The pattern of grainfall deposition in the lee of aeolian dunes

ABSTRACT
A simple model for the deposition pattern in the lee of aeolian dunes is presented that relies heavily upon a recently developed understanding of aeolian saltation. Grainfall deposition at any position on the lee face is the result of all saltation trajectories that leave any point on the surface of the dune upwind of the brink with sufficient initial velocity to travel the intervening distance. The deposition rate at any position on the lee slope is obtained by integrating over all combinations of initial position and required velocity, the velocity being weighted by its probability density.
The resulting calculated total deposition rate patterns show distinct maxima on the order of one to a few decimetres from the brink, beyond which deposition rates fall off roughly exponentially. An important length scale emerges that characterizes this decay with distance from the brink, the length increasing with wind velocity, and decreasing with grain diameter. It is shown that this length scale is on the order of one metre for typical grain size and wind conditions. That this is typically smaller than the length of the lee slope is what gives rise to the oversteepening and eventual avalanching of the lee sides of aeolian dunes. The position of a pivot point on the lee slope may be predicted, separating source regions from accumulation regions for grainflow avalanche deposits.
The calculated patterns provide not only a means for quantitative interpretation of active and fossil dune grainfall deposits, but they provide the initial geometry for grainflow avalanches. The initial failures should coincide with the steepest gradient in grainfall deposition, slightly downslope from the grainfall maximum.     

Experimental verification of aeolian saltation and lee side deposition models

We report results of experiments intended to test the validity of a model for aeolian saltation and the resulting pattern of deposition on the lee side of aeolian dunes. In steady sea-breeze conditions on a 3-m-tall dune at Point Año Nuevo, California, we measured simultaneously the near-brink wind speed and the deposition on both horizontal and lee face collector platforms. We then used the details of the deposition patterns to constrain approximate values of parameters in a numerical model of the deposition rate that incorporates the essence of the saltation process. Best fits to the data constrain a parameter that controls the probability distribution of liftoff speeds. In addition, the total vertical number flux of grains is constrained to roughly 10⁷?10⁸ grains m^?2 s^?1 at shear velocities of 0.33–0.40 m s^?1. The lee side deposition pattern, which shows the expected maximum in deposition rate at a distance of several decimetres from the brink, is also well fit by the model. In addition, simultaneous collection of horizontal and lee deposition patterns, along with the numerical simulation of these patterns, strongly implies that the windfield in the lee of this particular dune is best described as a non-recirculating wake. Grainflows on the lee face are caused by failure of grainfall depositional bumps. Our results suggest that the principal effect of increased wind speed is to increase the frequency of grainflows. rather than to increase their size, implying that very large, thick grainflows require a different mechanism.     

An empirical model of aeolian dune lee-face airflow

Airflow data, gathered over dunes ranging from 60-m tall complex-crescentic dunes to 2-m tall simplecrescentic dunes, were used to develop an empirical model of dune lee-face airflow for straight-crested dunes. The nature of lee-face flow varies and was found to be controlled by the interaction of at least three factors (dune shape, the incidence angle between the primary wind direction and the dune brinkline and atmospheric thermal stability). Three types of lee-face flow (separated, attached and deflected along slope, or attached and undeflected) were found to occur. Separated flows, characterized by a zone of low-speed (0–3O% of crestal speed) back-eddy flow, typically occur leeward of steep-sided dunes in transverse flow conditions. Unstable atmospheric thermal stability also favours flow separation. Attached flows, characterized by higher flow speeds (up to 84% of crestal speed) that are a cosine function of the incidence angle, typically occur leeward of dunes that have a lower average lee slope and are subject to oblique flow conditions. Depending on the slope of the lee face, attached flow may be either deflected along slope (lee slopes greater than about 20°), or have the same direction as the primary flow (lee slopes less than about 20°). Neutral atmospheric thermal stability also favours flow attachment. As each of the three types of lee-face flow is defined by a range of wind speeds and directions, the nature of lee-face flow is intimately tied to the type of aeolian depositional process (i.e. wind ripple or superimposed dune migration, grainflow, or grainfall) that occurs on the lee slope and the resulting pattern of dune deposits. Therefore, the model presented in this paper can be used to enhance the interpretation of palaeowind regime and dune type from aeolian cross-strata.     

