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.     

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.     

Turbulence fields in the lee of two‐dimensional transverse dunes simulated in a wind tunnel

The turbulence field of airflow in the lee of a dune has significant impacts on dune dynamics and related processes. We used particle image velocimetry in a wind tunnel simulation to obtain detailed velocity measurements in the lee of two‐dimensional transverse dune models, then used the results to analyse their turbulence fields. The dune models used in this study had a single lee angle of 30°, and a total of six stoss angles: 3°, 5°, 10°, 15°, 20° and 25°. We used vorticity, turbulence intensity, Reynolds stress and turbulent kinetic energy to characterize the turbulence fields. These parameters were functions of stoss angle, wind velocity, distance from the dune crest and height above the ground surface. The stoss angles could generally be divided into two groups based on the profiles of mean velocity, turbulence and Reynolds stress. Stoss angles of 3° and 5° usually had similar profiles, and angles of 15°, 20° and 25° formed a second group with similar profiles. The profiles for the stoss angle of 10° were usually transitional and were intermediate between the two groups. Vorticity, Reynolds stress and turbulent kinetic energy increased monotonically with increasing free‐stream wind velocity, but their variations with respect to the stoss angle were complex. The stoss angles of 15° and 20° had the maximum values of these three parameters, thus these angles may have special significance in dune development given the characteristics of the mean velocity fields and turbulence fields they produce within the lee airflow. It is the streamwise velocity component and its turbulence that determine the surface shear stress. Copyright © 2008 John Wiley and Sons, Ltd.     

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.     

Turbulence modeling of compound open-channel flows with and without vegetation on the floodplain using the Reynolds stress model

A Reynolds stress model for the numerical simulation of compound open-channel flows with vegetation on the floodplain is described. The Reynolds stress model consists of various sub-models such as Speziale et al.’s model, Mellor and Herring’s model, and Rotta’s model for the pressure–strain correlation term, the turbulent diffusion term, and the dissipation term, respectively. For validation of the model, plain compound open-channel flows are simulated. The computed results were compared with measured data by [Tominaga A, Nezu I. Turbulent structure in compound open-channel flows. J Hydraul Eng, ASCE 1991;117(1):21–41] and the results show that the Reynolds stress model successfully simulates the mean flow and turbulence structure of plain compound channel flows. The model was then applied to compound open-channel flows with vegetated floodplains. Good agreement between the simulated results and data from an algebraic stress model by [Naot D, Nezu I, Nakagawa H. Hydrodynamic behavior of partly vegetated open channels. J Hydraul Eng, ASCE 1996;122(11):625–33] was found. However, it was shown that the RSM is capable of predicting the velocity dip and lateral shift in the maximum streamwise velocity, which were not observed in the data from algebraic stress modeling. Finally, a depth-averaged analysis of the streamwise momentum equation was performed to investigate the lateral momentum transfer in compound channel flows with vegetated floodplains. Compared with components by the secondary currents and Reynolds stress, the drag force due to the presence of vegetation appears to be a factor in reducing the bottom shear stress in both main channel and floodplain.     

The influence of pool length on local turbulence production and energy slope: a flume experiment

The in?uence of pool length on the strength of turbulence generated by vortex shedding was investigated in a 6 m long recirculating ?ume. The experiment utilized a 38% constriction of ?ow and an average channel‐bed slope of 0·007. The base geometry for the intermediate‐length pool experiment originated from a highly simpli?ed, 0·10 scale model of a forced pool from North Saint Vrain Creek, Colorado. Discharge in the ?ume was 31·6 l/s, which corresponds to a discharge in the prototype channel of 10 m³/s. Three shorter and four longer pool lengths also were created with a ?xed bed to determine changes in turbulence intensities and energy slope with pool elongation. Three‐dimensional velocities were measured with an acoustic Doppler velocimeter at 31–40 different 0·6‐depth and near‐bed locations downstream of the rectangular constriction. The average velocity and root mean square (RMS) of the absolute magnitude of velocity at both depths are signi?cantly related to the distance from the constriction in most pool locations downstream of the constriction. In many locations, pool elongation results in a non‐linear change in turbulence intensities and average velocity. Based on the overall ?ow pattern, the strongest turbulence occurs in the center of the pool along the shear zone between the jet and recirculating eddy. The lateral location of this shear zone is sensitive to changes in pool length. Energy slope also was sensitive to pool length due to a combination of greater length of the pool and greater head loss with shorter pools. The results indicate some form of hydraulic optimization is possible with pools adjusting their length to adjust the location and strength of turbulent intensities in the center of pools, and lower their rate of energy dissipation. Copyright © 2004 John Wiley & Sons, Ltd.     

