Longitudinal velocity patterns and bed morphology interaction in a rill

Present‐day understanding of rill dynamics is hampered by a lack of detailed data on velocity distributions in rills. The latter are dif?cult to collect with traditional techniques due to the very low water depths and the relatively high ?ow velocities in rills. The objectives of this paper were to investigate the feasibility of miniaturized acoustic Doppler velocimeter (mADV) measurements in rill ?ow and to explore longitudinal variations in ?ow velocities and their relationship with rill bed morphology. Detailed data on longitudinal ?ow velocity were required to achieve these objectives. A 1·8 m long rill was formed freely in a ?ume at 5° slope and 0·001 m³ s^?1 discharge. Rill topography was characterized by an alternation of steps and pools. The ?ume surface was then ?xed to preserve rill roughness. A topographical scanning of the entire ?ume surface was made. Velocity was measured with a mADV along the rill, and at different depths. Flow depth in a longitudinal direction was also measured using an elevation gauge. A strong relationship exists between rill topography and ?ow hydraulics. Over steps, ?ow was unidirectional and rapidly accelerating until a threshold Froude number (Fn) value between 1·3 and 1·7 was reached and a hydraulic jump occurred leading to the formation of a pool. In the pool, the ?ow pattern was multidirectional and complex. The ?ow was subcritical when leaving the pool and accelerated over the next step until the threshold Froude number value was again reached. Energy loss in the rill was concentrated in the pools, mainly due to the action of a hydraulic jump. This mechanism of energy dissipation appeared to be an essential factor in rill formation and bedform evolution. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparing different methods of bed shear stress estimates in simple and complex flow fields

Bed shear stress is a fundamental variable in river studies to link ?ow conditions to sediment transport. It is, however, dif?cult to estimate this variable accurately, particularly in complex ?ow ?elds. This study compares shear stress estimated from the log pro?le, drag, Reynolds and turbulent kinetic energy (TKE) approaches in a laboratory ?ume in a simple boundary layer, over plexiglas and over sand, and in a complex ?ow ?eld around de?ectors. Results show that in a simple boundary layer, the log pro?le estimate is always the highest. Over plexiglas, the TKE estimate was the second largest with a value 30 per cent less than the log estimate. However, over sand, the TKE estimate did not show the expected increase in shear stress. In a simple boundary layer, the Reynolds shear stress seems the most appropriate method, particularly the extrapolated value at the bed obtained from a turbulent pro?le. In a complex ?ow ?eld around de?ectors, the TKE method provided the best estimate of shear stress as it is not affected by local streamline variations and it takes into account the increased streamwise turbulent ?uctuations close to the de?ectors. It is suggested that when single‐point measurements are used to estimate shear stress, the instrument should be positioned close to 0·1 of the ?ow depth, which corresponds to the peak value height in pro?les of Reynolds and TKE shear stress. Copyright © 2004 John Wiley & Sons, Ltd.     

A wind tunnel investigation of the influences of fetch length on the flux profile of a sand cloud blowing over a gravel surface

