Low Relative Depth Research Articles

Experimental Investigation Of Open Channel Flow Around A Hemisphere At Different Relative Depths Using 3D-PTV

In regulated rivers and small streams, the presence of large roughness elements like boulders and concrete structures significantly impacts the local flow field and creates complex hydraulic conditions important for aquatic habitats. This study focuses on investigating and analyzing the complex three-dimensional flow field around an idealized stone (represented as a hemisphere) to understand how the flow field changes for different relative depths i.e. water depth relative to boulder height, and flow rates. Time-resolved 3D Particle Tracking Velocimetry was employed in laboratory experiments conducted in an open-channel flume, to mimic varying river conditions and their impact on flow characteristics. Results reveal that the relative depth significantly influences the flow structure behind the hemisphere, impacting recirculation zones and wake characteristics. The flow field behind the hemisphere was found to be more sensitive to changes in relative depth than bulk velocity. The study also highlights the larger regions of lower streamwise velocity that occurred downstream of the hemisphere caused by the lower submergences combined with a higher magnitude of the downward vertical velocity. Furthermore, this study demonstrates the capability of the measurement technique and the time-resolved 3D Particle Tracking Velocimetry system used to effectively capture the complex flow dynamics around the boulder. This approach allowed for detailed visualization and quantification of flow parameters such as streamwise and vertical velocities within the wake region, which are important factors for aquatic habitats. Understanding the underlying flow dynamics around an idealized stone at low relative depths could yield insights into ecohydraulic engineering and ecological restoration in shallow streams. This can contribute to advancing our understanding of riverine flow dynamics and their ecological implications.

Влияние размера воздушной области на порог тепловой конвекции в системе «воздух–тепловыделяющая пористая среда–воздух»

The problem concerning convective stability of the motionless air state in a layered air–heat-generating porous medium–air system under the gravitational field is simulated numerically in the paper. We take into consideration the heat source strength dependent on solid volume fraction in the porous sublayer. Marginal stability curves are presented at different values of the relative depth of the air sublayer. It has been shown that the onset value of internal convection decreases with increasing this depth. Besides, the convective roller flow is of a large-scale character at low relative depths, but it can be localized within the upper air sublayer at high enough depths. A comparison of the threshold internal Rayleigh-Darcy numbers at equal ratios of the air to porous depths has shown that the enhancement of convection (or lowering its threshold) is more effective in the three-layered air–heat-generating porous medium–air system as compared to that of the two-layered air–heat-generating porous medium system.

Three-Dimensional Investigation of Hydraulic Properties of Vertical Drop in the Presence of Step and Grid Dissipators

In irrigation and drainage channels, vertical drops are generally used to transfer water from a higher elevation to a lower level. Downstream of these structures, measures are taken to prevent the destruction of the channel bed by the flow and reduce its destructive kinetic energy. In this study, the effect of use steps and grid dissipators on hydraulic characteristics regarding flow pattern, relative downstream depth, relative pool depth, and energy dissipation of a vertical drop was investigated by numerical simulation following the symmetry law. Two relative step heights and two grid dissipator cell sizes were used. The hydraulic model describes fully coupled three-dimensional flow with axial symmetry. For the simulation, critical depths ranging from 0.24 to 0.5 were considered. Values of low relative depth obtained from the numerical results are in satisfactory agreement with the laboratory data. The simultaneous use of step and grid dissipators increases the relative energy dissipation compared to a simple vertical drop and a vertical drop equipped with steps. By using the grid dissipators and the steps downstream of the vertical drop, the relative pool depth increases. Changing the pore size of the grid dissipators does not affect the relative depth of the pool. The simultaneous use of steps and grid dissipators reduces the downstream Froude number of the vertical drop from 3.83–5.20 to 1.46–2.00.