Particle simulations of dispersion using observed meandering and turbulence

A Lagrangian stochastic particle model driven by observed winds from a network of 13 sonic anemometers is used to simulate the transport of contaminates due to meandering of the mean wind vector and diffusion by turbulence. The turbulence and the meandering motions are extracted from the observed velocity variances using a variable averaging window width. Such partitioning enables determination of the separate contributions from turbulence and meandering to the total dispersion. The turbulence is described by a Markov Chain Monte Carlo process based on the Langevin equation using the observed turbulence variances. The meandering motions, not the turbulence, are primarily responsible for the 1-h averaged horizontal dispersion as measured by the travel time dependence of the particle position variances. As a result, the 1-h averaged horizontal concentration patterns are often characterized by streaks and multi-modal distributions. Time series of concentration at a fixed location are highly nonstationary even when the 1-h averaged spatial distribution is close to Gaussian. The results show that meandering dominates the travel-time dependence of the horizontal dispersion under all atmospheric conditions: weak and strong winds, and unstable and stable stratification.     

Double-averaged velocity and stress distributions for hydraulically-smooth and transitionally-rough turbulent flows

We analyse experimental measurements of turbulent open-channel flow over hydraulically-smooth and transitionally-rough beds using the double-averaging methodology. Oil with a viscosity of 15×10^?6 m2/s is used instead of water so that transitional-range roughness Reynolds numbers can be achieved with large (11.1 mm) roughness elements, allowing spatial variations in the mean velocity field to more easily be measured. Distributions of double-averaged velocities, turbulence intensities, form-induced intensities, and viscous, Reynolds, form-induced and total shear stresses are studied with comparisons made between distributions for hydraulically-smooth, transitionally-rough, and fully-rough boundaries. Measured streamwise turbulence intensities for all experiments peaked at a constant distance from the bed (z ⁺+d ⁺ = 15) when elevation scale is adjusted using the zero-plane displacement d for the logarithmic velocity distribution. This collapse suggests that turbulence intensity distributions may be useful in assessing appropriate values of d for transitionally-rough and fully-rough boundaries. Form-induced normal and shear stresses above the roughness tops were found to collapse towards a common curve independent of roughness Reynolds number.     

Modelling combined open channel flow by artificial neural networks

Combined open channel flow is encountered in many hydraulic engineering structures and processes, such as irrigation ditches and wastewater treatment facilities. Extensive experimental studies have conducted to investigate combined flow characteristics. Nevertheless, there is no simple relationship that can fully describe the velocity profiles in a turbulent flow. The artificial neural network (ANN) has great computational capability for solving various complex problems, such as function approximation. The main objective of this study is to evaluate the applicability of the ANN for simulating velocity profiles, velocity contours and estimating the discharges accordingly. The velocity profiles measured by an acoustic doppler velocimeter in the open channel of the Chihtan purification plant, Taipei, with different discharges at fixed measuring section and different depths are presented. The total number of data sets is 640 and the data sets are split into two subsets, i.e. training and validation sets. The backpropagation algorithm is used to construct the neural network. The results demonstrate that the velocity profiles can be modelled by the ANN, and the ANN constructed can nicely fit the velocity profiles and can precisely predict the discharges for the conditions investigated. Copyright © 2005 John Wiley & Sons, Ltd.     