Wind tunnel tests were conducted to examine the fetch effect of a gravel surface on the ?ux pro?le of the sand cloud blowing over it using typical dune sand. The results suggest that the ?ux pro?le of blown sand over a gravel surface differs from that over a sandy surface and is characterized by a peak ?ux at a height above the surface while that over a sandy surface decreases exponentially with height. The ?ux pro?le of a sand cloud over a gravel surface can be expressed by a Gaussian peak function: q = a + b exp (?0·5((h ? c)/d)²), where q is the sand transport rate at height h, and a, b, c and d are regression coef?cients. The signi?cance of the coef?cients in the function could be de?ned in accordance with the fetch length of the gravel surface and wind velocity. Coef?cient c represents the peak ?ux height and increases with both wind velocity and fetch length, implying that the peak ?ux height is related to the bounce height of the particles in the blowing sand cloud. Coef?cient d shows a tendency to increase with both wind velocity and fetch length. The sum of a and b, representing the peak ?ux, increases with wind velocity but decreases with fetch length. The average saltation height derived from the cumulative percentage curve shows a tendency to increase with both the fetch length and wind velocity. For any fetch length of a gravel surface the sand transport equation is expressed as Q = C(1 ? U_t/U)(ρ/g)U³, where Q is the sand transport rate, U is the wind velocity, U_t is the threshold velocity measured at the same height as U, g is the gravitational acceleration, ρ is the air density, C is a proportionality coef?cient that decreases with the fetch length of the gravel surface. At a given wind velocity, the sand transport rate over a gravel surface is only 52–68 per cent of that over a sandy surface. The ?ux rate in true creep over a gravel surface increases with wind velocity but decreases with the fetch length, whereas the creep proportion (the ratio of creep ?ux to the sand transport rate) decreases with both the wind velocity and fetch length. Two‐variable (including fetch length and wind velocity) equations were developed to predict the peak ?ux height, average saltation height and transport rate. Copyright © 2004 John Wiley & Sons, Ltd.     

Resistance to overland flow due to bed‐load transport on plane mobile beds

During bed‐load transport by overland ?ow, momentum is transferred from the ?ow to the bed via grain collisions, resulting in a decrease in ?ow velocity and an increase in ?ow resistance, herein termed bed‐load transport resistance. In overland ?ow on mobile plane beds, total ?ow resistance f consists of grain resistance f_g and bed‐load transport resistance f_bt. In order to identify and evaluate the relative importance of the factors controlling f_bt, 38 ?ume experiments were performed on slopes of 2·7 and 5·5° using sediment with median diameters of 0·74 and 1·16 mm. All ?ows were supercritical and turbulent. This study is an extension of a recent study by Gao and Abrahams (Earth Surface Processes and Landforms 2004, vol. 29, pp. 423–435). These authors found that f_bt is controlled by three factors: sediment concentration C, dimensionless sediment diameter D_*, and relative submergence h/D, where h is ?ow depth, D is median sediment diameter. However, a new dimensional analysis identi?es two additional factors: Froude number F and slope S. Multiple regression analyses reveal (1) that these ?ve factors together explain 97 per cent of the variance of f_bt, and (2) that S controls f_bt entirely through C. The variable C is therefore redundant, and a new functional equation relating f_bt to D_*, h/D, S and F is developed. This equation may be used to predict f_bt. An advantage of this equation is that it may be used to predict f_bt without measuring bed‐load transport rate. Copyright © 2004 John Wiley & Sons, Ltd.     

The influence of macrophyte growth,typical of eutrophic conditions,on river flow velocities and turbulence production

The influence of emergent and submerged macrophytes on flow velocity and turbulence production is demonstrated in a 140 m reach of the River Blackwater in Farnborough, Hampshire, UK. Macrophyte growth occurs in patches and is dominated by Sparganium erectum and Sparganium emersum. In May 2001, patches of S. erectum were already established and occupied 18% of the channel area. The flow adjusted to these (predominantly lateral) patches by being channelled through a narrower cross‐section. The measured velocity profiles showed a logarithmic form, with deviations attributable to topographic control. The channel bed was the main source of turbulence. In September 2001, in‐stream macrophytes occupied 27% of the channel, and overhanging bank vegetation affected 32% of the area. Overall flow resistance, described by Manning's n, showed a threefold increase that could be attributed to the growth of S. emersum in the middle of the channel. Velocity profiles showed different characteristic forms depending on their position relative to plant stems and leaves. The overall velocity field had a three‐dimensional structure. Turbulence intensities were generally higher and turbulence profiles tended to mirror the velocity profiles. Evidence for the generation of coherent eddies was provided by ratios of the root mean square velocities. Spectral analysis identified deviations from the Kolmogorov ?5/3 power law and provided statistical evidence for a spectral short‐cut, indicative of additional turbulence production. This was most marked for the submerged vegetation and, in some instances, the overhanging bank vegetation. The long strap‐like leaves of S. emersum being aligned approximately parallel to the flow and the highly variable velocity field created by the patch arrangement of macrophytes suggest that the dominant mechanism for turbulence production is vortex shedding along shear zones. Wake production around individual stems of S. emersum close to the bed may also be important locally. Copyright © 2006 John Wiley & Sons, Ltd.     

