Conditional statistics of Reynolds shear stress in flow over 2D dunes in the presence of surface waves

This study presents the analysis of the velocity fluctuations to describe the conditional statistics of Reynolds shear stress in flow over two‐dimensional dunes in the presence of surface waves of varying frequency. The flow velocity measurements over the dunes are made using a 16‐MHz 3D acoustic Doppler velocimeter. The joint probability distributions of the normalized stream‐wise and vertical velocity fluctuations at different vertical locations are calculated in the trough region of a selected dune in quasi‐steady region of the flow. Third‐order moments of the stream‐wise and vertical velocity components over one dune length are also calculated throughout the flow depth for understanding the effect of surface waves on relative contributions to the Reynolds shear stress due to the four quadrant events. The structure of instantaneous Reynolds stresses is analysed using quadrant analysis technique. It has been shown that the contributions of second and fourth quadrant events to the Reynolds shear stress increase with increase in the frequency of surface waves. In fact, the largest contribution to turbulent stresses comes from the second quadrant. The cumulant discard method is applied to describe the statistical properties of the covariance term u′w′. Conditional statistics and conditional sampling are used to compare the experimental and theoretical relative contributions to the Reynolds shear stress from the four quadrant events. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling raindrop impact and splash erosion processes within a spatial cell: a stochastic approach

A new approach is proposed to simulate splash erosion on local soil surfaces. Without the effect of wind and other raindrops, the impact of free‐falling raindrops was considered as an independent event from the stochastic viewpoint. The erosivity of a single raindrop depending on its kinetic energy was computed by an empirical relationship in which the kinetic energy was expressed as a power function of the equivalent diameter of the raindrop. An empirical linear function combining the kinetic energy and soil shear strength was used to estimate the impacted amount of soil particles by a single raindrop. Considering an ideal local soil surface with size of 1 m × 1 m, the expected number of received free‐falling raindrops with different diameters per unit time was described by the combination of the raindrop size distribution function and the terminal velocity of raindrops. The total splash amount was seen as the sum of the impact amount by all raindrops in the rainfall event. The total splash amount per unit time was subdivided into three different components, including net splash amount, single impact amount and re‐detachment amount. The re‐detachment amount was obtained by a spatial geometric probability derived using the Poisson function in which overlapped impacted areas were considered. The net splash amount was defined as the mass of soil particles collected outside the splash dish. It was estimated by another spatial geometric probability in which the average splashed distance related to the median grain size of soil and effects of other impacted soil particles and other free‐falling raindrops were considered. Splash experiments in artificial rainfall were carried out to validate the availability and accuracy of the model. Our simulated results suggested that the net splash amount and re‐detachment amount were small parts of the total splash amount. Their proportions were 0·15% and 2·6%, respectively. The comparison of simulated data with measured data showed that this model could be applied to simulate the soil‐splash process successfully and needed information of the rainfall intensity and original soil properties including initial bulk intensity, water content, median grain size and some empirical constants related to the soil surface shear strength, the raindrop size distribution function and the average splashed distance. Copyright © 2007 John Wiley & Sons, Ltd.     

A field study of mean and turbulent flow characteristics upwind,over and downwind of barchan dunes

Field‐measured patterns of mean velocity and turbulent airflow are reported for isolated barchan dunes. Turbulence was sampled using a high frequency sonic anemometer, deriving near‐surface Reynolds shear and normal stresses. Measurements upwind of and over a crest‐brink separated barchan indicated that shear stress was sustained despite a velocity reduction at the dune toe. The mapped streamline angles and enhanced turbulent intensities suggest the effects of positive streamline curvature are responsible for this maintenance of shear stress. This field evidence supports an existing model for dune morphodynamics based on wind tunnel turbulence measurements. Downwind, the effect of different dune profiles on flow re‐attachment and recovery was apparent. With transverse incident flow, a re‐attachment length between 2·3 and 5·0h (h is dune brink height) existed for a crest‐brink separated dune and 6·5 to 8·6h for a crest‐brink coincident dune. The lee side shear layer produced elevated turbulent stresses immediately downwind of both dunes, and a decrease in turbulence with distance characterized flow recovery. Recovery of mean velocity for the crest‐brink separated dune occurred over a distance 6·5h shorter than the crest‐brink coincident form. As the application of sonic anemometers in aeolian geomorphology is relatively new, there is debate concerning the suitability of processing their data in relation to dune surface and streamline angle. This paper demonstrates the effect on Reynolds stresses of mathematically correcting data to the local streamline over varying dune slope. Where the streamline angle was closely related to the surface (windward slope), time‐averaged shear stress agreed best with previous wind tunnel findings when data were rotated along streamlines. In the close lee, however, the angle of downwardly projected (separated) flow was not aligned with the flat ground surface. Here, shear stress appeared to be underestimated by streamline correction, and corrected shear stress values were less than half of those uncorrected. Copyright © 2011 John Wiley & Sons, Ltd.     

