Physical model tests were conducted on sand-trapping fences with different heights and porosities in an indoor subsonic, blowing-sand wind tunnel at the Institute of Hydraulic Engineering and Water Resources Management (IWW), Rheinisch Westfälische Hochschule (RWTH) Aachen University, Germany. Fence porosity and grain size distribution of the sediment is based on in situ measurements conducted in Langeoog and Norderney, where the influence of sand-trapping fences on the dune toe growth and its relation with potential aeolian sediment transport was already investigated by the authors (see Eichmanns and Schüttrumpf, 2020, 2021).

For this work, a wind tunnel was built by the IWW itself and was constructed mainly from wooden panels, except the test section was built from polymethylmethacrylate to allow visual observation of the experiments. The wind tunnel had a total length of L = 25.8 m, see Figure 1. The cross-sectional area was H = 1.0 m (height) and B = 0.58 m (width). The wind tunnel consisted of the following four parts: the power section with the wind machine, rectifier section followed by contraction section, channel with test section, and diffusion section. A sediment bed with a length of l = 4 m, a width of b = 0.4 m, and a depth of t = 0.15 m was installed in the test section. The sand-trapping fence as the focus of the investigation was installed within the sediment bed, d = 2 m from the edge of the sediment bed in the windward direction. In addition, a sediment source with a layer with a volume of V = 0.0435 m³ was placed about 1 m behind the roughness section in the main wind direction.

The Trotec TTW (Trotec) wind machine generates a continuous airflow of Q = 45.600 m³/h. The wind machine is equipped with an inverter that allowed mean wind velocities to be adjusted between u _mean ∼ 1–10 m/s. The wind first passes through a honeycomb, see Figure 2A, and second, through a coarser and a finer screen, see Figure 2B, to straighten the airflow. The honeycomb is designed following the findings of Barlow et al. (1999) and Mehta (1979) and was built out of ∼7.500 bounded polyvinylchloride tubes with an outer diameter of d = 16 mm and a length of l = 120 mm. In addition, the surface roughness is increased by four spires, a trip fence, and a 6-m-long artificial grass cover, see Figure 2C.

The flow field and sediment flux measurements were conducted separately. First, a fixed sediment surface was installed to measure the wind velocities via a hot-wire anemometer. Since the hot-wire anemometer is susceptible to damages from the windblown sediment, a thin layer of sediment glued to a wooden panel was installed while measuring the wind profiles in the test section. Only wind directions perpendicular to the fences were investigated in the wind tunnel. The experimental mean wind velocities were u ₁ = 6.1 m/s, u ₂ = 7.4 m/s, and u ₃ = 9.3 m/s. Then a moveable sediment bed combined with a sediment source was established, where a vertical sediment trap determined the sediment flux and a 2D LiDAR sensor SICK LMS4000, the sediment accretion around the sand-trapping fence. This fixed and moveable sediment bed procedure was already carried out in comparable wind tunnel experiments such as Hotta and Horikawa (1990). A GoPro Hero 8 recorded each experiment for visual observation. In Figure 3, the instrumentation setup for the test section is shown.

The sediment source is added, such as in experiments by Creyssels et al. (2009) or Ho et al. (2011, 2012), to favor the development of a steady state of saltation. Experiment’s duration is set to t = 10 min to ensure almost stationary sediment fluxes. This is in agreement with other investigations such as Chen et al. (2019, 2020), Wang et al. (2018), or Miri et al. (2019), where short measuring intervals, up to several minutes, are common. Some of these experiments were even shorter. Exceeding this experiment duration would empty the sediment source and the sediment bed. Furthermore, vertical mesh sand traps are limited to a constant sand-trapping capacity that will exceed if testing times are excessive. Moreover, we wanted to avoid the effects of supply limitations on the dune development (Swann et al., 2015) or increase the model effects at the physical boundaries (transition from wooden panels to the sediment bed).

Sediment from the study site Norderney was used for the experiments. To ensure the defined moisture content of M < 0.1%, for all investigations, the sediment was dried in a dry oven at a temperature of around T = 105°C. According to the specifications in DIN EN ISO 14688-1 (2018), a sedimentological analysis was conducted. The median grain size of the sediment was d ₅₀ ∼ 212 µm.