On the modelling of two-dimensional aeolian dunes

In this study the modelling of aeolian dunes is treated from the background of the physical processes that form them. The paper concentrates on two-dimensional modelling, which can be applied to transverse and barchan dunes. The basic assumptions and equations are discussed and three models are presented: (a) a kinematic model which is based on a linear variation of the sediment transport with the topographic height; (b) an analytical model based on a boundary-layer model of the wind velocity and Bagnold's linearized sediment transport formula; (c) a generalization of this analytical model in a computer program which includes a simple routine for simulating the redistribution of sediment through avalanching. The relative importance of the simplifications is considered and indications are given for the practical applications of these three models in field studies.     

Size segregation during aeolian saltation on sand dunes

Recent Monte Carlo computer simulations have modelled the local, geometric mechanism by which mixed populations of differently sized particles order themselves when shaken, such that larger particles rise at the expense of the smaller. This process, called size segregation, is distinct from the mechanism of sifting where smaller particles fall between the interstices of larger particles. Size segregation is applied here to the sand grain populations found on the surfaces of dunes, which are involved in a sorting process driven by the wind. We present data from four barchan dunes located in the Eastern Province of Saudi Arabia. A simple model is used to demonstrate that size segregation, driven by saltation impacts, is energetically plausible at the wind velocities typically encountered on dune surfaces. Laboratory tests which support this model are also discussed.     

Grainfall processes in the lee of transverse dunes, Silver Peak, Nevada

Grainfall deposition and associated grainflows in the lee of aeolian dunes are important in that they are preserved as cross‐beds in the geological record and provide a key to the interpretation of the aeolian rock record. Despite their recognized importance, there have been very few field, laboratory or numerical simulation studies of leeside depositional processes on aeolian dunes. As part of an ongoing study, the relationships among grainfall, wind (speed and direction), stoss sand transport rates and dune morphometry (height and aspect ratio) were investigated on four relatively small, straight‐crested transverse dunes at Silver Peak, Nevada. Between 55% and 95% of the total grainfall was found to be deposited within 1 m of the crest, and 84–99% within 2 m, depending primarily on dune size and shape. Grainfall decay rates on high dunes of large aspect ratio were observed to be very consistent, with a weak positive dependence on wind speed. For small dunes with low aspect ratios, grainfall deposition was more varied and decreased rapidly within 1 m of the dune crest, whereas at increased distance from the dune crest, it eventually approached the smaller decay rates observed on the large dunes. No dependence of grainfall on wind speed was observed for these small dunes. Comparison of field data with predictions from 1 ) saltation model of grainfall, based on the computation of saltation path lengths, indicates lack of agreement in the following areas: (1) deposition rate magnitude; (2) variation in decay rate with wind speed; and (3) the magnitude and location of the localized lee‐slope depositional maxima. The Silver Peak field results demonstrate the importance of dune aspect ratio and related wake effects in determining the rate and pattern of grainfall. This work confirms earlier speculation by 7 ) that temporary, turbulent suspension (or `modified saltation') of relatively large grains does occur within the dune wake, so that transport distances generally are larger than predicted by numerical simulations of `true' saltation.     

Grain-size sorting in grainflows at the lee side of deltas

The sorting of sediment mixtures at the lee slope of deltas (at the angle of repose) is studied with experiments in a narrow, deep flume with subaqueous Gilbert-type deltas using varied flow conditions and different sediment mixtures. Sediment deposition and sorting on the lee slope of the delta is the result of (i) grains falling from suspension that is initiated at the top of the delta, (ii) kinematic sieving on the lee slope, (iii) grainflows, in which protruding large grains are dragged downslope by subsequent grainflows. The result is a fining upward vertical sorting in the delta. Systematic variations in the trend depend on the delta height, the migration celerity of the delta front and the flow conditions above the delta top. The dependence on delta height and migration celerity is explained by the sorting processes in the grainflows, and the dependence on flow conditions above the delta top is explained by suspension of fine sediment and settling on the lee side and toe of the delta. Large differences in sorting trends were found between various sediment mixtures. The relevance of these results with respect to sorting in dunes and bars in rivers and laboratory flumes is discussed and the elements for a future vertical sorting model are suggested.     

