Threshold Shear Velocity Research Articles

The universal two-fifths law of pier scour

Understanding scour at bridge piers is crucial for safeguarding public safety, ensuring infrastructure resilience, and planning effective maintenance. Despite over six decades of extensive studies aiming to develop predictive formulas for the equilibrium scour depth at bridge piers, more than 20 000 highway bridges in the United States have been spotted “scour critical.” The traditional reliance on existing empirical formulas has posed a severe challenge for researchers, hindering to achieve a unified relation for the equilibrium scour depth from a fundamental scientific tenet. This perspective article presents a breakthrough—a universal law governing the equilibrium scour depth at a circular pier embedded in a sediment bed, specifically in clear-water scour condition. Derived from a phenomenological model, the universal law reveals that the equilibrium scour depth to pier diameter ratio obeys a consistent two-fifths scaling law with the introduction of a newly coined pier-scour number. This number accounts for all the key parameters involved in a local scour phenomenon, including the approach mean flow velocity, threshold shear velocity for sediment grain motion, approach flow depth, pier diameter, and sediment grain size. Importantly, the scaling law contains an additional term involving the drag coefficient raised to the power of 2/5, addressing the impact of the pier shape on the equilibrium scour depth. The derived universal law undergoes the validation through an extensive dataset of experimental measurements on circular pier scour.

Entrainment and horizontal atmospheric transport of microplastics from soil

Soils are an important source of microplastics (MPs) to the atmosphere but the fluxes and mechanisms involved in MPs entrainment are not well understood. In the present study, a series of horizontally aligned sediment traps have been deployed at different heights within 1 m above the ground for a two-month period at various locations in an arid region (Sarakhs, Iran). MPs were isolated from sediments and were quantified and characterised according to size, colour, shape and polymer composition by established techniques. Most MPs were <250 μm in length, fibres were the most important shape, black and blue-green were the dominant colours, and polymer abundance decreased in the order polyethylene > nylon > polypropylene > polystyrene > polyethylene terephthalate. The distributions of sediment mass (range <0.01–9 g) and number of MPs (range = 0 to 21) were heterogeneous, both between sites and at the different heights sampled, and yielded median, vertically-averaged horizontal fluxes for the region of about 450 g m−2 d−1 and 2600 MP m−2 d−1, respectively. However, when data were pooled, the number of MPs normalised to sediment mass exhibited a significant inverse relationship with sediment mass, an effect attributed to the presence of ambient suspended MPs and sediment that are diluted by the suspension of soil and deposited MPs at higher wind speeds. The mechanisms of MP saltation and entrainment were not ascertained but a theoretical framework for threshold shear velocity based on regularly-shaped particles and density considerations is presented. Further experimental work is required to verify this framework, and in particular for fibrous MPs with different aerodynamic properties to soil particles.

The fetch effect on sand transport above a farmland surface and conditions for saturation

The existing aeolian transport models have been developed for saturated sand flow. For unsaturated sand flow, these models produce larger errors. To mitigate this problem, this paper attempts to clarify the fetch effect on the sand transport rate above a farmland surface so as to improve sand transport model. We first defined the C value in the 1978 Lettau and Lettau model as a sand transport coefficient. For saturated sand flow, the C value equals the saturated sand transport coefficient (i.e., C=Csat=6.7); but for unsaturated flow, the C values would be less than 6.7. We found that C increased with increasing fetch length (L) and shear velocity (u*) using data from a field investigation above a farmland surface. The measured C was far less than Csat even at the maximum fetch length (100 m) and the largest shear velocity (0.809 m s−1) during the sand collection in field observations. Based on the relationships among C, L, and u*, we developed an aeolian transport model that accounted for the shear velocity and fetch length. We confirmed that the essential condition for the sand flow to reach saturation was wind speed is strong enough to transport most of the surface soil particles. Thus, the critical shear velocity at which the sand flow can reach saturation (u*c-sat) is close to the threshold shear velocity for entrainment of the largest soil particles. When u* >u*c-sat, the sand transport saturation fetch length decreased rapidly with increasing wind speed. However, due to the high wind speed requirement, it is difficult for the sand flow to reach saturation, which leads to the farmland surface in an environment dominated by wind erosion under normal wind conditions.