The investigated sand-trapping fences were modeled using locally available brushwood branches with a diameter of d ∼ 2–10 mm. In total, nine different fence configurations were investigated in the wind tunnel, varying in both fence height (h = 40, 80, 120 mm) and fence porosity (ε ∼ 20–58%). The two-dimensional porosity was determined as the open to total surface ratio. The exact porosities are shown in Figure 4 and were determined by evaluating photographs of the sand-trapping fences. Therefore, the photographs were processed with the MATLAB, 2018’s (R2018b, version 9.510.944444) Color Thresholder Application. The areas overlaid by the brushwood branches were identified and colored in black with a chosen threshold value. The contrast toward the background was increased and colored in white to indicate that there is no brushwood. For more information about the segmentation of the photographs, refer Eichmanns and Schüttrumpf (2021).

The porosity of the different sand-trapping fence configurations varies slightly over height due to the uneven nature of the branches. Thus, the modeled fences tend to become a little more porous in their upper parts. In the following, the mean porosity is determined for the three different fence heights and used for low (ε ₁ = 22.6%), medium (ε ₂ = 41.6%), and high (ε ₃ = 56.5%) porosity. The mean porosities generally correspond to the porosities of Langeoog and Norderney’s sand-trapping fences (Eichmanns and Schüttrumpf, 2021). However, the brushwood bundles differ in their stem characteristics, such as the stem diameter (d ∼ 2–10 mm). At present, the authors are not aware that the stem diameter significantly influences the sediment accretion around the sand-trapping fence, especially since, in a scientific research, the fence’s porosity was identified as a significant influence on trapping sediments (e.g., Arens et al., 2001; Zhang et al., 2010; Li and Sherman, 2015; Miri et al., 2019; Yu et al., 2020).

To measure the wind fields, all fence heights and porosities were investigated (27 cases); to measure the sediment accretion around the sand-trapping fence, only the highest fence height was installed (nine cases), see also Figure 4. Researching this fence height ensures that the saltation layer height does not significantly exceed the fence height, allowing the fence to capture most of the windblown sediment, see also Sediment Transport Fluxes. The influence would be more remarkable for other fence heights since the fence heights are considerably lower than the saltation layer height, and thus, the aeolian sediment would also blow over the fence.

The type of aerodynamic flow in the wind tunnel can be characterized by the Mach number M (-), as follows M =   u  c   , (1) where c ∼ 343 m/s (temperature T = 20°C) is the speed of sound of the medium. At any point in the wind tunnel, the velocity is less than the speed of sound of the air (M < 1), and thus it is a subsonic flow (Barlow et al., 1999; Anderson, 2017). The thickness of the boundary layer in the test section was determined to be approximately δ ∼ 650 mm. Incompressible airflows are primarily characterized by their Reynolds number and are decisive for their dynamic similarity. The following conditions must be met: Reynolds number of the flow must be greater than Re _flow >10 ⁵ and the roughness Reynolds number must be greater than Re _R > 2.5 (Barlow et al., 1999; Cattafesta et al., 2010). The Reynolds number of the flow is defined as follows: R e f l o w =   u ∞   ⋅  δ ν , (2) where u_∞ (m/s) is the free flow velocity in front of the test section and ν ∼ 1.516·10⁻⁵ m²/s (T = 20°C) is the kinematic viscosity of air (White, 1996; Barlow et al., 1999; Cattafesta et al., 2010). The roughness Reynolds number Re _R (-) is defined as follows: R e R =   z 0   ⋅   u ∗ ν   , (3) where u _* (m/s) is the shear velocity and z ₀ (mm) is the aerodynamic roughness length (Nikuradse, 1933; Vithana, 2013), see also Measurement of Wind Velocity Characteristics. The first criterion was achieved with Re _flow ∼ 3 × 10 ⁵ , whereas the roughness Reynolds number was not achieved. The roughness Reynolds number could only be determined for experiments with the immobile sand bed, as the sensitive hot-wire probe could otherwise be destroyed by saltating sediment grains. However, we assumed that the roughness Reynolds number independence was achieved during experiments with the moveable sediment bed because the saltation process generally increases the roughness Reynolds number (Cermak, 1987; White, 1996; Barlow et al., 1999).