沙波迎流面流速分布公式

为进一步揭示沙波水流运动特性及提高沙波迎流面流速计算精度,采用两种概化模型,通过小水深沙波水槽试验,运用声学多普勒流速仪,对沙波沿程及垂线流速分布进行了测量。基于乐培九次生流理论公式,结合沙波水流特性,假定次生流在沙波迎流面上处于一个不断发展演变的过程,提出了发展函数和修正函数,得到了适用于沙波迎流面的流速垂线分布公式。研究结果表明:相对水深越小,沙波地形对迎流面水流作用越显著,使得上部流速减小、近底流速增大,且越靠近波峰这种现象越明显;建立的沙波流速公式与实测值吻合较好,能够准确地反映出迎流面流速变化规律。     

Internal structure of aeolian dunes in Abu Dhabi determined using ground-penetrating radar

A ground-penetrating radar survey of aeolian dunes in the Al Liwa area of Abu Dhabi reveals a variety of dipping reflectors which are interpreted as primary sedimentary structures. The interpretation of the radar profiles has been confirmed by bulldozing trenches through the study area and comparing logged sections in the trenches with the radar profiles. NNW— SSE-orientated radar profiles, approximately parallel to the prevailing wind direction, show two sets of dipping reflectors which are interpreted as sets of cross-stratification and second- and third-order bounding surfaces. Radar profiles orientated WSW—ENE across the prevailing wind direction are dominated by concave-up reflectors which are interpreted as trough-shaped scours and sets of trough cross-stratification produced by oblique progradation of barchanoid dunes. Nested troughs, with small sets of trough cross-stratification within larger troughs, may be due to reactivation following wind reversal, or the superposition of small dunes on larger dunes and the fill of large dune troughs by smaller dunes. Convex-upwards reflectors are interpreted as linear spurs on the convex portions of sinuous dunes or erosional remnants between troughs. Overall there is a tendency for the larger second-order bounding surfaces to dip downwind, which confirms Brookfield's ideas of the relative migration paths of dunes and draa.     

Relationship of spatial heterogeneity for vegetation and aeolian sand soil properties on longitudinal dunes in Gurbantunggut Desert, China

On longitudinal dunes in the southern Gurbantunggut Desert, the vegetation was investigated, and the texture, water content, organic matter, total nitrogen, salt content and pH of aeolian sand soil were measured. By means of geostatistical methods, the spatial heterogeneity for vegetation and aeolian sand soil properties was analyzed. The vegetation pattern and aeolian sand soil properties were moderately to strongly spatially heterogeneous as a whole, with a spatially dependent range of 8.8–74.8 m. Because both of them had a nest structure of grading system, their spatial heterogeneity needed to be described by the fractal dimensions at different sampling scales. The autocorrelated spatial range A ₀ and fractal dimensions of the cover of vegetation and the diversity of herberious synusium were similar to these of soil water contents (SM). The coarse grain size (φ1) and sorting (σ) of soil, the diversity of herbaceous synusium and the cover of vegetation had a closer dependent range A₀, being 37.8–57.8 m. The trends of spatial variation for organic matter and total nitrogen contents were very similar to that of vegetation cover. The spatial heterogeneities of soil pH and salt content were mainly restricted by terrain and basically not related to vegetation.     

A theoretical model for aeolian impact ripples

New insights into the grain-bed impact process arising from both numerical and physical experiments involving single grain impacts lead to a more complete conceptual model of the aeolian saltation process that in turn allows a simple model of aeolian impact ripples to be developed. The saltating population may be idealized as consisting of (1) long trajectory, high impact-energy, constant impact-angle ‘successive saltations’, and (2) short trajectory, low impact-energy ‘reptations’. It is argued that the spatial variations in mass flux due to the reptating population lead to the growth and translation of impact ripples. Using the sediment continuity equation, an expression for the spatial variation in the ejection rate of reptating grains from a sinusoidally perturbed bed, and a probability distribution for the reptation lengths, a simple stability analysis demonstrates that the flat bed is unstable to small amplitude perturbations. A fastest-growing wavelength emerges that is roughly six times the mean reptation length, and is only weakly dependent upon the detailed shape of the probability distribution of reptation lengths. The results match well with the observed initial wavelengths in wind tunnel experiments.     