Aeolian sand transport over a dry playa surface: Sand flux density profiles, saltation layer height, and flux scaling laws and implications for dust emission dynamics

Dry playa surfaces under saltation bombardment release abundant atmospheric dust particles. Understanding aeolian sand transport over dry playa surfaces is vital for gaining insight into the process of dust emission from these surfaces. Here, we report characteristics of aeolian sand transport over a dry playa surface based on systematic field measurements of three transport events, and the sand flux density profiles, saltation layer height, and flux scaling laws were examined. The results show that sand flux density decreases exponentially with increasing height over the dry playa surface, and 90 % of the sand flux is concentrated within 0.3 m above the surface. The average saltation layer height (zq) for the dry playa surface, with an average value of 0.13 m, is 2.6 times larger than that of the sand surface and only half of that over the gobi surface with similar median grain size. Sand transport rate (Q) over the dry playa surface is proportional to a quadratic equation of the shear velocity (u*) over the threshold shear velocity (u*t), u*2-u*t2, and this flux scaling law is supported by the negligible variation of zq with u*. This study indicates that sand transport rate model for the dry playa surface is consistent with the splash-dominated model of aeolian saltation over sand surfaces. Our results are significant for studies of dust emission from dry playa surfaces under saltation bombardment.

Multi-year measurements of ripple and dune migration on Mars: Implications for the wind regime and sand transport

Aeolian sand dunes are observed across the Martian surface. The arrival of the HiRISE camera on Mars Reconnaissance Orbiter at Mars in 2006 enabled detection of modern-day movement of dunes and ripples from orbit for the first time. Since 2006, HiRISE collected a long timeseries of repeat imagery at a few Martian dune fields. We analyze this timeseries of imagery at two of these dune fields, using COSI-Corr for image registration and correlation, to study the movement and dynamics of dunes and meter-scale ripples at the Nili Patera and Meroe Patera barchan dune fields. We present measurements of whole-dune translational sand fluxes extracted at both dune fields via manual tracking of dune crestlines and slipfaces in HiRISE images. We also present a multi-Mars year timeseries of ripple flux measurements. Ripple migration shows a consistent pattern of seasonal variation, with maxima in flux during northern-hemisphere autumn and winter at both dune fields. Ripple migration is also observed to decrease away from the upwind margins of dune fields. We compare our observations with predicted sand transport using winds output from the MarsWRF atmospheric circulation model and theories of sand motion. The model predicts half-hourly, mesoscale winds, from which we estimate the 1 Hz, local-scale winds by assuming a Weibull distribution of wind speed, with parameters chosen based on landed wind data. This approach uses remote sensing observations of bedform migration, and comparisons with model output, to place constraints on the wind regime. Our measurements of the seasonal pattern of sand flux variation agree, to first order, with predictions based on modeled wind speeds. Comparison of the magnitudes of predicted and observed sand fluxes is not feasible due to the high uncertainties in our calculated sand fluxes caused by uncertainties in input parameters, most importantly the assumed fluid threshold for sand transport. However, we note that model predictions fit our observed sand fluxes best when relatively low values of the fluid threshold shear velocity of ~0.6–0.8 m/s (or shear stresses of O(10−3) Pa) are assumed.

A fully predictive model for aeolian sand transport, part 2: Description and calibration of models and effect of moisture and coarse materials

This paper presents new research results on the effect of moisture and coarse materials (gravel and shells) on aeolian transport and is a continuation of earlier work. Two mini wind tunnels have been designed and used to study the effect of moisture and coarse materials on the threshold shear velocity and on the sand transport rate at wind velocities in the range of 10–16 m/s. Extensive attention was given to the determination of the drying time of the beach surface after a period with rainfall for a range of temperatures and wind conditions. A new equation to include the effects of coarse materials on aeolian sand transport is derived from the mini wind tunnel data. Two prediction methods for aeolian sand transport were evaluated: the modified Bagnold-transport equation and the new VR-transport equation. Both methods include the effects of sand diameter and the threshold shear stress, which is essential for accurate determination of sand transport at low wind speeds. The cessation-related threshold shear velocity produces the best results. The grain-related shear velocity is the basic driving parameter of both prediction methods. The wind tunnel data of Belly (1964) have been used to calibrate the new VR-sand transport equation.