The minimal entrance length L _in,min ∼ 10–25· δ (m) for describing the logarithmic wind profile is considered sufficiently long with L _in = 15 m under the assumption that saltation is present and the Froude criterion Fr (-) is fulfilled, as follows: F r   =   u ∞ g · H , (4) where g = 9.81 m/s² is the gravitational acceleration and H (m) is the wind tunnel height. The smaller the Froude number, the faster a constant shear stress velocity, and thus, a constant velocity profile is achieved during saltation (White, 1996). The Froude criterion is fulfilled for the investigated flow velocities u _1–3 = 6.1–9.3 m/s with Fr << 20 (Owen and Gillette, 1985). Sidewall effects are not expected with the investigated low wind velocities and corresponding shear stress velocities in the wind tunnel. For the blockage ratio two criteria exist. The maximum blockage ratio BR ₁ (-) defined as B R 1 =   A f e n c e A < !   0.1   , (5) which is fulfilled for fence models with heights h ₁ = 40 mm and h ₂ = 80 mm, whereas the blockage ratio BR ₂ (-) can only be met for the lowest fence height h ₁ = 40 mm. It is defined as the ratio of the fence height h (mm) to the height of the boundary layer δ (mm): B R 2 =   h δ < !   0.15. (6) These criteria were not always met in past studies either, such as Dong et al. (2007), Wang et al. (2018), and Yu et al. (2020), but assumed to have a minor influence as long as the fence height was at least smaller than the height of the boundary layer. Since the selected fence heights are considerably smaller than the boundary layer height, it can be assumed that no significant influence is expected by exceeding this limit value.

The Testo hot-wire anemometer (testo, 2021), equipped with an external data logger Testo 440 dp, was placed in the center of the wind tunnel at predefined heights (z = 3, 6, 12, 24, 40, 80, 120, 200, and 250 mm) above the surface to measure wind velocities. For this purpose, the hot-wire anemometer was inserted via a hole in the wind tunnel cover, and after measurement of the wind profile, the anemometer was moved to the next position downwind. The respective holes in the lid were sealed tightly with plugs, see Figure 3. For the flow field test, the wind velocity profiles near the sand-trapping fence were measured on the leeward side at a distance of 2, 5, 8, 10, 12, 15, and 20 h from the fence, on the windward side at distances of −2h, −5h, and −10h, and at a reference position over the wooden panel at x = −2,200 mm from the fence, where h is the height of the sand-trapping fence. We recorded a steady and uniform airflow field in the test section without a sand-trapping fence, see also Figure 7. The hot-wire anemometer has an accuracy of ±0.03 m/s and 3% of the mean wind velocity. In order to obtain reliable measurement results, the measurement duration is decisive. A measurement duration that is too short can lead to incorrect measurement results. The longer the measurement duration, the more representative the measurement results. The wind velocity was measured for 10 min at two locations and then analyzed. The 10-min measurement period is divided into ten intervals of equal time (t = 1 min), and the difference between the mean flow velocity over each 1-min interval over the whole 10-min interval is determined. The maximum difference was ±1.2%. Therefore, a measurement interval of 1 min is defined as sufficiently accurate for this investigation. Moreover, the reproducibility of the measured data for the wind profiles was ensured by repeating several measurements randomly with a maximum deviation of ±4% at one measuring point.