Experimental investigation of the impacts of coherent flow structures upon turbulence properties in regions of crescentic scour

This study examines the spatial distributions of third‐order moments of velocity fluctuations, the turbulent kinetic energy (TKE) fluxes, and the conditional statistics of Reynolds shear stress across the equilibrium crescentic scour structures generated upstream of short horizontal static cylinders. Detailed velocity data were collected using three‐dimensional (3D) micro‐acoustic Doppler velocimeter (ADV) across and within the equilibrium scour marks. The analysis reveals that the positive and negative values of third‐order moments associated with the level bed surface and the scour holes are directly related to coherent structures. The components of TKE flux are discussed for the near‐bed region of the level bed surface and scour holes in relation to sweep–ejection events. A cumulant‐discard method is applied to the Gram‐Charlier probability distribution of two variables to describe the statistical properties of the term u′w′. The conditional statistics of the Reynolds shear stress show a good agreement with the experimental data. The distribution of the joint probability density function in the near‐bed region changes cyclically along the scour hole depending on the bottom fluid velocity, which implies a change from upward to downward flux of momentum and vice versa. Both the ejection and sweep events at near‐bed points on the level surface are more important than within the scour region; and in contrast, both events are stronger for the scour marks than the level bed surface at the outer layer. Sweeps dominate over ejections for the scour hole induced by smaller diameter and ejections dominate for larger diameter. Copyright © 2013 John Wiley & Sons, Ltd.     

Spatial variability of three‐dimensional Reynolds stresses in a developing channel bend

Experimental results of the mean flow field and turbulence characteristics for flow in a model channel bend with a mobile sand bed are presented. Acoustic Doppler velocimeters (ADVs) were used to measure the three components of instantaneous velocities at multiple cross sections in a 135° channel bend for two separate experiments at different stages of clear water scour conditions. With measurements at multiple cross sections through the bend it was possible to map the changes in both the spatial distribution of the mean velocity field and the three Reynolds shear stresses. Turbulent stresses are known to contribute to sediment transport and the three‐dimensionality inherent to flow in open channel bends presents a useful case for determining specific relations between three‐dimensional turbulence and sediment entrainment and transport. These measurements will also provide the necessary data for validating numerical simulations of turbulent flow and sediment transport. The results show that the magnitude and distribution of three‐dimensional Reynolds stresses increase through the bend, with streamwise‐cross stream and cross stream‐vertical components exceeding the maximum principal Reynolds stress through the bend. The most intriguing observation is that near‐bed maximum positive streamwise‐cross stream Reynolds stress coincides with the leading edge of the outer bank scour hole (or thalweg), while maximum cross stream‐vertical Reynolds stress (in combination with high negative streamwise‐cross stream Reynolds stress near the bend apex) coincides with the leading edge of the inner bank bar. Maximum Reynolds stress and average turbulent kinetic energy appear to be greater and more localized over the scour hole before final equilibrium scour is reached. This suggests that the turbulent energy in the flow is higher while the channel bed is developing, and both lower turbulent energy and a broader distribution of turbulent stresses near the bed are required for cessation of particle mobilization and transport. Copyright © 2010 John Wiley & Sons, Ltd.     