Experimentally Derived Thresholds for Windblown Sand on Mars

AbstractAeolian sand transport frequently occurs on Mars despite wind speeds rarely exceeding predicted thresholds for motion. This dissonance is problematic for understanding aeolian processes and the resulting geomorphologic responses in contemporary and ancient atmospheres. To address the apparent discrepancy between speeds required to initiate sand motion and transport observed from orbital and in situ observations, we conducted a series of wind tunnel experiments at Martian atmospheric pressures and used buoyancy as the similitude parameter to simulate the force required to initiate particle motion on Mars. Shear velocities were derived from velocity profiles corresponding to the onset of sporadic transport, which can induce downwind cascading motion. Here, we find that threshold shear velocities are slower than previously thought by a factor of 1.6 to 2.5. Measured wind speeds on Mars exceed our observed thresholds, thus offering one mechanism behind the dissonance between observations of transport below previous thresholds of motion.

A fully predictive model for aeolian sand transport

This paper presents the development, calibration and verification of a fully predictive model for wind-blown dry sand. The model is based on the modification of the well-known Bagnold equation by including the threshold shear velocity, which is also slightly modified to ensure a smoother transition from the non-transport regime to the transport regime. The sand transport rate is related to the static and dynamic grain roughness by using a semi-empirical roughness predictor, which is calibrated based on sand transport data from wind tunnel experiments with a flat mobile sand surface. The model input for dry sand is the wind velocity at one height above the surface and the sand characteristics (d50, d90). The effects of moisture, vegetation and shells on the sand transport process are included by fairly simple expressions which are acting on the shear velocity, the threshold value and the transport rate. In all, 105 high-quality data sets have been used for verification of the proposed predictive model. About 72% of the predicted values are within a factor of 2 of measured values of the transport rate.

Influence of salinity and moisture on the threshold shear velocity of saline sand in the Qarhan Desert, Qaidam Basin of China: A wind tunnel experiment

Determination of the threshold shear velocity is essential for predicting sand transport, dust release and desertification. In this study, a wind tunnel experiment was conducted to evaluate the influence of salinity and moisture on the threshold shear velocity of saline sand. Saline sand samples (mean particle size of 164.50–186.08 µm and the total silt, clay and salt content of 0.80%–8.25%) were collected from three saline sand dunes (one barchan dune and two linear dunes) in the Qarhan Desert, Qaidam Basin of China. Original saline sand samples were placed in two experimental trays for wet and dry processing to simulate deliquescence and desiccation, respectively. Surface moisture content ranging from 0.30% to 1.90% was generated by the steam method so that the saline sand can absorb water in a saturated water vapor environment. The motion of sand particles was determined by the observers with a solid laser. The laser sheet (0.80 cm thick), which was emitted by the solid laser, horizontally covered the sand surface and was bound to the sand. Results show that the cohesion of saline sand results from a combination of salt and water. The threshold shear velocity increases exponentially with the increase in crust thickness for the linear sand dunes. There is a positive linear correlation between the original moisture content and relative threshold shear velocity. The threshold shear velocity of dewatered sand is greater than that of wet sand with the same original moisture content. Our results will provide valuable information about the sand transport of highly saline soil in the desert.

