the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Dec 2025
Near-threshold aeolian sand transport: Effects of boundary layer flow conditions
Abstract. Boundary layer thickness is a critical factor in aeolian sand transport, as it governs the scale of energy-containing turbulent structures, yet its specific mechanisms remain inadequately quantified. Previous studies have established the role of turbulence in particle entrainment but often overlook systematic variations in boundary layer thickness. This study aims to clarify how boundary layer thickness modulates wall-shear stress fluctuations, threshold wind velocities, sand flux, and particle kinematics. We use the three-dimensional large-eddy simulation coupled with a saltation model to investigate these interactions. Results reveal that increased boundary layer thickness enhances extreme-value probability density of wall-shear stress and significantly lowers impact entrainment and rebound thresholds—the latter dropping to less than 50 % of conventional wind-tunnel values. Sand transport response is velocity-dependent: at low velocities, transport rises markedly with thickness under fluid-driven entrainment; the effect diminishes at moderate velocities; and at high velocities, transport scales proportionally with thickness under splash-dominated entrainment. Moreover, thicker boundary layers intensify near-bed particle activity, elevating particle velocities and concentrations, reducing intermittency, increasing saltation height, and enlarging mean and variance of airborne particle diameters. These findings elucidate how boundary layer thickness modulates aeolian sand transport via turbulence–particle interactions, offering key insights for improving atmospheric and climate models and advancing the physics of turbulence-driven sediment transport in atmospheric boundary layer.
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Status: final response (author comments only)
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CC1: 'Comment on egusphere-2025-5135', Ning Huang, 17 Jan 2026
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AC1: 'Reply on CC1', Ting Jin, 19 Jan 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-5135/egusphere-2025-5135-AC1-supplement.pdf
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AC1: 'Reply on CC1', Ting Jin, 19 Jan 2026
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RC1: 'Comment on egusphere-2025-5135', Anonymous Referee #1, 04 Feb 2026
This paper studies the effect of the boundary layer thickness on several properties of windblown sand using a LES-based model. It is first shown that increasing boundary layer thickness leads to a widening of the probability distribution of the wall shear stress (Fig. 2), as expected. It is then shown that, as a consequence of the widening, two distinct thresholds of aeolian sand transport decrease (Fig. 3). Likewise, vertical profiles of the mass flux, particle volume fraction, horizontal velocity, and others are also affected (Figs. 4-9). The strength of this study is to look at the effect of a quantity, the boundary layer thickness, that is often being ignored as a sand-transport-influencing factor by the community, even though it may arguably play an important role. In fact, I only know a few studies to have looked into this ever. The main weakness of this study is the methodology used to model the motion of the particle phase. It uses the same aerodynamic entrainment and splash models as the one by Anderson and Haff (1991), which is problematic for a variety of reasons (explained below). Furthermore, the particle phase model does not resolve the bed as a whole and it seems to neglect collision between particles. Both have been shown to be quite important in recent years (explained below). This being said, I still think overall this study can be valuable, since the observed boundary layer thickness effects are quite interesting. However, more data analyses are needed, especially in what regards transport intermittency (see below), and I also think the authors should make sure their definitions of the “rebound threshold”, and the conclusions they draw from it, are consistent with the definition of this threshold in the literature (which I think it is not, see below).
Methodology concerns
By now, numerous research groups, for the purpose of simulating aeolian sand transport, have moved to using coupled CFD-DEM simulations that resolve the particle phase, including many layers of the bed, at the particle scale. Given that such simulations are now relatively quick due to much better computers, there is no longer a good justification to resort to approximating grain-bed and grain-grain interactions by splash functions derived from experiments and simulations for the impact of a single grain onto a static granular bed. We now know from quite a number of DEM-based studies that the bed cannot be treated as stationary and that cooperative effects resulting from residual motion within the sediment bed and its surface can alter splash characteristics quite dramatically: for example, Jia & Wang (2022, doi: 10.1016/j.catena.2022.106191), Tholen et al (2023, doi: 10.1103/PhysRevLett.130.058204), Wang et al. (2024, doi: 10.1111/sed.13225; 2025, doi: 10.1111/sed.70038), Lester et al. (2025, doi: 10.1038/s41561-025-01672-w). What is worse is that the static-bed splash function the authors use is the one by Anderson and Haff (1991), which models the rebound probability using an unphysical dimensional parameter that should be related to grain properties but is not. There are better ways out there to model static-bed splash: for example, Lammel et al. (2017, doi: 10.1103/PhysRevE.95.022902), Comola and Lehning (2017, doi: 10.1002/2016GL071822).
I strongly suggest the authors to change their methods to DEM-based techniques in the future, though I reiterate that, for the present studies, I can overlook these problems as the authors focus on a very rarely studied aspect of aeolian transport, the boundary layer thickness.