Microbial Geochemistry of the Acidic Saline Pit Lake of Brunita Mine (La Unión, SE Spain)

We present the first study of a unique acidic lake formed in the Brunita open pit (La Union mines, Cartagena, SE Spain). This pit lake exhibits chemical characteristics typical of AMD, such as low pH (pH 2.2–5.0) and high iron content (500–6400 mg/L total Fe). It also has some of the highest sulfate concentrations reported to date in pit lakes (26,000–38,400 mg/L $${\text{SO}}_{ 4}^{ 2- }$$ ) and transition metals like Mn (up to 2000 mg/L), Zn (500 mg/L), or Cu (250 mg/L). In addition, we found abnormally high concentrations of salt-forming ions (e.g. 5500 mg/L Mg, 750–1300 mg/L Cl, and 300–630 mg/L Na). The resulting high salinity (58‰) at the bottom creates a meromictic lake despite the lake’s low relative depth (9%), with an anoxic, reducing monimolimnion isolated from the oxygenated mixolimnion. In the monimolimnion, we observed decreased metal concentrations (e.g. Cu, Zn, Cd, Cr, Pb, Th). We hypothesize that these metals are being removed by interaction with biogenic H2S and subsequent precipitation as metal sulfides. Scanning electron microscopy shows sub-micron, spherical particles of ZnS in close association with cocci and rod-like bacteria. Analysis of the microbial community composition through 16S rRNA gene amplicon sequencing revealed different genera of sulfate-reducing bacteria (SRB) in the monimolimnion, including Desulfobacca, Desulfomonile, Desulfurispora, and Desulfosporosinus. Their apparent ability to reduce sulfate and selectively precipitate potentially toxic metals, and their resistance to this lake’s extreme geochemical conditions, makes these bacteria of great interest for biotechnological applications (e.g. bioremediation and biomining).

Ground state of the Frenkel–Kontorova model with a globally deformable substrate potential

The classical ground state of the Frenkel–Kontorova model is investigated for the case of a globally deformable substrate potential, whose amplitude is a function of the position of all particles. This system serves as an idealised description of a one-dimensional crystal of trapped ions in an optical cavity, where the deformable potential originates from the cavity back action due to the dynamical Stark shift. In the limit of a low relative substrate depth, a sine-Gordon field theory is obtained with coefficients that are functionals of the chain configuration. It is shown that the back action modifies the phase diagram, where the order and scaling of the phase-transition can be controlled by the cavity parameters. Due to the back action, the kinks, which constitute topological soliton solutions in the sine-Gordon model, are shown to exhibit two stable profiles with qualitatively different properties. The choice between the stable configurations is made collectively, all kinks taking either one form or the other.

Depth-averaged modelling of vegetated meandering compound channel

Advances of computing capabilities have increased the interest of using computational fluid dynamics to simulate more complex flow structures in open channel. A two-dimensional model, Telemac-2D was used to simulate flows with the presence of vegetation on the floodplain along the main channel inside a meandering compound channel. The simulation was done for two different relative depth for both non- and vegetated floodplain cases. The measured and simulated depth-averaged velocities were compared at the bend apex cross-section of the meandering compound channel for validation. Vegetation reduced the magnitude of the overbank flows and directed most of the overbank into the direction of the main channel. The effects of the vegetation on the overbank flows are more significant at low relative depth. The model shows good simulating capabilities of the depth-averaged velocities for the vegetated meandering compound channel and the numerical results also capable to generally capture the complex interaction between the overbank and inbank flows due to the presence of vegetation.

CO2-rich fluid inclusions in mantle xenoliths from Barombi-Mbo and Nyos maars (Cameroon volcanic line, central Africa): Upper mantle equilibria and history of magma ascension