Aeolian Ripple Migration and Associated Creep Transport Rates

Wind-formed ripples are distinctive features of many sandy aeolian environments, and their development and migration are basic responses to sand transport via saltation. Using data from the literature and from original field experiments, we presented empirical models linking dimensionless migration rates, u r / g d ( u r is the ripple migration speed, g is the gravity acceleration, and d is the grain diameter) with dimensionless shear velocity, u*/u*t (u* is shear velocity and u*t is fluid threshold shear velocity). Data from previous studies provided 34 usable cases from four wind tunnel experiments and 93 cases from two field experiments. Original data comprising 68 cases were obtained from sites in Ceará, Brazil (26) and California, USA (42), using combinations of sonic anemometry, sand traps, photogrammetry, and laser distance sensors and particle counters. The results supported earlier findings of distinctively different relationships between u r / g d and u*/u*t for wind tunnel and field data. With our data, we could also estimate the contribution of creep transport associated with ripple migration to total transport rates. We calculated ripple-creep transport for 1 ≤ u*/u*t ≤ 2.5 and found that this accounted for about 3.6% (standard deviation = 2.3%) of total transport.

A stochastic model for cell adhesion to the vascular wall.

Cell dynamics in the vicinity of the vascular wall involves several factors of mechanical or biochemical origins. It is driven by the competition between the drag force of the blood flow and the resistive force generated by the bonds created between the circulating cell and the endothelial wall. Here, we propose a minimal mathematical model for the adhesive interaction between a circulating cell and the blood vessel wall in shear flow when the cell shape is neglected. The bond dynamics in cell adhesion is modeled as a nonlinear Markovian Jump process that takes into account the growth of adhesion complexes. Performing scaling limits in the spirit of Joffe and Metivier (Adv Appl Probab 18(1):20, 1986), Ethier and Kurtz (Markov processes: characterization and convergence, Wiley, New York, 2009), we obtain deterministic and stochastic continuous models, whose analysis allow to identify a threshold shear velocity associated with the transition from cell rolling and firm adhesion. We also give an estimation of the mean stopping time of the cell resulting from this dynamics. We believe these results can have strong implications for the understanding of major biological phenomena such as cell immunity and metastatic development.

Laboratory Experiments of Volcanic Ash Resuspension by Wind

AbstractFresh volcanic eruption deposits tend to be loose, bare, and readily resuspended by wind. Major resuspension events in Patagonia, Iceland, and Alaska have lofted ash clouds with potential to impact aircraft, infrastructure, and downwind communities. However, poor constraints on this resuspension process limit our ability to model this phenomenon. Here, we present laboratory experiments measuring threshold shear velocities and emission rates of resuspended ash under different environmental conditions, including relative humidity of 25–75% and simulated rainfall with subsequent drying. Eruption deposits were replicated using ash collected from two major eruptions: the 18 May 1980 eruption of Mount St. Helens and the 1912 eruption of Novarupta, in Alaska's Valley of Ten Thousand Smokes. Samples were conditioned in a laboratory chamber and prepared with bulk deposit densities of 1,300–1,500 kg/m3. A control sample of dune sand was included for comparison. The deposits were subjected to different wind speeds using a modified PI‐SWERL® instrument. Under a constant relative humidity of 50% and shear velocities 0.4–0.8 m/s, PM10 emission by resuspension ranged from 10 to &gt;100 mg·m−2·s−1. Addition of liquid water equivalent to 5 mm of rainfall had little lasting effect on Mount St. Helens wind erosion potential, while the Valley of Ten Thousand Smokes deposits exhibited lower emissions for at least 12 days. The results indicate that particle resuspension due to wind erosion from ash deposits potentially exceeds that of most desert surfaces and approaches some of the highest emissions ever measured.

Saltation under Martian gravity and its influence on the global dust distribution

Dust and sand motion are a common sight on Mars. Understanding the interaction of atmosphere and Martian soil is fundamental to describe the planet’s weather, climate and surface morphology.We set up a wind tunnel to study the lift of a mixture between very fine sand and dust in a Mars simulant soil. The experiments were carried out under Martian gravity in a parabolic flight. The reduced gravity was provided by a centrifuge under external microgravity. The onset of saltation was measured for a fluid threshold shear velocity of 0.82 ± 0.04 m/s. This is considerably lower than found under Earth gravity.In addition to a reduction in weight, this low threshold can be attributed to gravity dependent cohesive forces within the sand bed, which drop by 2/3 under Martian gravity. The new threshold for saltation leads to a simulation of the annual dust cycle with a Mars GCM that is in agreement with observations.