Velocity characteristics along a small step–pool channel

This paper summarizes measurements of velocity along three reaches of a small mountain channel with step–pool bedforms. A one‐dimensional electromagnetic current meter was used to record velocity fluctuations at 37 fixed measurement points during five measurement intervals spanning the peak of the annual snowmelt hydrograph. Measurement cross‐sections were located upstream from a bed‐step, at the step lip, downstream from the step, and in a uniform‐gradient run. Data analyses focused on characteristics of velocity profiles, and on correlations between velocity characteristics and the potential control variables bedform type, reach gradient and flow depth. To test the hypothesis that velocity characteristics are related to channel bedform types, ANOVA and ANCOVA tests were performed for the average velocity and coefficient of variation of point velocity data. Results indicate that high frequency velocity variations correlate to some degree with both channel characteristics and discharge. Velocity became more variable as stage increased, particularly at low‐gradient reaches with less variable bed roughness. Velocity profiles suggest that locations immediately downstream from bed‐steps are dominated by wake turbulence from mid‐profile shear layers. Locations immediately upstream from steps, at step lips, and in runs are dominated by bed‐generated turbulence. Adverse pressure gradients upstream and downstream from steps may be enhancing turbulence generation, whereas favourable pressure gradients at steps are suppressing turbulence. The bed‐generated turbulence and skin friction of runs appear to be less effective energy dissipators than the wake‐generated turbulence and form drag of step–pool bedforms. Copyright © 2000 John Wiley & Sons, Ltd.     

Turbulence structures in non-uniform flows

This study investigates turbulence structures in steady and non-uniform flows. Equations of Reynolds shear stress and turbulent velocity fluctuations are derived and their physical interpretations are explained. The theoretical results show that, different from previous studies, the variation of water surface can generate the wall-normal velocity, resulting in deviations of Reynolds shear stress and turbulence intensities from those in uniform flows. A self-similarity relationship is found between the Reynolds shear stress and turbulence intensities in non-uniform flows. The existence of self-similarity indicates that the effect of non-uniformity does not influence the mixing length. An empirical equation has been proposed to express the relationship based on experimental data available in the literature. Good agreement is achieved between the measured and predicted turbulence intensities by applying the self-similarity relationship.     

Numerical simulation of three‐dimensional flow hydraulics in a braided channel

Results are presented from a numerical simulation of three‐dimensional flow hydraulics around a mid‐channel bar carried out using the FLUENT/UNS computational fluid dynamics (CFD) software package. FLUENT/UNS solves the three‐dimensional Reynolds‐averaged form of the Navier–Stokes equations. Turbulence closure is achieved using a RNG k–ϵ model. Simulated flow velocities are compared with measured two‐dimensional velocities (downstream and cross‐stream) obtained using an electromagnetic current meter (ECM). The results of the simulation are qualitatively consistent with the flow structures observed in the field. Quantitative comparison of the simulated and measured velocity magnitudes indicates a strong positive correlation between the two (r=0·88) and a mean difference of 0·09 m s⁻¹. Deviations between simulated and measured velocities may be identified that are both random and systematic. The former may reflect a number of factors including subgrid‐scale natural spatial variability in flow velocities associated with local bed structures and measurement uncertainty resulting from problems of ECM orientation. Model mesh configuration, roughness parameterization and inlet boundary condition uncertainty may each contribute to systematic differences between simulated and measured flow velocities. These results illustrate the potential for using CFD software to simulate flow hydraulics in natural channels with complex configurations. They also highlight the need for detailed spatially distributed datasets of three‐dimensional flow variables to establish the accuracy and applicability of CFD software. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

金银岛岩土台阵原位剪切波速剖面评估

土层的剪切波速是描述土动力学特性的重要参数之一。利用金银岛岩土台阵记录的8次浅源地方震的弱震动数据,使用解卷积的地震干涉测量法识别的剪切波走时,评估了该台阵两个水平方向的原位剪切波速剖面。结果表明:在44.2m深度以上,估计与实测的平均剪切波速剖面基本一致,而在44.2m到103.6m深度范围前者大于后者;本研究估计的平均剪切波速剖面比MEHTA等（2007）估计的平均剪切波速剖面更接近实测结果,在44.2m到103.6m深度范围,本研究估计的平均剪切波速与MEHTA等（2007）估计的平均剪切波速相近,二者均大于实测的平均剪切波速。     