INITIATION OF SEDIMENT MOTION IN LAMINAR OVERLAND FLOW

IINTRODUCTIONWhileriverflowsareusuallydeepandturbulent,overlandflowisextremelyshallowandcanbelaminar,transitionalandturbulent.Becauseoftheshallownessoftheflolw,overlandflowhydraulicsisgreatlyaffectedbysurfaceroughness,raindropimpact,andinthecaseoflaminarflow,flui(Iviscosity.Theinitiationofsedimentmovementinoverlandflowisthereforeexpectedtodifferfromthatinriverflows.InriverstUdies,bedshearStressgbhastraditionallybeenusedtocharacterizethecriticalflowconditionatwhichsedimentbeginstomove.At…     

The impact of slope length on the discharge of sediment by rain impact induced saltation and suspension

Simulations using a mechanistic model of raindrop driven erosion in rain‐impacted flow were performed with particles travelling by suspension, raindrop induced saltation and flow driven saltation. Results generated by both a high intensity storm, and a less intense one, indicate that, because of the effect of flow depth on the delivery of raindrop energy to the bed, there is a decline in sediment concentration, and hence soil loss per unit area, with slope length when particles are transported by raindrop induced saltation. However, that decline is reversed when the critical velocities that lead to flow driven saltation are episodically exceeded during an event. The simulations were performed on smooth surfaces and a single drop size but the general relationships are likely to apply for rain made up of a wide range of drop size. Although runoff is not always produced uniformly, as a general rule, flow velocities increase with slope length so that, typically, the distance particles travel before being discharged during an event increase with slope length. The effect of slope length on soil loss per unit area is often considered to vary with slope length to a power greater than zero and less that 1·0. The simulations show that effect of slope length on sediment discharge is highly dependent on the variations in runoff response resulting from variations in rainfall duration‐intensity‐infiltration conditions rather than plot length per se. Consequently, predicting soil loss per unit area using slope length with positive powers close to zero when sheet erosion occurs may not be as effective as commonly expected. Erosion by rain‐impacted flow is a complex process and that complexity needs to be considered when analysing the results of experiments associated with rain‐impacted flow under both natural and artificial conditions. Copyright © 2009 John Wiley & Sons, Ltd.     

Pressure and shear stress caused by raindrop impact at the soil surface: Scaling laws depending on the water depth

Raindrop impact is an important process in soil erosion. Through its pressure and shear stress, raindrop impact causes a significant detachment of the soil material, making this material available for transport by sheet flow. Thanks to the accurate Navier–Stokes equations solver Gerris, we simulate the impact of a single raindrop of diameter D, at terminal velocity, on water layers of different thickness h: , , D, 2D, in order to study pressures and shear stresses involved in raindrop erosion. These complex numerical simulations help in understanding precisely the dynamics of the raindrop impact, quantifying in particular the pressure and the shear stress fields. A detailed analysis of these fields is performed and self‐similar structures are identified for the pressure and the shear stress on the soil surface. The evolution of these self‐similar structures are investigated as the aspect ratio h/D varies. We find that the pressure and the shear stress have a specific dependence on the ratio between the drop diameter and the water layer thickness, and that the scaling laws recently proposed in fluid mechanics are also applicable to raindrops, paving the road to obtain effective models of soil erosion by raindrops. In particular, we obtain a scaling law formula for the dependence of the maximum shear stress on the soil on the water depth, a quantity that is crucial for quantifying erosion materials. Copyright © 2016 John Wiley & Sons, Ltd.     

MODELING OF INTERRILL EROSION IN THE LOESS PLATEAU OF CHINA

IINTRODUCTIONTheinterrillerosiononafieldplotisaffectedbythekineticenergyoftherainfall,wind,topographyfactors,propertiesofsoilandthecanopy.Theinterrillerosionoccursasthefirstdropimpactsthehillslopes.Theinterrillerosionoccursinallkindsofrainfallandtheamountofthesplasherosion,whichisthemainpartofinterrillerosion,canaccountforagreatpanofthetotalerosionamountinaheavystorm(Baner1990,Glymph1957,QianandWan1986,Zhou1981).Therefore,itisveryimportanttorevealthemechanismtoestimatetheamountofinterri…     