Flow resistance in gravel‐bed channels with large‐scale roughness

A previously published mixing length (ML) model for evaluating the Darcy–Weisbach friction factor for a large‐scale roughness condition (depth to sediment height ratio ranging from 1 to 4) is brie?y reviewed and modi?ed (MML). Then the MML model and a modi?ed drag (MD) model are experimentally tested using laboratory measurements carried out for gravel‐bed channels and large‐scale roughness condition. This analysis showed that the MML gives accurate estimates of the Darcy–Weisbach coef?cient and for Froude number values greater than 0·5 the MML model coincides with the ML one. Testing of the MD model shows limited accuracy in estimating ?ow resistance. Finally, the MML and MD models are compared with the performance of a quasi‐theoretical (QT) model deduced applying the P‐theorem of the dimensional analysis and the incomplete self‐similarity condition for the depth/sediment ratio and the Froude number. Using the experimental gravel‐bed data to calibrate the QT model, a constant value of the exponent of the Froude number is determined while two relationships are proposed for estimating the scale factor and the exponent of the depth/sediment ratio. This indirect estimate procedure of the coef?cients (b₀, b₁ and b₂) of the QT model can produce a negligible overestimation or underestimation of the friction factor. Copyright © 2003 John Wiley & Sons, Ltd.     

Testing slope effect on flow resistance equation for mobile bed rills

In this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, is tested experimentally on plots of varying slopes in which mobile bed rills are incised. Initially, measurements of flow velocity, water depth, cross‐sectional area, wetted perimeter and bed slope conducted in 106 reaches of rills incised on an experimental plot having a slope of 14% were used to calibrate the flow resistance equation. Then, the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number, which was calibrated using the 106 rill reach data, was tested using measurements carried out in plots having slopes of 22% and 9%. The measurements carried out in the latter slope conditions confirmed that (a) the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the data were supportive of the slope independence hypothesis of rill velocity stated by Govers.     

Shear velocity estimates in rough‐bed open‐channel flow

Shear velocity u_* is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D₅₀ = 1·5 cm) under sub‐threshold conditions. The analysis is based on quasi‐instantaneous three‐dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough‐bed flows. Results from all methods fall into a range of ± 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough‐bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u_* from a single point measurement at one level in the intermediate range (0·3 < h < 0·6). Copyright © 2013 John Wiley & Sons, Ltd.     

Uncertainty analysis of flow velocity estimation by a simplified entropy model

The velocity field in a river flow cross‐sectional area can be determined by applying entropy as done in 1978 by Chiu, who developed a two‐dimensional model of flow velocity based on the knowledge of maximum velocity, u_max, and the dimensionless entropic parameter, characteristic of the river site. This is appealing in the context of discharge monitoring, particularly for high floods, considering that u_max occurs in the upper portion of flow area and can be easily sampled, unlike velocity in the lower portion of flow area. The simplified form of Chiu's entropy‐based velocity model, proposed in 2004 by Moramarco et al., has been found to be reasonably accurate for determining mean flow velocity along each vertical sampled in the flow area, but no uncertainty analysis has been reported for this simplified entropy‐based velocity model. This study, therefore, performed uncertainty analysis of the simplified model following a procedure proposed by Misirli et al. in 2003. The flow velocity measurements at the Rosciano River section along the Chiascio River, central Italy, carried out for a period spanning 20 years were used for this purpose. Results showed that the simplified entropy velocity model was able to provide satisfactory estimates of velocity profiles in the whole flow area and the 95% confidence bands for the computed estimated mean vertical velocity were quite representative of observed values. In addition, using these 95% confidence bands, it was possible to have an indication of the uncertainty in the determination of mean cross‐sectional flow velocity as well. Copyright © 2012 John Wiley & Sons, Ltd.     