Blowing dust and highway safety in the southwestern United States: Characteristics of dust emission “hotspots” and management implications

Despite the widespread media attention of chain-reaction traffic incidents and property damage caused by windblown dust in the U.S. and elsewhere in the world, very few studies have provided in-depth analysis on this issue. Remote sensing and field observations reveal that wind erosion in the southwestern U.S. typically occurs in localized source areas, characterized as “hotspots”, while most of the landscape is not eroding. In this study, we identified the spatial and temporal distribution patterns of hotspots that may contribute dust blowing onto highways in the southwestern U.S. We further classified the hotspots for the potential of blowing dust production based upon field observations and wind erosion modeling. Results of land use and land cover show that shrubland, grassland, and cropland accounted for 42%, 31%, and 21% of the overall study area, respectively. However, of the 620 total hotspots identified, 164 (26%), 141 (22%), and 234 (38%) are located on shrubland, grassland, and cropland, respectively. Barren land represented 0.9% of the land area but 8% of the dust hotspots. While a majority of these hotspots are located close to highways, we focused on 55 of them, which are located <1km to adjacent highways and accessible via non-private roads. Field investigations and laboratory analysis showed that soils at these hotspot sites are dominated by sand and silt particles with threshold shear velocities ranging from 0.17–0.78m s−1, largely depending on the land use of the hotspot sites. Dust emission modeling showed that 13 hotspot sites could produce annual emissions >3.79kg m−2, yielding highly hazardous dust emissions to ground transportation with visibility <200m. Results of location, timing, and magnitude of the dust production at the hotspots are critical information for highway authorities to make informed and timely management decisions when wind events strike.

Uncertainty propagation in aeolian processes: From threshold shear velocity to sand transport rate

The accurate estimation of aeolian saltation events is a fundamental requirement in the modelling of wind erosion, dust emission, dune movement and aeolian hazard prediction. A large number of semi-empirical sand transport rate models exist, with many relying on a single value for a shear velocity threshold above which saltation is initiated. However, measuring and modelling the sand transport rate suffers from the effects of a number of epistemic and aleatory uncertainties which make the identification of a single threshold value for shear velocity problematic. This paper focuses on the uncertainty propagation evident in calculations that use a threshold shear velocity to estimate sand transport rate. Probability density functions of threshold shear velocity are provided from the authors' previous studies. Grain diameter and shear velocity are considered as deterministically varying parameters. Several sand transport rate statistical metrics are estimated via the Monte Carlo approach adopting four different sand transport models. The sand transport rate estimation in probabilistic terms allows us to assess the amplification/reduction in the uncertainty and to provide a deeper insight into established transport rate models. We find that if the wind speed is close to the erosion threshold, every tested model amplifies the variability of the resulting estimated sand transport rate, especially in the case of coarse sand. If the wind speed is large, the adopted models present substantial differences in uncertainty. An interpretation of these differences is given by conditioning the sand transport rate models to the type of erosion threshold adopted, the fluid or impact threshold.

To the theory of particle lifting by terrestrial and Martian dust devils

The combined Rankine vortex model is applied to describe the radial profile of azimuthal velocity in atmospheric dust devils, and a simplified model version is proposed of the turbulent surface boundary layer beneath the Rankine vortex periphery that corresponds to the potential vortex. Based on the results by Burggraf et al. (1971), it is accepted that the radial velocity near the ground in the potential vortex greatly exceeds the azimuthal velocity, which makes tractable the problem of the surface shear stress determination, including the case of the turbulent surface boundary layer. The constructed model explains exceeding the threshold shear velocity for aeolian transport in typical dust-devil vortices both on Earth and on Mars.