Suspended sediment concentration and the ripple–dune transition

Flume experiments were conducted in order to monitor changes in flow turbulence intensity and suspended sediment concentration at seven stages across the ripple–dune transition and at three different positions above the bed surface. Three‐dimensional velocity measurements were obtained using an acoustic Doppler velocimeter (ADV). Suspended sediment concentration (SSC) was monitored indirectly using ADV signal amplitude. Although limited to time‐averaged parameters, the analysis reveals that SSC varies significantly with stage across the transition and with sampling height. The statistical analysis also reveals an apparent uniformity of suspended sediment concentration with height above the bed in the lower half of the flow depth at the critical stage in the transition from ripples to dunes. This is also the stage at which turbulence intensity is maximized. Statistically significant correlations were also observed between suspended sediment concentrations and root‐mean‐square values of vertical velocity fluctuations. These correlations reflect the various levels of shear‐layer activity and the distinct turbulent flow regions across the transition. Conversely, time‐averaged values of Reynolds shear stress exhibit a very weak relationship with suspended sediment concentrations. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Evaluation of an interrill soil erosion model using laboratory catchment data

Physically based soil erosion simulation models require input parameters of soil detachment and sediment transport owing to the action and interactions of both raindrops and overland flow. A simple interrill soil water transport model is applied to a laboratory catchment to investigate the application of raindrop detachment and transport in interrill areas explicitly. A controlled laboratory rainfall simulation study with slope length simulation by flow addition was used to assess the raindrop detachment and transport of detached soil by overland flow in interrill areas. Artificial rainfall of moderate to high intensity was used to simulate intense rain storms. However, experiments were restricted to conditions where rilling and channelling did not occur and where overland flow covered most of the surface. A simple equation with a rainfall intensity term for raindrop detachment, and a simple sediment transport equation with unit discharge and a slope term were found to be applicable to the situation where clear water is added at the upper end of a small plot to simulate increased slope length. The proposed generic relationships can be used to predict raindrop detachment and the sediment transport capacity of interrill flow and can therefore contribute to the development of physically‐based erosion models. Copyright © 1999 John Wiley & Sons, Ltd.     

Investigation of turbulence characteristics in channel with dense vegetation

In this experimental study,the turbulent flow in a channel with vegetation by using sprouts of wheat on channel bed was investigated.Two different aspect ratios of channel were used.An Acoustic Doppler Velocimetry was used to measure parameters of turbulent flow over submerged sprouts of wheat,such as velocity profiles.The log law and the Reynolds shear stress distribution were applied. Results indicate that the position of the maximum turbulence intensity superposes on the inflection point situated over the top of submerged vegetation cover.Quadrant analysis shows that near the vegetation bed,the sweeps and ejections appear to be the most dominant phenomenon,while far from the vegetated bed,the outward is dominant event.Results also show that the aspect ratio plays an important role on the contribution of the different bursting events for Reynolds stress determination.     

Effect of non‐uniformity of flow on velocity and turbulence intensities over a cobble‐bed

Non‐uniform flows encompassing both accelerating and decelerating flows over a cobble‐bed flume have been experimentally investigated in a flume at a scale of intermediate relative submergence. Measurements of mean longitudinal flow velocity u, and determinations of turbulence intensities u′, v′, w′, and Reynolds shear stress ?u_fw_f have been made. The longitudinal velocity distribution was divided into the inner zone close to the bed and the outer zone far from the bed. In the inner zone of the boundary layer (near the bed) the velocity profile closely followed the ‘Log Law’; however, in the outer zone the velocity distribution deviated from the Log Law consistently for both accelerating and decelerating flows and the changes in bed slopes ranging from ?2% to + 2% had no considerable effect on the outer zone. For a constant bed slope (S = ±0·015), the larger the flow rate, the smaller the turbulence intensities. However, no detectable pattern has been observed for u′, v′ and w′ distributions near the bed. Likewise, for a constant flow rate (Q = 0·040 m³/s), with variation in bed slope the longitudinal turbulent intensity profile in the longitudinal direction remained concave for both accelerating and decelerating flows; whereas vertical turbulent intensity (w′) profile presented no specific form. The results reveal that the positions of maximum values of turbulence intensities and the Reynolds shear stress depend not only on the flow structure (accelerating or decelerating) but also on the intermediate relative submergence scale. Copyright © 2009 John Wiley & Sons, Ltd.     