An appropriate analytical approach to describe the wind velocity distribution over the viscous sub boundary layer for aerodynamically rough surfaces is the law of the wall, which is valid for neutral atmospheric stability conditions, as follows (Bagnold, 1954): u z =   u * ĸ ⋅ ln z z 0 , (7) where u _z (m/s) is the wind velocity at height z (m) and κ (−) is the Kármán constant (here 0.41) (Nikuradse, 1933; Vithana, 2013). Figure 5 exemplifies the velocity profiles for u ₁ = 6.1 m/s, u ₂ = 7.4 m/s, and u ₃ = 9.3 m/s at the reference position with corresponding shear velocities u _1* = 0.21 m/s, u _2* = 0.25 m/s, and u _3* = 0.28 m/s, and coefficient of determination R ² = 0.95–0.98 is shown. It describes the approaching airflow entering the test section.

For all measurement heights at the reference position, the corresponding standard deviations were less with σ _min = 0.19 m/s, σ _max = 0.61 m/s, and σ _mean = 0.39 m/s, respectively.

When a particular critical value of drag and lift force on the sediment grain is exceeded, sediment transport is initiated. This is the so-called critical shear stress u _*t (18): u ∗ t = A  ⋅ ( ρ s ρ a − 1 ) ⋅  g  ⋅   d 50   . (8) The empirical constant is given with A (-) (here 0.11), the density of air is given with ρ _a (kg/m³) (here 1.2 kg/m³), and the density of sediment grains with ρ _s (kg/m³) (here 2,650 kg/m³). The empirical constant considers the effect of cohesion; however, the influence of the protective layer of shells or moisture contents is not taken into account (Shao and Lu, 2000; Han et al., 2011; van Rijn and Strypsteen, 2019). The critical shear velocity was calculated for the wind tunnel investigations as u _*t = 0.24 m/s. However, it was noted that sediment transport occurred with critical shear velocities above u _*t = 0.20 m/s.

To describe the influence of different fence porosities and fence heights on the wind profile at a certain height z (mm) and distance x (mm) from the fence, the wind reduction coefficient R _c (-) is used (Cornelis and Gabriels, 2005; Wang et al., 2018; Yu et al., 2020): R c = 1 − u x , z u 0 x , z . (9) The horizontal wind velocity is given with u _x,z (m/s) and the horizontal wind velocity at that exact position without any fence with u _0x,z (m/s). A high value indicates a high wind reduction.

For each experimental mean wind velocity, mean sediment transport rates were measured to determine the incoming sediment flux from the sediment source. Thus, vertical mesh sand traps constructed according to Sherman et al. (2014) and already used in field experiments of Eichmanns and Schüttrumpf (2020), covering a height of z = 0.3 m above the surface, see Figure 3, were used. The vertical mesh sand trap consists of six rectangular aluminum tubes arranged one above the other. One rectangular aluminum tube has the dimensions of 0.1 m (width) × 0.05 m (height) × 0.25 m (length) and 2 mm (edges). One rectangular aluminum tube is equipped with a nylon monofilament with opening sizes of size = 50 µm. The vertical mesh sand traps were exposed to sediment flow during the defined time interval of t = 10 min, and, afterward, the collected sand was weighed per height. The empirical exponential decay function is used to describe the vertical distribution of sediment transport as follows (Ellis et al., 2009; Poortinga et al., 2014): q z = q 0   ⋅   exp ( − β  ⋅  z ) , (10) where q _z (kg/m²/s) is the sediment transport rate at a predefined height z (m), q ₀ (kg/m²/s) is the extrapolated saltating sediment mass transport at the surface, and the decay rate ß (1/m) is a constant to describe the vertical concentration gradient. A regression analysis of the experimental data gives the parameters ß and q ₀ (Bauer and Davidson-Arnott, 2014). According to the scientific literature, the range of values for the fitting coefficient can vary significantly due to the weak correlation to physical aeolian parameters such as grain size or shear velocity (Bauer and Davidson-Arnott, 2014). Integrating Eq. 10 gives the total mass transport, as follows: Q s = ∫ 0 ∞ q z   ⋅ d z = q 0 β   . (11) The total mass transport by saltation is given as Qs (kg/m/s) (Bauer and Davidson-Arnott, 2014). Since aeolian sediment transport is highly variable spatially and temporally, the experiments were repeated three times and the average value was used for further analysis (Baas and Sherman, 2006; Bauer and Davidson-Arnott, 2014; Strypsteen, 2019; van Rijn, 2019).