A detailed study of fluid inclusions hosted within minerals of mantle xenoliths from the Barombi-Mbo (BM) and Nyos maars provides information on the trapping conditions of fluids and subsequent upper mantle equilibria and the history of the host en route to the surface. These porphyroclastic to protogranular spinel lherzolites and their fluid inclusions were investigated using petrography, microprobe, microthermometry and Raman Microspectroscopy. They are mostly composed of olivine (Fo93-88), orthopyroxene (En91-88Fs11-8Wo2.2-0.8), Cr-diopside, aluminous spinel (Cr#: 0.32–0.08) and occasional accessory pargasite and labradorite. Thermobarometric calculations based on the mineral chemistry of the BM xenoliths indicate temperatures of 1205 to 800 °C at pressures of 23 to 14 kbar while the results on Nyos xenoliths give temperatures of 1134 to 1044 °C at pressures of 12 to 9 kbar consistent with mantle depths of 75–42 km to BM and 36-27 km to Nyos. Olivine and pyroxene crystals contain abundant CO2-rich inclusions (48-1 μm). In Nyos, Raman spectra allow the detection of CO2 and unknown species containing NH2 while CO2 and traces of nahcolite (NaHCO3) were detected in fluid inclusions in the Barombi-Mbo mantle xenoliths. The melting point (Tm) of CO2 varies from −56.6 to −58.0 °C and from −56.8 to −63.0 °C respectively in BM and Nyos xenoliths. 95% of inclusions homogenized in the liquid phase (ThL; L + V →L) and 5% in the vapor phase (ThV; L + V →V) at temperatures ranging from +31.1 to −48.1 °C in BM xenoliths, and from +31.1 to −38.1 °C in Nyos xenoliths. Densities of CO2 inclusions in minerals range from 1.1 to 0.35 g/cm3 at Nyos, and from 1.15 to 0.2 g/cm3 at BM. The high fluid pressures deduced and the corresponding depths are 11 to 8 kbar (33-24 km) at Nyos and 12 to 10 kbar (36-30 km) at BM. Taking into account the post-trapping stretch, the corrected inclusions densities and corresponding pressures and depths set the minimum xenoliths entrainment depths to 50 km beneath BM and 36 km under Nyos maars. Fluid inclusion pressures also reveal that the Moho and Conrad discontinuities lie at depths of 24 and 15 km and of 30 and 13.5 km, respectively at Nyos and BM. The estimated Moho depths are consistent with the geophysical observations along the CVL. Low densities and relative depths probably indicate short magma stops in intermediate magmatic chambers. Before eruption, the last short magma storage and fluid mixing occurred at a depth of less than 1.8 km at BM and 3 km at Nyos.

Analysing breast tissue composition with MRI using currently available short, simple sequences

To determine the most robust commonly available magnetic resonance imaging (MRI) sequence to quantify breast tissue composition at 1.5 T. Two-dimensional (2D) T1-weighted, Dixon fat, Dixon water and SPAIR images were obtained from five participants and a breast phantom using a 1.5 T Siemens Aera MRI system. Manual segmentation of the breasts was performed, and an in-house computer program was used to generate signal intensity histograms. Relative trough depth and relative peak separation were used to determine the robustness of the images for quantifying the two breast tissues. Total breast volumes and percentage breast densities calculated using the four sequences were compared. Dixon fat histograms had consistently low relative trough depth and relative peak separation compared to those obtained using other sequences. There was no significant difference in total breast volumes and percentage breast densities of the participants or breast phantom using Dixon fat and 2D T1-weighted histograms. Dixon water and SPAIR histograms were not suitable for quantifying breast tissue composition. Dixon fat images are the most robust for the quantification of breast tissue composition using a signal intensity histogram.