Incoming windblown sand drift to civil infrastructures: A probabilistic evaluation

The accurate prediction of windblown sand drift events approaching human infrastructures and activities is fundamental in arid lands. In both scientific literature and technical practice sand drift estimation is carried out in mean terms. Typically, sand drift net direction and intensity are assessed by means of the resultant drift potential. However, windblown sand suffers a number of epistemic and aleatory uncertainties, related to both the wind and the sand fields. The windblown sand drift estimation in probabilistic terms is useful in the infrastructure design perspective and allows to obtain characteristic values of windblown sand transport. In this study windblown sand is considered as an environmental action in analogy to wind action. Several uncertainties involved in the phenomenon are considered: threshold shear velocity and 10-min average wind velocity are assumed as random variables. Monte Carlo approach is adopted within a bootstrapping technique in order to assess sand drift in probabilistic terms. The proposed approach is applied to five sites in the Arabian Peninsula. Directional statistics of the sand drift are given for each site.

Windblown sand saltation: A statistical approach to fluid threshold shear velocity

The reliable prediction in probabilistic terms of the consequences of aeolian events related to sand transport phenomena is a key element for human activities in arid regions. Threshold shear velocity generating sand lifting is a key component of such a prediction. It suffers from the effect of uncertainties of different origin, such as those related to the physical phenomena, measurement procedures, and modelling. Semi empirical models are often fitted to a small amount of data, while recent probabilistic models needs the probability distribution of several random variables. Triggered by this motivation, this paper proposes a purely statistical approach to fluid threshold shear velocity for sand saltation, treated as a single comprehensive random variable. A data set is derived from previously published studies. Estimates of conditional probability distributions of threshold shear velocity for given grain diameters are given. The obtained statistical moments are critically compared to some deterministic semi empirical models refitted to the same collected data. The proposed statistical approach allows to obtain high order statistics useful for practical purposes.

Characterizing the sediment bed in terms of resistance to motion: Toward an improved model of saltation thresholds for aeolian transport

Abstract Models of aeolian transport thresholds generate a wide range of predictions, and error in threshold modeling leads to uncertainty in predicting aeolian events. This paper proposes a new characterization of the representative grain size for use in prediction of transport thresholds. This characterization is based on the distribution of resistance to motion in the sediment bed. The traditional grain size distribution uses a mean diameter to represent the sediment bed. However, the distribution of inertial forces resisting motion is not linearly proportional to the distribution of grain diameters, so that an arithmetic mean does not adequately represent the distribution of the resisting forces. A simple relation of shear stress to weight force is used to represent the threshold condition. Based on comparison with threshold observations drawn from the literature, the model provides reliable predictions of threshold stress and shear velocity for dry quartz grains over a wide range of grain sizes. Given that the dataset was drawn from studies employing a variety of experimental conditions and techniques, and that these studies spanned a range of nearly eight decades, the model is considered to provide a robust approximation of threshold conditions.

Testing the performance of state-of-the-art dust emission schemes using DO4Models field data

Abstract. Within the framework of the Dust Observations for Models (DO4Models) project, the performance of three commonly used dust emission schemes is investigated in this paper using a box model environment. We constrain the model with field data (surface and dust particle properties as well as meteorological parameters) obtained from a dry lake bed with a crusted surface in Botswana during a 3 month period in 2011. Our box model results suggest that all schemes fail to reproduce the observed horizontal dust flux. They overestimate the magnitude of the flux by several orders of magnitude. The discrepancy is much smaller for the vertical dust emission flux, albeit still overestimated by up to an order of magnitude. The key parameter for this mismatch is the surface crusting which limits the availability of erosive material, even at higher wind speeds. The second-most important parameter is the soil size distribution. Direct dust entrainment was inferred to be important for several dust events, which explains the smaller gap between modelled and measured vertical dust fluxes. We conclude that both features, crusted surfaces and direct entrainment, need to be incorporated into dust emission schemes in order to represent the entire spectra of source processes. We also conclude that soil moisture exerts a key control on the threshold shear velocity and hence the emission threshold of dust in the model. In the field, the state of the crust is the controlling mechanism for dust emission. Although the crust is related to the soil moisture content to some extent, we are not as yet able to deduce a robust correlation between state of crust and soil moisture.