We deployed a 2D LiDAR scanner at the centerline of the wind tunnel, where the wind velocity profiles were also measured. We found that the centerline represents the sediment accretion around the sand-trapping fence well based on the camera recordings. The laser scanner detected the sediment surface elevations every Δt = 2 min with a systematic error of ±1.5 mm and a statistical error of ±2.5 mm (distances between 1.97–2.40 m). The measuring frequency was set to 10 Hz, and the angular resolution was 0.0833°.

In the following, the trap efficiency is used to evaluate the different sediment accretions around the configurations of the sand-trapping fence. In order to eliminate model effects on the sediment accretion caused by the fence, the sediment fluxes were distinguished based on the continuity equation. Thus, Figure 6 presents a schematic side view of the wind tunnel test section with the sediment accretion around the fence at timestep t ₀ = 0 min and t ₅ = 10 min. The yellow areas show the typical erosion areas, whereas the colored areas in orange give the accretion areas. The zero-crossing between two sediment surface elevations at different timesteps is defined as boundary condition distinguishing between the different sediment changes (sf ₂ , sf ₃ , and sf ₄ ), see red crosses in Figure 6.

During the experiments, local scouring always occurred at the transition between the wooden panel and sediment bed and vice versa, see Sediment Accretion Around the Sand-Trapping Fence Configurations. These sediment changes sf ₂ and sf ₄ were caused by increasing shear stress associated with increasing surface roughness, which lead to fluctuations and turbulences, thus, initiating erosion processes (Swann et al., 2015). Since in a steady-state equilibrium, foredunes generally oscillate about a geomorphic equilibrium, accreting (recovery) and eroding (response), it is assumed that the scour sf ₄ at the end of the sediment bed would extend over a longer distance followed by a sediment accretion (Swann et al., 2015). Thus, this sediment change sf ₄ is excluded from further analysis. Excluding the sediment flux sf ₄ (sf ₄ << sf ₃ ) still provides valid results.

It is assumed that during the experimental time frame of t = 10 min, the scours have a minor effect on the accretion of sediment around the sand-trapping fence. According to experiments of Hotta and Horikawa (1990) and Ning et al. (2020), the zero-crossing between two surface elevations at different timesteps shifts insignificantly toward the fence (maximum x/h ∼ 2) such as in our experiments. Thus, it is assumed that the morphodynamics around the sand-trapping fence is modeled correctly in our experiments, see also Sediment Accretion Around the Sand-Trapping Fence Configurations. However, this can only be determined adequately with a sufficiently long wind tunnel and extensive test durations.

For evaluating the sand-trapping of different fence configurations, the trap efficiency E (-), see for example, Ning et al. (2020) or Chen et al. (2019), is defined as follows: E = Q t Q s   . (12) The trapped sediment transport Q _t (kg/m/s) is estimated as the product of the bulk density of the sediment γ (kg/m³) and the cross-sectional dune area ΔA (m²) (sediment change sf ₃ ) in the time interval Δt (s), as follows: Q t = γ   ·   Δ A Δ t   . (13) The sediment transport for initiating the sediment accretion around the sand-trapping fence is calculated based on total mass transport Q _s , see Eq. 11, from which the sediment change sf ₂ is subtracted. The bulk density was γ = 1,550 kg/m³ (average out of three measurements).

Since windblown sediment transport is highly variable both spatially and temporally, the experiments were repeated three to four times (Baas and Sherman, 2006; Bauer and Davidson-Arnott, 2014; van Rijn, 2019).

Figure 7A presents the flow field in the x-direction (mm) over the height z (mm) without a sand-trapping fence; Figures 7B–D depicts the flow fields in the vicinity of a sand trapping. The free mean velocity was u ₃ = 9.3 m/s, and the x-axis and the y-axis were normalized by the fence height. The black dots represent the measurement positions of a hot-wire anemometer with the mean wind velocity values over the 1-min measuring interval, and the brown lines indicate the fence. Generally, the airflow slows down on the upwind side of the fence. Above the fence, the airflow accelerates, and on the leeward side, the vertical eddy zone occurs, resulting from the difference of the wind velocity above and through the fence.