Bedload transport resistance in rough open‐channel flows

During bedload movement by saltation, streamwise momentum is transferred from the ?ow to the saltating grains. When the grains collide with other grains on the bed or in the ?ow, streamwise momentum is reduced, and there is a decrease in streamwise ?ow velocity and an increase in ?ow resistance, herein termed bedload transport resistance f_bt. Based on experiments in two ?umes with ?xed and mobile plane beds and previously published data, an equation is developed that may be used to predict f_bt for both capacity and non‐capacity ?ows. The variables in this equation are identi?ed by dimensional analysis and the coef?cients are determined by non‐linear regression. This equation applies to rough turbulent open‐channel ?ows, where the relative submergence is between 1 and 20 and the entire sediment load moves by saltation. An investigation of the relative magnitudes of f_bt and grain resistance f_c suggests that where dimensionless shear stress θ is less than 1 and saltation is the dominant mode of bedload transport, f_bt/f_c increases with θ but never exceeds 1. Copyright © 2004 John Wiley & Sons, Ltd.     

Morphometric controls and geomorphic responses on fans in the Southern Alps,New Zealand

Morphometric variables associated with 41 debris‐?ow and 18 ?uvial fans and their basins in the Southern Alps of New Zealand are examined. The results show statistically signi?cant differences in the area, maximum elevation, relief and ruggedness (Melton's R) of the basin and the area, gradient, and apex and toe elevations of the fan between debris‐?ow and ?uvial sites. Concavity of the fan longitudinal pro?le also differs between the two fan types, although this could not be tested statistically. Most of these morphometric differences re?ect differences in processes and environmental controls on them. Discriminant analysis indicates that basin area and fan gradient best differentiate the two fan types by process. Moderately strong correlations exist, on both debris‐?ow and ?uvial fans, between basin area or Melton's R and fan area. Correlations between basin area or Melton's R and fan gradient are generally weaker. The results of this study also indicate that on debris‐?ow‐prone fans the fan gradient and basin Melton's R have lower thresholds which overlap little with upper thresholds associated with basins where only stream?ow reaches the fan. These thresholds may therefore have value in preliminary morphometric assessments of debris‐?ow hazard on fans in the Southern Alps. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimating depth‐averaged velocities in rough ­channels

Profiles of streamwise velocity obtained from North Boulder Creek, Colorado, typically are non‐logarithmic in form and exhibit the strong influence of form drag associated with coarse bed roughness. The spatially averaged profile is consistent with recent theoretical profile forms suggested for rough channels that are based on a partitioning of the total stress between a fluid part and a part associated with form drag on bed particles. Estimates of local depth‐averaged velocity using algorithms that are based on several measurements in the flow column improve with explicit Riemann averaging, versus simple averaging, of the measurements. Estimates based on a single‐point measurement at 0·6 of the flow depth, assuming a logarithmic or approximately logarithmic velocity profile, are the least reliable. Copyright © 2000 John Wiley & Sons, Ltd.     

