at the end of Stage II, when fence is almost buried with wind shear between impact threshold and fluid threshold across the whole profile and no further deposition or erosion occurs. It is obvious that the introduction of fence into the aeolian system makes the original wind-sand-dune system a three-way interaction into a wind-fence-sand-dune four-way interaction. This makes the fenced dune’s equilibrium profile looks substantially different from unfenced mature dune profile (c.f. last two dunes in Fig. 8). Moreover, unlike the fenced dune that has fixed location, the unfenced dune is still migrating due to continuous erosion on the stoss slope and deposition on the lee slope (Kocurek et al., 1992). However, as the wind field was not measured during the experiments, this framework is hypothetical and should be further examined.

The porosity of all the eight fences are designed to be around 50%. As porosity is considered as the primary control of wind field (Li and Sherman, 2015), similar air flows are expected to be formed. Therefore, it is not surprising to see all fences have similar two-dune-one-trough patterns. Although the dune development process shows little difference for some fences, we have also found that some fences have significant different dune profiles, especially in the near lee, which should be attributed to different configurations because porosity distribution, opening size, and opening geometry mostly affect the flows near fences (Jensen, 1954; Li and Sherman, 2015).

The dune profiles of LG and RLG fences are very similar to each other. This indicates the impact of opening orientation in this case (45° rotation) on the wind field was not significant. However, the HS fence and VS fence (90° rotation) have detectable impact on the profiles very close to the fences while the profiles in other places are very close. This may be because the horizontal slats create a continuous gap parallel to the surface, which allows the jets flows always greater than the threshold. However, for vertical slat, as flows were split into vertical jets, near surface flows are generally weaker, allowing more sand deposition at the fence. Compared to other fences, UD fence has the largest opening size near surface. This makes the surface wind reduction is generally smaller which leads to the largest trough area between the two peaks.

The dune peak heights from this study (0.8 to 1.2 times of fence height) is compatible with the results of other sand fence studies (Hotta and Horikawa, 1991; Tabler, 1980; Iversen, 1981; Ning et al., 2020). This is mainly because there is a strong shear flow at the level of fence height (Ning et al., 2020). However, the distance of the leeward peak to fence is apparently controlled by the configurations of fences. Fences with smaller openings, such as SG and LD fences, appears more effective in trapping sand closer to fence during Stage I, which is consistent with previous studies (Hotta and Horikawa, 1991) . This is mainly due to their stronger reduction effect on wind speed (Dong et al., 2011).

Fences with non-uniform porosities tend to have the largest trapping efficiency and fences with larger grids have the smaller efficiency during Stage I. This is consistent with a previous study that slat fences with smaller gaps have higher efficiency (Manohar and Bruun, 1970). This may be also because fences with smaller porosities are more efficient in wind reduction and thus sand deposition. Considering sand transport is proportional to wind speed cubed (Bagnold, 1941), with the similar porosity, fences with more smaller grids can have higher trapping efficiency. With similar reasons, the UD fences can trap most sand than other fences because it had the smallest opening after sand buried the lower section of these fences. However, after the whole fence is buried, the ultimate topographic profile can be only determined after understanding how newly formed dunes interact with sand-laden flows.

The erosion pins utilized in the third experiment leads to low resolution of the profile measurements in the third experiment, which makes it harder to compare with results from other experiments. Another limitation of this study was the inadequate scan area for dunes around HS fence, making it impossible to derive its trapping efficiency. Although the final stage of the UD and LD fences were recorded, the duration from the end of Stage I to the fully developed status was not captured by TLS.

The findings from this study indicate that UD fence is probably an optimal design for sand trapping efficiency and sand trapping capacity. Moreover, the peak of its fully merged dune is at the same location of the fence, which would be convenient for researchers and engineers to deploy the fence at the desired location of the dune.