The complexity of the airflow fields decreased while the fence porosity increased. For the low porosity fence, the wind velocity profiles show a higher range of measured wind velocities between u = 2.3–11.3 m/s than the high porosity fence profiles showing wind velocities between u = 6.3–11.1 m/s. In addition, the wind velocities in front of and behind the fence are reduced to a greater extent. For better illustration, Figure 8 represents the mean wind velocities in the x-direction for the different fence configurations, divided into the following fence heights: (A) h ₁ = 40 mm (B) h ₂ = 80 mm, and (C) h ₃ = 120 mm. The mean wind velocity in the x-direction was averaged by values of wind velocities at heights of z = 3, 6, 12, 24, 40, 80, 120, 200, and 250 mm. The mean wind velocities were averaged up to a height of z = 250 mm within the boundary layer rather than the entire wind tunnel height of H = 1,000 mm.

Comparing the wind fields for the different fence heights (h ₁ = 40 mm, h ₂ = 80 mm, and h ₃ = 120 mm), we detected no significant differences in the mean wind velocities under constant porosity and constant free wind velocity.

For the lowest fence porosity (ε ₁ = 22.6%) and the highest fence height (h ₃ = 120 mm), the wind reduction is most significant at position x/h = 5. For the mean free wind velocity u ₁ = 6.1 m/s, the lowest mean wind velocity in the x-direction was u _mean = 3.4 m/s, whereas for the lowest fence height (h ₁ = 40 mm) and the lowest fence porosity (ε ₁ = 22.6%), the lowest mean wind velocity was u _mean = 4.4 m/s at position x/h = 5. In the downwind direction, the wind velocity increased, reached their minimum at position x/h = 5, and then increased again to the initial wind velocity. For all fences with the characteristics of ε ₂ = 41.6%, the minimum value was already reached at position x/h = 2. The higher the porosity of the fence was, the earlier the initial wind velocity of the fence was reached in the free stream.

Figure 9 exemplifies the vertical distribution of sediment transport fluxes obtained from the vertical mesh sand traps for the wind velocity u ₃ = 9.3 m/s. We found that sediment was mainly caught in heights of less than z ≤ 0.05 m for all wind velocities studied. This finding is in agreement that most sediment transport in coastal areas occurs for z < 0.05 m above the surface (Strypsteen, 2019). No sediment was caught in heights over z > 0.15 m, so the saltation layer height does not significantly exceed the fence height (h ₃ = 120 mm), see Experimental Setup.

Table 1 presents the results of the trapped sediment from the vertical mesh sand traps with the total mass flux Qs (kg/m/s), the decay rate ß (1/m), the extrapolated saltating sediment mass transport at the surface q ₀ (kg/m²/s), and the correlation coefficients R ² (-) of the regression analysis. The measuring duration was t = 10 min. The transport fluxes varied between Qs = 0.005–0.078 kg/m/s for wind velocities ranging between u ₁ = 6.1 m/s and u ₃ = 9.3 m/s. For the lowest wind velocity u ₁ = 6.1 m/s, the total mass fluxes show larger fluctuations than those at higher wind velocity u ₂ = 7.4 m/s and u ₃ = 9.3 m/s.

The regression parameters varied between ß = 83–105/m and q ₀ = 0.44–6.79 kg/m²/s, indicating that the higher the wind velocity, the higher the extrapolated saltating sediment mass transport at the surface and the amount of the total sediment transport rate. However, the decay rate and the sediment transport height did not vary significantly during the experiments for different wind velocities.

Figure 10 shows sediment accretion around the investigated sand-trapping fences h ₃ = 120 mm over time, starting at t ₀ = 0 min and ending at t ₅ = 10 min. Both the x-axis (-) and the y-axis (-) are normalized over the fence height. The results for the investigated wind velocity u ₁ = 6.1 m/s are shown in Figures 10A,D,G, u ₂ = 7.4 m/s in Figures 10B,E,H, and u ₃ = 9.3 m/s in Figures 10C,F,I, respectively. The first row shows the results for ε ₁ = 22.6%, the second row for ε ₂ = 41.6%, and the third row for ε ₃ = 56.5%. The different colors of the lines indicate the different timesteps Δt = 2 min. The sediment changes are Δsf ₂ and Δsf ₃ is given in the legend.