青藏高原东缘盐源盆地古近纪风成沙丘及其古地理意义*

盐源盆地始新世丽江组沉积时期发育了一套具大型高角度交错层理的红色砂岩,其确切成因对于厘定青藏高原东缘古近纪古地理格局、恢复东亚新生代干旱带与古气候演化过程具有重要意义。文中通过对盐源盆地始新统丽江组红色砂岩的沉积特征进行系统分析,证明该套砂岩的岩性、粒度分布、石英颗粒表面特征与沉积构造等明显不同于水成沉积,而与典型风成沙丘相应特征完全一致,表明其为风成沙丘沉积。结合古近纪研究区的古气候条件、大气环流样式与大地构造背景,笔者进一步推断盐源盆地始新世风成沙丘可能沉积于中国古近纪干旱带内的沙漠环境。根据目前相关研究资料,确认青藏高原东缘存在一个厚度稳定的古近纪风成沙丘富集带。     

Major bounding surfaces in aeolian sandstones—a climatic model

Large areas of fixed, vegetated dunes occur in the Sahel and southern margin of the Sahara. These dunes were active during Late Pleistocene times and have been stabilized as a result of a change to more humid, less windy conditions in the Holocene. The stabilized surfaces, which are in part of erosional origin, are of regional extent. Within aeolian sand sequences, such surfaces form the highest order bounding surfaces. Since regional bounding surfaces of this type occur in all the world's major deserts, it is suggested that they should also be present in some ancient aeolian sandstone sequences.     

Sedimentological characteristics and morphology of the aeolian sand dunes in the eastern part of the UAE,a case study from Ar Rub' Al Khali

The Umm Az Zimul–Al Wijan area is located in the southeastern part of the UAE and covers about 1600 km². It is bounded to the east by the Oman Mountains and to the south and west by the extensive dune area of Ar Rub' Al Khali. Field investigation revealed the common occurrence of parallel to sub-parallel sand ridges with a general east–west orientation. Also present, but less frequent, are barchan, barchanoid and star dunes. Interdune areas are classified into four types that include: dolomite, mixed ancient sabkha and ophiolitic rock fragments, mixed sand sheet and ophiolitic rock fragments, and recent sabkha. The textural characteristics of the sand forming the dunes are unimodal with a modal class in fine sand size, moderately to very well sorted, positively skewed and mesokurtic. Quartz grains are mainly subrounded to subangular. The similarity in roundness properties in different dune types in the eastern province of the UAE seems not to be influenced by dune form. Based on the heavy mineral suites and the angularity of quartz grains, it is believed that the sand sediments are mostly derived from the ultrabasic rocks forming the ophiolitic sequence of the Oman Mountains, acidic rocks of Iran and from the coastal area.     

Developmental characteristics of aeolian dunes and environmental changes in the adjoining region of Puruogangri ice sheet, North Tibetan Plateau

A large area of moraine sediments and cryogenic weathering products, formed by glacial action and a cold environment, are the main source of aeolian sand in the high and cold region of the Qinghai–Tibetan Plateau in China. The evolution of aeolian dunes is closely related to the periglacial environment. Owing to the freezing of dune-land surfaces, the evolution of sand dunes is dominated by expanding dune bases and vertical accretion, thereby forming large barchan dunes. The migration rates of these large barchan dunes are very slow at an average rate of 1.7–0.7 cm·a^–1. The temperature mainly controls the environmental changes in the adjoining region of Puruogangri ice sheet. The ¹⁴C dating of humus layers in the studied area of the sand dune are 10,780±130, 9,549±130, 8,320±110, 7,450±100, 5,970±95, 5,330±90, 4,420±80, 3,460±80, 2,280±70, 980±70 aBP, respectively. The regions high temperature rising up during summer from the southwest monsoon intensity might be an important factor. As long as both water and temperature conditions are suitable, the plants will grow well, sand dunes will be stabilized, forming humus layers. Otherwise, sand dunes are bare and re-activate.     