Variable and conflicting shear stress estimates inside a boundary layer with sediment transport

This paper presents a comparison between two methods for estimating shear stress in an atmospheric internal boundary layer over a beach surface under optimum conditions, using wind velocities measured synchronously at 13 heights over a 1.7 m vertical array using ultrasonic anemometry. The Reynolds decomposition technique determines at‐a‐point shear stresses at each measurement height, while the Law‐of‐the‐Wall yields a single boundary layer estimate based on fitting a logarithmic velocity profile through the array data. Analysis reveals significant inconsistencies between estimates derived from the two methods, on both a whole‐event basis and as time‐series. Despite a near‐perfect fit of the Law‐of‐the‐Wall, the point estimates of Reynolds shear stress vary greatly between heights, calling into question the assumed presence of a constant stress layer. A comparison with simultaneously measured sediment transport finds no relationship between transport activity and the discrepancies in shear stress estimates. Results do show, however, that Reynolds shear stress measured nearer the bed exhibits slightly better correlation with sand transport rate. The findings serve as a major cautionary message to the interpretation and application of single‐height measurements of Reynolds shear stress and their equivalence to Law‐of‐the‐Wall derived estimates, and these concerns apply widely to boundary layer flows in general. © 2015 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Mean and turbulent flow fields in a simulated ice‐covered channel with a gravel bed: some laboratory observations

Northern rivers experience freeze‐up over the winter, creating asymmetric under‐ice flows. Field and laboratory measurements of under‐ice flows typically exhibit flow asymmetry and its characteristics depend on the presence of roughness elements on the ice cover underside. In this study, flume experiments of flows under a simulated ice cover are presented. Open water conditions and simulated rough ice‐covered flows are discussed. Mean flow and turbulent flow statistics were obtained from an Acoustic Doppler Velocimeter (ADV) above a gravel‐bed surface. A central region of faster flow develops in the middle portion of the flow with the addition of a rough cover. The turbulent flow characteristics are unambiguously different when simulated ice covered conditions are used. Two distinct boundary layers (near the bed and in the vicinity of the ice cover, near the water surface) are clearly identified, each being characterized by high turbulent intensity levels. Detailed profile measurements of Reynolds stresses and turbulent kinetic energy indicate that the turbulence structure is strongly influenced by the presence of an ice cover and its roughness characteristics. In general, for y/d > 0·4 (where y is height above bed and d is local flow depth), the addition of cover and its roughening tends to generate higher turbulent kinetic energy values in comparison to open water flows and Reynolds stresses become increasingly negative due to increased turbulence levels in the vicinity of the rough ice cover. The high negative Reynolds stresses not only indicate high turbulence levels created by the rough ice cover but also coherent flow structures where quadrants one and three dominate. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic simulation on hydraulic characteristic values of overland flow

The economic forest management is one of the main land use models on low hill gentle slope. In order to investigate the soil erosion properties of bare slope under economic forest, dynamic simulation on hydraulic characteristic values of overland flow was carried out under 0.5 mm min^?1, 1.2 mm min^?1 and 1.8 mm min^?1 rainfall intensities. Results indicated that runoff shear stress increased with increasing of slope length and their relationship can be described by quadratic equation. There were abnormal points at the length of 4 m and 5.5 m under rainfall intensity of 1.8 mm min^?1. The shallow flow was pseudo-laminar flow under 0.5 mm min^?1, 1.2 mm min^?1 and 1.8 mm min^?1 rainfall intensities, and the runoff at upslope was sluggish flow then changed to torrential flow at downslope with increasing of slope length. Critical Reynolds number varied from sluggish flow to torrential flow with 1.8 mm min^?1 rainfall intensity and was more than that under 0.5 mm min^?1. Reynolds number can be estimated by power function of slope length. And there was a positive correlation between runoff shear stress and both Froude number Fr and Reynolds number Re. We hope this study can provide scientific gist for soil erosion control under economic forest.     