The sediment accretion occurred predominantly horizontally and vertically, which corresponds to the first phase of dune growth, see for example Ning et al. (2020). Longer experiment durations would probably lead to the sediment accretion according to the second dune growth phase with almost exclusive horizontal dune growth if a sufficient sediment supply is provided. It is well seen that the higher the investigated wind velocity, the higher the total amount of deposited sediment at the sand-trapping fence at a given time, caused by a higher aeolian sediment transport rate. Furthermore, the denser the fence porosity, the higher the deposited sediment on the windward side of the sand-trapping fence at any given time. For example, for the lowest fence porosity of ε ₁ = 22.6%, the deposited sand reached a height of maximum z/h ∼ 0.4, whereas for the highest fence porosity of ε ₃ = 56.5%, the maximum height of z/h = 0.28 was reached. Generally, it can be recognized that for fences with ε ₂ = 41.6% and ε ₃ = 56.5%, scouring occurred in the main wind direction directly behind the fence at position x/h ∼ 1, whereas for ε ₁ = 22.6%, only little scouring was recorded at this position.

The sediment accretion on the leeward side developed simultaneously but faster than the sediment accretion on the windward side of the fence. For the lower and middle wind velocities (u ₁ , u ₂ ), the height of the sediment accretion of the windward side is approximately the same as the height of the leeward side of the fence. For the fence with the lowest porosity, the sediment accretion on the leeward side of the fence occurred until x/h ∼ six to eight, whereas fence with the medium porosity until x/h ∼ seven to nine and for the most porous fence until x/h ∼ 8–12.

The wind profile could be measured well and provide reproducible data in repeated experiments with the applied methodology. In Figure 11, the wind reduction factors R _u (-), according to Eq. 9, for the fence heights h = 40, 80, 120 mm are shown along the x-axis, normalized over the fence heights.

In Figure 12, the wind reduction factors R _u (-) for the fence porosities of ε = 22.6, 41.6, 56.5% are shown respectively.

Note that a higher wind reduction factor indicates a more substantial reduction in wind velocity and thus favors sediment deposition around the sand-trapping fence. We recognized that the wind reduction coefficients were almost the same for varying free wind velocities but varied significantly for different fence porosities and fence heights. The results show that, with increasing distance from the fence, the wind reduction coefficient increased to the maximum value and then decreased or stabilized again. The position at which R _u begins to decrease or stabilize, the protection range, generally lies between x/h = 2–5. The wind reduction coefficient was substantially greater for higher fences (R _u,max = 0.48) than lower fences (R _u,max = 0.21) and also higher for less porous fences (R _u,max = 0.48) than for more porous fences. Furthermore, it becomes clear that for the medium and high fences, the influence of the porosity is greater than for the low fences since the variety of R _u is also smaller. However, the fence height plays a minor role in the case of the most porous fence. This is in agreement with findings of Perera (1981), who found in wind tunnel experiments with vertical and horizontal slats (porosity >30–50%) or Lee and Kim (1999) who found with perforated fences (circular openings with porosity >40%), no recirculating zone occurred due to the strong bleed flow. For ε ₁ = 22.6% and ε ₂ = 41.6%, the typical airflow conditions around a single porous fence can be identified (Plate, 1971). However, for the fence of porosity ε ₃ = 56.5%, a strong bleed flow leads to smaller wind velocity reduction, the recirculating zone disappears, and the airflow zones become less complex (Dong et al., 2007).