A fast method of flood discharge estimation

Discharge, especially during flood periods, is among the most important information necessary for flood control, water resources planning and management. Owing to the high flood velocities, flood discharge usually cannot be measured efficiently by conventional methods, which explains why records of flood discharge are scarce or do not exist for the watersheds in Taiwan. A fast method of flood discharge estimation is presented. The greatest advantage of the proposed method is its application to estimate flood discharge that cannot be measured by conventional methods. It has as its basis the regularity of open‐channel flows, i.e. that nature maintains a constant ratio of mean to maximum velocities at a given channel section by adjusting the velocity distribution and the channel geometry. The maximum velocity at a given section can be determined easily over a single vertical profile, which tends to remain invariant with time and discharge, and can be converted to the mean velocity of the entire cross‐section by multying by the constant ratio. Therefore the mean velocity is a common multiple of maximum velocity and the mean/maximum velocity ratio. The channel cross‐sectional area can be determined from the gauge height, the water depth at the y‐axis or the product of the channel width multiplied by the water depth at the y‐axis. Then the most commonly used method, i.e. the velocity–area method, which determines discharge as the product of the cross‐sectional area multiplied by mean velocity, is applied to estimate the flood discharge. Only a few velocity measurements on the y‐axis are necessary to estimate flood discharge. Moreover the location of the y‐axis will not vary with time and water stage. Once the relationship of mean and maximum velocities is established, the flood estimation can be determined efficiently. This method avoids exposure to hazardous environments and sharply reduces the measurement time and cost. The method can be applied in both high and low flows in rivers. Available laboratory flume and stream‐flow data are used to illustrate accuracy and reliability, and results show that this method can quickly and accurately estimate flood discharges. Copyright © 2004 John Wiley & Sons, Ltd.     

Laboratory flume studies of microflow environments of aquatic plants

The microflow environments of aquatic plants with reference to Myriophyllum and Hydrilla are simulated in a laboratory flume. A Nix Streamflow microflow meter was used to measure the mean velocity profiles of flow at different densities of plants, flow ranges and measurement positions. Each mean velocity profile consists of three hydrodynamic regimes (i.e. within‐canopy zone, above‐canopy zone and a transitional zone between them), which indicate the presence of two benthic boundary layers (internal and external ones). Out of 38 measured mean velocity profiles, most do not fit a logarithmic relationship. The following hydrodynamic parameters are used in characterizing the flow regimes: local shear velocity (u_*), roughness length (z_o), canopy roughness Reynolds number (Re_*), bed shear stress (τ_o) and laminar sublayer (σ). Copyright © 2002 John Wiley & Sons, Ltd.     

Flume experiments on the horizontal stream offset by strike‐slip faults

Flume experiments, in which the middle section of an erosion channel is displaced horizontally, have been conducted to assess the response of streams to horizontal displacement by a strike‐slip fault. The experimental erosion channel was developed in a mixture of sand and clay, which provided relatively stable banks with its cohesiveness. Horizontal displacement of a strike‐slip fault perpendicular to the channel is expected to add a ?at section to its longitudinal pro?le along the fault line. The experimental stream eliminated this ?at section with downstream degradation, upstream aggradation, and lateral channel shift. As a result, a roughly continuous longitudinal pro?le was maintained. This maintenance of a continuous longitudinal pro?le along channel is considered to be the principle of stream response to horizontal displacement by a strike‐slip fault. Downstream degradation was the dominant process of this stream response in the overall tendency of erosion without sand supply. When the rate of fault displacement was low (long recurrence interval), the experimental stream eroded the fault surface, jutting laterally into the channel like a scarp, and de?ected the channel within the recurrence interval. This lateral channel shift gave some gradient to the reach created by fault displacement (offset reach), and the downstream degradation occurred as much as completing the remaining longitudinal pro?le adjustment. When the rate of fault displacement was high (short recurrence interval), the lateral erosion on the ?rst fault surface was interrupted by the next fault displacement. The displacement was then added incrementally to the existing channel offset making channel shift by lateral erosion increasingly dif?cult. The channel offset with sharp bends persisted without much modi?cation, and downstream degradation and upstream aggradation became evident with the effect of the offset channel course, which worked like a dam. In this case, a slight local convexity, which was incidentally formed by downstream degradation and upstream aggradation, tended to remain in the roughly continuous longitudinal pro?le, as long as the horizontal channel offset persisted. In either case, once the experimental stream obtained a roughly continuous gradient, further channel adjustment seemed to halt. Horizontal channel offset remained to a greater or lesser extent at the end of each run long after the last fault displacement. Copyright © 2004 John Wiley & Sons, Ltd.     