Influence of crack distribution of rocks on P‐wave velocity anisotropy – a laboratory and field scale study‡

The purpose of this paper is the comparison of P‐wave velocity and velocity anisotropy, measured at different scales under laboratory and field conditions. A shallow seismic refraction survey with shot/receiver spacing of up to 10 m was carried out on a flat outcrop of lhertzolite in the southern part of the Balmuccia massif. Oriented rock samples were also obtained from the locality. The particular advantage of the laboratory method used is the possibility of measuring velocity in any direction under controlled conditions. Laboratory tests were made on spherical peridotite samples, 50 mm in diameter, by ultrasonic velocity measurements in 132 directions (meridian and parallel networks) under confining stress ranging from atmospheric to 400 MPa. The mean P‐wave velocity of the field and laboratory data differed by between 20–30%. In addition, P‐wave velocity anisotropy of 25% was detected in the field data. Whereas the anisotropy in the laboratory samples in the same orientation as the field surveys was less than 2%. This observed scaling factor is related to the different sampling sizes and the difference in frequencies of applied elastic waves. With an ultrasonic wavelength of 10 mm, laboratory samples represent a continuum. The field velocities and velocity anisotropy reflect the presence of cracks, which the laboratory rock samples do not contain. Three sub‐vertical fracture sets with differing strikes were observed in the field outcrop. Estimates of fracture stiffness from the velocity anisotropy data are consistent with other published values. These results highlight the difficulty of using laboratory velocity estimates to interpret field data.     

A supplementary approach for estimating reaeration rate coefficients

Different commonly used predictive equations for the reaeration rate coefficient (K₂) have been evaluated using 231 data sets obtained from the literature and 576 data sets measured at different reaches of the River Kali in western Uttar Pradesh, India. The data sets include stream/channel velocity, bed slope, flow depth, cross‐sectional area and reaeration rate coefficient (K₂), obtained from the literature and generated during the field survey of River Kali, and were used to test the applicability of the predictive equations. The K₂ values computed from the predictive equations have been compared with the corresponding K₂ values measured in streams/channels. The performance of the predictive equations has been evaluated using different error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and coefficient of determination (r²). The results show that the reaeration rate equation developed by Parkhurst and Pomeroy yielded the best agreement, with the values of SE, NME, MME and r² as 33·387, 4·62, 3·58 and 0·95, respectively, for literature data sets (case 1) and 37·567, 3·57, 2·6 and 0·95, respectively, for all the data sets (literature data sets and River Kali data sets) (case 2). Further, to minimize error estimates and improve correlation between measured and computed reaeration rate coefficients, supplementary predictive equations have been developed based on Froude number criteria and a least‐squares algorithm. The supplementary predictive equations have been verified using different error estimates and by comparing measured and computed reaeration rate coefficients for data sets not used in the development of the equations. Copyright © 2003 John Wiley & Sons, Ltd.     

Two-phase modeling of sheet-flow beneath waves and its dependence on grain size and streaming

We study erosion depth and sediment fluxes for wave-induced sheet-flow, and their dependency on grain size and streaming. Hereto, we adopt a continuous two-phase model, applied before to simulate sheet-flow of medium and coarse sized sand. To make the model applicable to a wider range of sizes including fine sand, it appears necessary to adapt the turbulence closure of the model. With an adapted formulation for grain–carrier flow turbulence interaction, good reproductions of measured erosion depth of fine, medium and coarse sized sand beds are obtained. Also concentration and velocity profiles at various phases of the wave are reproduced well by the model. Comparison of sediment flux profiles from simulations for horizontally uniform oscillatory flow as in flow tunnels and for horizontally non-uniform flow as under free surface waves, shows that especially for fine sand onshore fluxes inside the sheet-flow layer increase under influence of progressive wave effects. This includes both the current-related and the wave-related contribution to the period-averaged sheet-flow sediment flux. The simulation results are consistent with trends for fine and medium sized sediment flux profiles observed from tunnel and flume experiments. This study shows that the present two-phase model is a valuable instrument for further study and parameterization of sheet-flow layer processes.     