We found that the two-dimensional development of the sediment accretion around the sand-trapping fences could be measured well with the 2D LiDAR scanner and is quantitatively reproducible in repeated experiments (maximum standard deviation of the sediment accretion σ ∼ 0.15). However, for low wind speeds, the ratio of the measurement error to the deposition heights is so small that the measurement error has a significant influence on the results. In addition, the aeolian sediment fluxes showed large temporal fluctuations, which were noticed especially during experiments with the wind velocity u ₁ = 6.1 m/s, see Table 1. As far as the authors know, the reproducibility of the sediment accretion around a sand-trapping fence is investigated for the first time with the results presented herein.

Figure 13A gives the changes of cross-sectional area and Figure 13B the trap efficiency for all configurations over time. The changes of cross-sectional areas ΔA (m²) and the trap efficiencies E (-) are shown as the average value of three up to four repeated measurements. Generally, as the sediment transport rates increase, the cross-sectional areas around the sand-trapping fence also increase; with the densest fence tending to accumulate the most sediment, then the medium-density fence, and then the porous fence. At the beginning of the experiments, the trap efficiency increases, and as time passes, the efficiency decreases or stabilizes.

For the medium (u ₂ = 7.4 m/s) and high wind velocity (u ₃ = 9.3 m/s), the maximum trap efficiency is reached between t = 360–600 s, whereas, for the lowest wind velocity (u ₁ = 6.1 m/s), the maximum is reached at t = 360 s. After the trap efficiency increases to its maximum, it decreases slightly or stagnates to equilibrium during the time investigated in our experiments. This is in accordance with findings of Ning et al. (2020), where the sand-trapping is highest at the beginning of the first phase, drops significantly until the end of the first phase, and continues to drop slowly until the end of the second phase.

For the different investigated sand-trapping fence’s porosities (ε ₁ = 22.6%, ε ₂ = 41.6%, ε ₃ = 56.5%) and wind velocities (u ₁ = 6.1 m/s, u ₂ = 7.4 m/s, u ₃ = 9.3 m/s), the calculated trap efficiencies, see Eq. 12, are shown as boxplots (Figure 14). Since the efficiencies vary over time, all timesteps of the experiments are included showing the variations. The mean trap efficiencies for the dense fence (ε ₁ = 22.6%) E _h120,e22.6 are 0.69 (u ₁ = 6.1 m/s), 0.57 (u ₂ = 7.4 m/s), 0.63 (u ₃ = 9.3 m/s) and for the medium fence E _h120,e41.6 are 0.66 (u ₁ = 6.1 m/s), 0.52 (u ₂ = 7.4 m/s), 0.58 (u ₃ = 9.3 m/s). For the highest fence porosity (ε ₃ = 56.5%), the efficiencies E _h120,e56.6 are 0.45 (u ₁ = 6.1 m/s), 0.41 (u ₂ = 7.4 m/s), 0.52 (u ₃ = 9.3 m/s).

Generally, the trap efficiency for the dense and medium fence are higher than for the lowest porosity fence. However, the shape of the resulting sediment accretion differs for the fences. Sand-trapping fences with lower porosities (ε ₁ = 22.6% and ε ₂ = 41.6%) favor localized sediment accretion directly at their brushwood lines. Fences with higher porosity (ε ₃ = 56.5%), allow for more sediment accretion further downwind, see also Figure 10. Thus, denser fence porosities are more suitable for constructing sand-trapping fences to initiate and facilitate the coastal dune toe growth. Fences with higher porosity could be used where the sediment accretion would occur over a longer downwind distance, for example, to allow a smoother transition between the foredunes and the white dunes.

Moreover, for the same porosity, the low wind velocity (u ₁ = 6.1 m/s) always gives the highest trap efficiency, followed by efficiency for the highest wind velocity (u ₃ = 9.3 m/s) and the medium wind velocity (u ₂ = 7.4 m/s). This can be explained by the fact that the critical shear stress velocity is minimally exceeded at the lowest wind velocity.

We strongly recommend extending the wind tunnel experiments over longer test sections to gain more quantitative data. This would require much larger wind tunnel dimensions with a larger sediment bed as well as a continuous sediment supply. With these proposed boundaries, it could be measured over more extended periods. Furthermore, installing numerous rows of fences in a larger wind tunnel would allow us to evaluate the optimal distance between numerous rows of fences to favor sediment accretion.