A stratigraphic model to account for complexity in aeolian dune and interdune successions

Wet aeolian systems, in which the water table or its capillary fringe are in contact with the accumulation surface, such that moisture influences sedimentation, are well‐known from modern aeolian systems and several ancient preserved successions are recognized from outcrop. One common mechanism by which accumulation of wet aeolian system deposits occurs is via a progressive rise in the relative water‐table level that is coincident with ongoing dune and interdune migration, the angle of dune climb being determined by the ratio between the rate of relative water‐table rise and the rate of downwind migration of the bedforms. Accumulations of wet aeolian system deposits tend to be characterized by units of climbing dune strata separated by units of damp or wet interdune strata. For simple geometric configurations, where the size of the dune and interdune units, the rate of bedform migration and the rate of aggradation all remain constant over space and time, the resulting accumulation has a simple architecture characterized by sets of uniform thickness inclined at a constant angle. However, the dynamic nature of most aeolian dune systems means that such simple configurations are unlikely in nature. The complexity inherent in these systems is accounted for here by a numerical model in which key controlling parameters, including dune and interdune wavelength and spacing, migration rate and aggradation rate, are allowed to vary systematically both spatially (from a dune‐field centre to its margin) and temporally (in response to changes in sediment availability or water‐table level). The range of synthetic stratigraphic architectures generated by the model accounts for all the best‐known examples of aeolian dune and interdune stratigraphic configurations documented from the stratigraphic record. Modelling results have enabled the erection of a scheme for the classification of dune system type whereby the many elaborate stratal architectures known to exist in nature can effectively be accounted for by only four parameters that are allowed to vary over space and time: dune and interdune wavelength and spacing, rate of bedform migration and rate of accumulation. Results have applied implications, including the modelling of reservoir heterogeneity and the prediction of fluid flow pathways of hydrocarbons, water, CO₂ and contaminants in subsurface reservoirs and aquifers, in which low permeability interdune units might act as baffles or barriers.     

Toward a quantitative model of metamorphic nucleation and growth

The formation of metamorphic garnet during isobaric heating is simulated on the basis of the classical nucleation and reaction rate theories and Gibbs free energy dissipation in a multi-component model system. The relative influences are studied of interfacial energy, chemical mobility at the surface of garnet clusters, heating rate and pressure on interface-controlled garnet nucleation and growth kinetics. It is found that the interfacial energy controls the departure from equilibrium required to nucleate garnet if attachment and detachment processes at the surface of garnet limit the overall crystallization rate. The interfacial energy for nucleation of garnet in a metapelite of the aureole of the Nelson Batholith, BC, is estimated to range between 0.03 and 0.3?J/m² at a pressure of ca. 3,500?bar. This corresponds to a thermal overstep of the garnet-forming reaction of ca. 30°C. The influence of the heating rate on thermal overstepping is negligible. A significant feedback is predicted between chemical fractionation associated with garnet formation and the kinetics of nucleation and crystal growth of garnet giving rise to its lognormal??shaped crystal size distribution.     

Morphology, internal structure and mechanics of small longitudinal (seif) dunes in an aeolian horizon of the Proterozoic Dhandraul Quartzite, India

The excellently preserved metre-scale, linear bedforms in an aeolian horizon of the Proterozoic Dhandraul Quartzite, India, show oppositely dipping strata arranged in a zigzag pattern. The strata are dominantly of translatent type, deposited by along-crest migrating ripples preserved on the flanks of dunes. The bedforms thus may be interpreted in a morphodynamic sense as longitudinal (seif) dunes. In order to determine the regional palaeoflow pattern, the migration directions of ripples preserved at the top of sheet sandstones that are associated with the dune cross-strata and internally show subhorizontal translatent strata were measured. A directionally varying flow with a mean direction nearly parallel to the mean axial trend of the dunes is indicated. The kinematics of the dunes were thus largely the result of alternate operation of two oblique flow components, each of which was deflected at a dune crest into an along-crest flow on the downwind flank of the dune. The deflected flow formed along-crest migrating ripples, which in turn deposited climbing ripple strata. Alternate deposition on the two opposite flanks resulted in near vertical accretion of the dunes, as is indicated by the zigzag pattern of stratal arrangement.     

On the existence of characteristic shapes for desert dunes

The existence of an angle of repose for sand implies that, in any given wind regime, there is at least one configuration of sand dunes which will not be altered by that wind regime. The existence of implies that the land forms constitute a convex compact subset of a Banach space, and the result then follows from Shauder's theorem.