Aeolian transport thresholds
The authors use the terms “rebound threshold” and “impact entrainment threshold”, which were first introduced by Pahtz and Duran (2018, doi: doi.org/10.1029/2017JF004580), as far as I know. These authors also discussed these thresholds more thoroughly in a 2020 review paper (Pahtz et al, doi: 10.1029/2019RG000679). It seems to me that, while the present authors adapt the same definition of the impact entrainment threshold (threshold of continuous transport), the manner in which they obtain the rebound threshold differs from the original definition. They seem to extrapolate the intermittent transport rate to vanishing transport, which I infer from Fig. 3. By contrast, Pahtz et al. (2020) state that the rebound threshold results from the extrapolation of the continuous transport rate to vanishing transport. For this reason, I suggest the authors to use a different terminology. In addition, I think the authors should, if possible, also compute the actual rebound threshold. This requires dealing with intermittency in a more sophisticated manner (see below).
Intermittency definition
I find the authors’ quantity “particle spatial occupancy”, alpha_p, to be a very poor measure of intermittency. As far as I understand, it represents the ratio between the number of numerical grid cells occupied by at least one simulated particle (which represents many particles at the same time) and the total number of grid cells. The problem with this definition is that it depends strongly on the grid cell size. In particular, in the limit of zero grid cell size, alpha_p becomes zero everywhere and therefore meaningless, since the probability to find a point within an interval of measure zero is zero. This conflicts with a basic requirement of any numerical simulation: that any result obtained from it should converge in the limit of zero grid size.
A much better way to define intermittency is through bursts of overall activity, e.g., see Carneiro et al. (2015, doi: 10.1038/srep11109), Martin and Kok (2018, doi: 10.1029/2017JF004416), Comola et al. (2019, doi: 10.1029/2019GL085739). For example, the latter two studies looked at the fraction of time, fQ, at which aeolian transport is active, defined through a non-zero overall particle count over a period of 2s (approximate particle response time to turbulent wind fluctuations). The authors could adapt a similar measure. If it is defined appropriately, the ratio Q/fQ between the intermittent transport rate Q and fQ should behave like a universal function (see Comola et al., Eq. (3)), independent of the boundary layer thickness. In regard to my previous comment, this function could then be extrapolated to zero to obtain the actual rebound threshold.
Citation: https://doi.org/10.5194/egusphere-2025-5135-RC1 -
AC2: 'Reply on RC1', Ting Jin, 19 Feb 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-5135/egusphere-2025-5135-AC2-supplement.pdf
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AC2: 'Reply on RC1', Ting Jin, 19 Feb 2026
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RC2: 'Comment on egusphere-2025-5135', Anonymous Referee #2, 04 Feb 2026
This manuscript explores the role of boundary-layer thickness in modulating aeolian sand transport through turbulence–particle interactions using Euler–Lagrangian simulations. The topic is relevant to the aeolian research community, and the study provides interesting insights into the coupling between boundary-layer dynamics and particle transport. The following comments are intended to help clarify the physical interpretation of the results and to improve the manuscript.
Major comments
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A number of experimental studies have previously examined how turbulent shear stress distributions or turbulence structures affect aeolian sand transport (e.g., Li et al., 2020; Zhang et al., 2022; Tan et al., 2023). In this context, it would be helpful if the authors could further clarify how the effect of boundary-layer thickness considered here differs physically from changes in turbulence structure, for example, those associated with atmospheric stability. A brief discussion of the atmospheric or environmental conditions under which different boundary-layer thicknesses would occur in nature would also strengthen the interpretation of the results.
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From Fig. 2, it appears that the simulated boundary-layer thicknesses (1–10 m) mainly reflect differences in Reynolds number. Under this interpretation, the resulting shear stress distributions may correspond to different stages of boundary-layer development under the same pressure-gradient forcing (i.e., with the same friction velocity). This setup seems conceptually similar to the experimental studies of Williams et al. (1990, 1994). The authors may wish to clarify whether this interpretation is correct and to discuss the relationship between their simulations and those earlier experiments.
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The manuscript refers to the fluid threshold, rebound threshold, and impact threshold, but their definitions are not explicitly provided. Clarification of how these thresholds are defined and diagnosed from the simulation results (e.g., the mathematical or statistical criteria used) would improve the transparency and reproducibility of the study.
Minor comments
Line 224: Li et al. (2020a) is cited in the text but does not appear in the reference list.
Citation: https://doi.org/10.5194/egusphere-2025-5135-RC2 -
AC3: 'Reply on RC2', Ting Jin, 19 Feb 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-5135/egusphere-2025-5135-AC3-supplement.pdf
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RC3: 'Comment on egusphere-2025-5135', Anonymous Referee #3, 19 Feb 2026
This work performs a suite of numerical simulations using LES to investigate the sensitivity of particle saltation processes to boundary layer thickness. The boundary layer thickness partly controls the spectrum of turbulent scales of motion (for a fixed wind shear), and thus controls (in some capacity) the turbulence fluctuation intensity and range of surface stresses experienced by the particles. I enjoy reading about work that focuses on the role of turbulent fluctuations in particle emission processes (rather than simply considering emission by the mean), as these fluctuations can be remarkably strong at high Reynolds number. Based on the authors' results, it certainly seems like the boundary layer thickness (and thus the Reynolds number of the flow) plays a meaningful role for the mass flux. I agree with the authors that more models should include the role of turbulent fluctuations in saltation processes, and including information about boundary layer height (and its consequences for turbulence intensity) is certainly one way to do that.