Analysis of bedload transport in laminar flows

Bedload transport generally depends on the bed shear stress and Reynolds number. Many studies conducted for the condition of turbulent flows have revealed the dependence of the transport rate on the bed shear stress, while knowledge of the Reynolds number effect on the transport rate is very limited. As an extreme case to reflect the viscous effect on sediment transport, sediment transport in laminar flows is considered in this paper. A stochastic approach is adopted to explore how the transport rate can be associated with characteristics of laminar flows. First, the probability of erosion in the absence of turbulence is assumed to depend only on the randomness of bed particles. The probability is then applied to formulate the sediment transport rate, of which the derivation is made largely based on Einstein’s bedload theory. The theoretical result indicates that the dimensionless transport rate for laminar flows is dependent on the dimensionless shear stress and dimensionless particle diameter or the shear Reynolds number. Comparisons are finally made between the derived formula and an empirical correlation available in the literature.     

Measuring water velocity in highly turbulent flows: field tests of an electromagnetic current meter (ECM) and an acoustic Doppler velocimeter (ADV)

Two field tests were completed to compare the performance of an electromagnetic current meter (ECM) with that of an acoustic Doppler velocimeter (ADV) in gravel‐bed rivers. Research was particularly motivated by the need to measure flow properties in highly energetic turbulent flows. Measurements were made at two field sites, one at moderate velocities (up to 70 cm/s) and with moderate turbulence intensities (10–20% of mean flow), and the other in an area of non‐uniform flow that included locations with fast mean velocities (up to 1.75 m/s) and high turbulent intensities (up to 50% of mean flow). Comparison of means, standard deviations, turbulent kinetic energy and Reynolds shear stress confirm the general agreement between the ECMs and ADVs. The general agreement is subject to limitations associated with the sample volume and frequency response of the instruments, and only applies within restricted velocity (up to ≈1.25 m/s) and turbulence intensity ranges (up to ≈0·125 m/s). At higher turbulence intensities, spectral analysis showed anomalous behavior of the ADV signal, especially in the vertical velocity component. Quadrant analysis of the Reynolds stress suggests that these problems occur predominantly in quadrants 1 and 3. Errors in ADV measurements were estimated using four different methods: one that utilized the characteristic noise floor in spectral plots, one based on internal ADV measurements of signal correlation and two techniques that aggregate errors related to various sub‐factors. Estimates were divergent at high flows. Techniques that rely on sub‐factors appeared to underestimate the impact of high turbulence on signal quality. The key conclusion for future field applications is that the older ECM technology provides the more reliable estimates of flow parameters in high turbulence. Copyright © 2007 John Wiley & Sons, Ltd.     

Space time evolution of sand bed topography and associated flow turbulence: experiments with statistical analysis

A series of flume experiments were conducted with varying the flow discharges at the Fluvial Mechanics Laboratory of Indian Statistical Institute (Kolkata) to understand the co-evolution patterns of generating bed forms and the corresponding flow turbulence. Instantaneous bed elevations and velocity components were recorded continuously for sufficient time using high resolution instruments, such as, Ultrasonic Ranging System and acoustic Doppler velocimeter, at some spatial location over the deformed bed for each flow discharge. Increase in mean bed elevations and bed-slopes was found to be increased in discharge. Heavy-tailed nature of the probability density functions of magnitude of bed elevation increments, magnitude of single continuous bed elevation increments and instantaneous Reynolds shear stresses along three planes were analyzed using Pareto and truncated Pareto distributions. The spectral analysis of bed elevations revealed that the slope of log–log linearity increased with increase in flow discharge. Wavelet cross-correlations depicted strong dependence of bed form evolution on the corresponding instantaneous Reynolds shear stress along xz-plane. A Gram–Charlier type of distribution was used to estimate the probability density function of fluctuating velocity components, instantaneous Reynolds shear stresses along three planes and the joint probability density functions of the fluctuating velocity components, which showed good fit with the experimental data.