Flow resistance equation for rills

In this paper, a new flow resistance equation for rill flow was deduced applying dimensional analysis and self‐similarity theory. At first, the incomplete self‐similarity hypothesis was used for establishing the flow velocity distribution whose integration gives the theoretical expression of the Darcy–Weisbach friction factor. Then the deduced theoretical resistance equation was tested by some measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope carried out in 106 reaches of some rills shaped on an experimental plot. A relationship between the velocity profile, the channel slope, and the flow Froude number was also established. The analysis showed that the Darcy–Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power–velocity profile.     

Phase‐shifts in shear stress as an explanation for the maintenance of pool–riffle sequences

The stability of the pool–rif?e sequence is one of the most fundamental features of alluvial streams. For several decades, the process of velocity, or shear stress, reversal has been proposed as an explanation for an increase in the amplitude of pool–rif?e sequence bars during high ?ows, offsetting gradual scour of rif?es and deposition in pools during low ?ows. Despite several attempts, reversal has rarely been recorded in ?eld measurements. We propose that, instead of being reversed, maxima and minima in shear stress are phase‐shifted with respect to the pool–rif?e sequence bedform pro?le, so that maximum shear stress occurs upstream of rif?e crests at high ?ow, and downstream at low ?ow. Such phase‐shifts produce gradients of shear stress that explain rif?e deposition, and pool scour, at high ?ow, in accord with sediment continuity. The proposal is supported by results of a one‐dimensional hydraulic model applied to the surveyed bathymetry of a pool–rif?e sequence in a straight reach of a gravel‐bed river. In the sequence studied, the upstream phase‐shift in shear stress at high ?ow was associated with variations in channel width, with width minima occurring upstream of rif?e crests, approximately coincident with shear stress maxima, and width maxima occurring downstream of rif?e crests. Assuming that the width variation is itself the result of ?ow de?ection by rif?e crests at low ?ow, and associated bank‐toe scour downstream, low and high ?ow can be seen to have complementary roles in maintaining alluvial pool–rif?e sequences. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling suspended sediment concentration and load in a transport‐limited alluvial gully in northern Queensland,Australia

Alluvial gullies are often formed in dispersible sodic soils along steep banks of incised river channels. Field data collected by Shellberg et al. (Earth Surface Processes and Landforms 38: 1765–1778, 2013) from a gully outlet in northern Australia showed little hysteresis between water discharge and fine (<63 µm) and coarse (>63 µm) suspended sediment, indicating transport‐limited rather than source‐limited conditions. The major source of the fine (silt/clay) component was the sodic soils of upstream gully scarps, and the coarser (sand) component was sourced locally from channel bed material. In this companion paper at the same study site, a new method was developed for combining the settling velocity characteristics of these two sediment source components to estimate the average settling velocity of the total suspended sediment. This was compared to the analysis of limited sediment samples collected during flood conditions. These settling velocity data were used in the steady‐state transport limit theory of Hairsine and Rose (Water Resources Research 28: 237–243, 245–250, 1992) that successfully predicted field data of concentrations and loads at a cross‐section, regardless of the complexity of transport‐limited upstream sources (sheet erosion, scalds, rills, gullies, mass failure, bank and bed erosion, other disturbed areas). The analysis required calibration of a key model parameter, the fraction of total stream power (F ≈ 0.025) that is effective in re‐entraining sediment. Practical recommendations are provided for the prediction of sediment loads from other alluvial gullies in the region with similar hydrogeomorphic conditions, using average stream power efficiency factors for suspended silt/clay (F_w ≈ 0.016) and sand (F_s ≈ 0.038) respectively, but with no requirement for field data on sediment concentrations. Only basic field data on settling velocity characteristics from soil samples, channel geometry measurements, estimates of water velocity and discharge, and associated error margins are needed for transport limit theory predictions of concentration and load. This theory is simpler than that required in source‐limited situations. Copyright © 2015 John Wiley & Sons, Ltd.     