I (cautiously) agree with the author's findings, but I am skeptical of the numerical method used in this work. The authors employ a standard wall-bounded flow setup, and since the horizontal boundary conditions are periodic, one might assume that a spectral (or hybrid spectral-finite difference) method would be more suitable than a second order centered difference scheme. The spectral method would preserve the finer fluctuations which may have a meaningful impact on the particle emission, one way or the other. For example, these fine scale features could decrease the coherence of the stress fluctuations, and may affect the author's results, but I am not certain.
Overall, I found that the captions of almost every figure lacked the information necessary to properly interpret the figures. I think that the authors should consider revising the captions to include more relevant information about the figures, such as reminding the reader what each symbol means.
Specifically regarding figure 6, the particles almost appear to be stacked in columns, i.e. they seem far too organized. Can the authors explain this phenomenon? I assume the particles are able to move horizontally, as they mention that the particles have horizontal boundary conditions, but this figure makes me think that they only mover vertically.One major point I have is that the Reynolds number is probably what matters here, not the boundary layer height independently. The authors mention as much when they reference that the boundary layer height (which increases the Reynolds number) controls the spectrum of turbulence scales. I think this article would benefit from a passage discussing the dynamical importance of the Reynolds number, and how the boundary layer height is actually only one part of the story (the other two being viscosity, and the wind velocity, or friction velocity).
Minor comments and typographical errors: The authors use the word "intermittency" many times. That has a specific meaning in the turbulence literature, and could easily be misunderstood. The authors should consider using the word "variability" as it seems to be what they mean, based on my reading.
Line 132: is u(x_p) the filtered velocity (i.e. what comes right out of the LES?), or is the sampled velocity re-constructed (i.e.Line 238: "Increasing"
The particle spatial occupancy: isn't this just the concentration? Is it markedly different?
Line 362: Perhaps it's worth mentioning that the maximum magnitude of the fluctuations occur in the buffer layer and this is a well recognized phenomenon, i.e. u_rms is maximal around y^+ = 10-20 and has some influence from outer layer motions (i.e. the boundary layer height). This can be seen in many papers on wall-bounded turbulence i.e. fig 4 in Smits et. al (2010) 10.1146/annurev-fluid-122109-160753
Line 368: I'm having trouble following this part. Please revise.
I'm unclear on the meaning of the cyan arrow in figure 9(b)
Line 385-386: I can't quite follow the inline math. Please revise
Citation: https://doi.org/10.5194/egusphere-2025-5135-RC3
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This study accurately addresses a long‑standing yet insufficiently quantified issue in aeolian physics—the role of boundary layer thickness. Using a large‑eddy simulation–saltation coupled model, it systematically reveals how boundary layer thickness modulates turbulent structures and thereby significantly affects the physical mechanisms of near‑threshold particle entrainment, transport flux, spatial distribution, and grain‑size characteristics. The conclusions provide a clear physical explanation for the discrepancies between wind tunnel and field observations, and offer direct guidance for improving dust emission parameterization schemes in climate models. The paper features a clear structure, sound methodology, and comprehensive data. It is recommended for acceptance after minor revisions. Below are several suggestions for the authors to consider during revision:
1) To reduce computational costs, the study employs the approach where each numerical particle represents multiple physical particles (lines 166-168), with the representative ratio varying widely (from 50 to 2000) depending on the boundary layer thickness and friction velocity. This is a practical strategy. Please briefly explain the potential impact of this assumption on the key results and its validity, especially under near-threshold conditions characterized by low particle concentration and high representative ratios.
2) The friction velocity typically refers to a parameter of the airflow itself, whereas the saltation friction velocity or effective friction velocity often accounts for the feedback from sand particles. Please briefly clarify the specific meaning of the saltation friction velocity used in this paper: is it the bed shear velocity under particle-laden conditions (i.e., the friction velocity that incorporates particle feedback), or is it derived through a specific formulation?
3) The text mentions classic models such as the cubic law of Bagnold (1941) and the quadratic relationship of Creyssels et al. (2009), and points out that near the threshold state, the relationship between sand transport rate and shear stress follows different patterns (exponential or power law). It is recommended to quantitatively compare the fitted relationships obtained in this study with those from existing research.
4) In the text, the transport intensity is defined as a key metric linking microscopic mechanisms to macroscopic flux, and its variations with height and boundary layer thickness are presented (Fig. 4b). The authors are requested to provide a clear mathematical definition or calculation formula for the transport intensity in the main text (e.g., at line 257), as this would significantly enhance the interpretability and reproducibility of the results in Fig. 4(b).
5) Lines 387-389 are slightly cumbersome in syntax. It is suggested to revise them into a clearer structure.