Flow analysis in a channel with flexible vegetation using double-averaging method

The paper addresses the problem of the resistance due to vegetation in an open channel flow, characterized by partially and fully submerged vegetation formed by colonies of bushes. The flow is characterized by significant spatial variations of velocity between vertical profiles that make the traditional approach based on time averaging of turbulent fluctuations inconvenient. A more useful procedure, based on time and spatial averaging (Double-Averaging Method) is applied for the flow field analysis and characterization. The vertical distribution of mean velocity and turbulent stresses at different spatial locations has been measured with a 3D Acoustic Doppler Velocimeter (ADV) for two different vegetation densities where fully submerged real bushes (salix pentandra) have been used. Velocity measurements were completed together with the measurements of drag exerted on the flow by bushes at different flow depths. The analysis of velocity measurements allows depicting the fundamental characteristics of both the mean flow field and turbulence. The experimental data show that the contribution of form-induced stresses to the momentum balance cannot be neglected. The mean velocity profiles and the spatially averaged turbulent intensity profiles allow inferring that the vegetation density is a driving parameter for the development of a mixing layer at the canopy top in the case of submerged vegetation. Moreover, the net upward turbulent momentum flux, evaluated with the methodology proposed by Lu and Willmarth (1973), appears to be damped for increased vegetation density; this finding can rationally explain the reduction of the suspended sediment transport capacity typically observed in free surface flows over a vegetated bed.     

An experimental investigation of the effects of thawed soil depth on rill flow velocity

Water flow velocity is an important hydraulic variable in hydrological and soil erosion models, and is greatly affected by freezing and thawing of the surface soil layer in cold high-altitude regions. The accurate measurement of rill flow velocity when impacted by the thawing process is critical to simulate runoff and sediment transport processes. In this study, an electrolyte tracer modelling method was used to measure rill flow velocity along a meadow soil slope at different thaw depths under simulated rainfall. Rill flow velocity was measured using four thawed soil depths (0, 1, 2 and 10 cm), four slope gradients (5°, 10°, 15° and 20°) and four rainfall intensities (30, 60, 90 and 120 mm·h⁻¹). The results showed that the increase in thawed soil depth caused a decrease in rill flow velocity, whereby the rate of this decrease was also diminishing. Whilst the rill flow velocity was positively correlated with slope gradient and rainfall intensity, the response of rill flow velocity to these influencing factors varied with thawed soil depth. The mechanism by which thawed soil depth influenced rill flow velocity was attributed to the consumption of runoff energy, slope surface roughness, and the headcut effect. Rill flow velocity was modelled by thawed soil depth, slope gradient and rainfall intensity using an empirical function. This function predicted values that were in good agreement with the measured data. These results provide the foundation for a better understanding of the effect of thawed soil depth on slope hydrology, erosion and the parameterization scheme for hydrological and soil erosion models.     

Magnitude of deviatoric terms in vertically averaged flow equations

The depth‐integrated momentum and kinetic energy equations contain velocity correlation terms that involve products of local deviations in velocity components about depth‐averaged values. Based on velocity data obtained from North Boulder Creek, Colorado, a simple scaling analysis suggests that certain of these terms, which normally can be neglected in the case of smooth channels, can be significant parts of the momentum and energy balances in steep, rough channels owing to the occurrence of non‐logarithmic velocity profiles. A linearized version of the kinetic energy equation suggests that, for flow accelerations over small‐amplitude bed forms, the energy of the mean motion is spatially partitioned between a form involving the depth‐averaged velocity and a form involving the deviatoric part of the velocity profile; this partitioning is associated with spatial variations in the uniformity of the vertical profile of the streamwise velocity. These points are consistent with published flume measurements involving flow over sand‐roughened dunes, and with published field measurements of flow over a gravel bar. Copyright © 2000 John Wiley & Sons, Ltd.