Gelifluction: viscous flow or plastic creep?

This paper reports results from two scaled centrifuge modelling experiments, designed to simulate thaw‐related geli?uction. A planar 12° prototype slope was modelled in each experiment, using the same natural ?ne sandy silt soil. However two different scales were used. In Experiment 1, the model scale was 1/10, tested in the centrifuge at 10 gravities (g) and in Experiment 2, the scale was 1/30, tested at 30 g. Centrifuge scaling laws indicate that the time scaling factor for thaw consolidation between model and prototype is N², where N is the number of gravities under which the model was tested. However, the equivalent time scaling for viscous ?ow is 1/1. If geli?uction is a viscosity‐controlled ?ow process, scaling con?icts will therefore arise during centrifuge modelling of thawing slopes, and rates of displacement will not scale accurately to the prototype. If, however, no such scaling con?icts are observed, we may conclude that geli?uction is not controlled by viscosity, but rather by elasto‐plastic soil deformation in which frictional shear strength depends on effective stress, itself a function of the thaw consolidation process. Models were saturated, consolidated and frozen from the surface downwards on the laboratory ?oor. The frozen models were then placed in the geotechnical centrifuge and thawed from the surface down. Each model was subjected to four freeze–thaw cycles. Soil temperatures and pore water pressures were monitored, and frost heave, thaw settlement and downslope displacements measured. Pore water pressures, displacement rates and displacement pro?les re?ecting accumulated shear strain, were all similar at the two model scales and volumetric soil transport per freeze–thaw cycle, when scaled to prototype, were virtually identical. Displacement rates and pro?les were also similar to those observed in earlier full‐scale laboratory ?oor experiments. It is concluded therefore that the modelled geli?uction was not a time‐dependent viscosity‐controlled ?ow phenomenon, but rather elasto‐plastic in nature. A ?rst approximation ‘?ow’ law is proposed, based on the ‘Cam Clay’ constitutive model for soils. Copyright © 2003 John Wiley & Sons, Ltd.     

Experimental investigation of the velocity of a sand cloud blowing over a sandy surface

The velocity of a wind‐blown sand cloud is important for studying its kinetic energy, related erosion, and control measures. PDA (particle dynamics analyser) measurement technology is used in a wind tunnel to study the probability distribution of particle velocity, variations with height of the mean velocity and particle turbulence in a sand cloud blowing over a sandy surface. The results suggest that the probability distribution of the particle velocity in a blowing sand cloud is stochastic. The probability distribution of the downwind velocity complies with a Gaussian function, while that of the vertical velocity is greatly complicated by grain impact with the bed and particle–particle collisions in the air. The probability distribution of the vertical velocity of ?ne particles (0·1–0·3 mm sands) can be expressed as a Lorentzian function while that of coarse particles (0·3–0·6 mm sands) cannot be expressed by a simple distribution function. The mean downwind velocity is generally one or two orders greater than the mean vertical velocity, but the particle turbulence in the vertical direction is at least two orders greater than that in the downwind direction. In general, the mean downwind velocity increases with height and free‐stream wind velocity, but decreases with grain size. The variation with height of the mean downwind velocity can be expressed by a power function. The particle turbulence of a blowing sand cloud in the downwind direction decreases with height. The variations with height of the mean velocity and particle turbulence in the vertical direction are very complex. It can be concluded that the velocity of a sand cloud blowing over a sandy surface is mainly in?uenced by wind velocity, grain impact with the bed and particle–particle collisions in the air. Wind velocity is the primary factor in?uencing the downwind velocity of a blowing sand cloud, while the grain impact with the bed and particle–particle collisions in the air are the primary factors responsible for the vertical velocity. Copyright © 2004 John Wiley & Sons, Ltd.