정상류 수몰 사각실린더에 작용하는 항력 특성에 관한 수치모의 연구

본 연구에서는 수치모의를 통해서 월류 흐름이 존재하는 수몰 사각 실린더의 항력 특성에 대하여 분석하였다. 모의의 신뢰성을 검토하기 위하여 실험자료와 비교하였으며 실험에서 측정하기 어려운 실린더 접촉면의 압력에 대한 분석을 통해서 상대 수심에 따른 항력의 특성을 분석하였다. 3차원 동수역학 모형을 이용한 수몰 사각 실린더의 항력 계산 결과는 실험자료의 상대 수심의 변화에 따른 항력계수의 변화를 유사하게 모의하고 있음을 확인할 수 있었다. 수치모의 결과 분석에 의하면 수몰 사각 실린더에 작용하는 항력은 대부분 압력이며 상대 수심이 증가함에 따라 전단력의 비중은 감소하였다. 실린더 접촉면의 압력계수 분석 결과에 의하면 상대 수심이 낮은 경우에는 전면부에 높은 압력계수가 형성되고 후면부에 낮은 압력계수가 형성되어 결과적으로 높은 항력계수가 나타남을 확인하였다. 상대수심이 증가하면 전면부의 압력계수는 감소하고 후면부의 압력계수는 증가하여 2차원 흐름 내의 사각 실린더와 유사한 양상을 나타낸다. 정수압 영향 분석에 의하면 전면부와 후면부의 수위 차에 의한 정수압은 항력에 미치는 영향이 제한적이며 사각 실린더에 의해 형성되는 국부적인 수위와 함께 3차원적인 흐름에 의해 형성되는 동수압의 영향이 크다는 것을 확인하였다. In this study, the drag forces on a submerged square cylinder were analyzed using a three dimensional hydrodynamic model. The numerical results were compared with the experimental results to check the reliability of the numerical simulations, and the characteristics of the drag forces with the relative depths were analyzed by analyzing the pressure acting on the cylinder surface, which are normally difficult to measure experimentally. The numerical results showed that the drag forces acting on a submerged square cylinder originate mainly from the pressure forces, and component of the shear forces decreased with increasing relative depth. The pressure coefficient distributions showed that in the case of a low relative depth, a relatively high pressure was formed in the front of a cylinder, and a relatively low pressure was formed in the rear, which gives a high drag coefficient. In a high relative depth, the pressure in the front decreased and pressure in the rear increased, which is a similar phenomenon to that normally observed in two dimensional square cylinder flow. The effect of the static pressure was analyzed and the surface elevation difference between the front and rear zone of a cylinder has a limited effect on the drag forces. Finally, the numerical results showed that the drag forces acting on a submerged square are dominated by the dynamic pressure formed by three dimensional flow and the distribution of local surface elevation.

Morphological characterization of eighteen lakes of the north and middle coast of Rio Grande do Sul, Brazil

AIMS: The present study aimed at a morphological characterization of 18 lakes of the municipalities of Cidreira, Balneário Pinhal and Palmares do Sul, situated in the northern and middle coastal plain of Rio Grande do Sul, Brazil. METHODS: The morphometric survey was conducted in the summer of 2011/2012, based on echo sounder coupled with GPS and the application of remote sensing and GIS procedures. The morphometric parameters used for the characterization were: surface area, perimeter, perimeter development, volume, relative fetch, maximum depth, average depth, relative depth, median depth of volume, length and width. The statistical interpretation included Test of Normality, Coefficient of Variation, Correlation and Regression Analysis, Cluster Analysis, Discriminant Analysis and Principal Component Analysis. RESULTS: Eighteen lakes were described and five of them are presented by aerial photo and bathymetric map. They represent the proposed morphological lake types. The calculation of the coefficient of variation revealed larger amplitudes of parameters related to lake size than to depth. The application and interpretation of cluster analysis, confirmed by discriminant analysis, distinguished those lakes in five morphological groups, which differ mainly by size and subsequently by depth. The Principal Component Analysis identified the first component with positively charged variables of size and negatively charged relative depth, and a second component with positive charge of maximum and average depths. CONCLUSIONS: The low relative depths and the exposure to constant northeastern winds reduce the transparency of the lakes. Consequently, they are light limited by suspension of inorganic and organic matter. A property that limits the application of trophic state indices. The high dynamic of the water bodies produces an oxygenated sediment surface that facilitates the settlement by aerobic organisms all over the bottom area. The shallowness and the low median depths of volume are limiting factors for sustainable water supply management. The morphological characteristics of the coastal lakes make very difficult an accurate ecological assessment based on usual trophic state criterions and a sustainable water resource management using general guidelines.

Morphometric features of a tropical flood plain lake (Hoyo swamp Los Bagres, Colombia)

In this paper the morphometric characteristics of Hoyo swamp’s in Los Bagres (Colombia) and the theoretical predictions made from these characteristics are presented. The swamp was characterized as a shallow system with a large area about the size of the water column, the shape of a convex conical depression without turning points in V shape, with a broad line development coast generating a high influence on the watershed ecosystem. It has a high value of the fetch and the dynamic radius and a low relative depth, factors which together foster wide track action for the wind, so that trend is expected to dip to the thermal stability of the water column (polimixis). From the standpoint of trophic state may be considered as mesotrophic floodplain, as it presents low values of transparency and light attenuation coefficient. It was found that it presents morphometric differences regarding water system which is a part, so it follows that each body within the complex has its own characteristics, which are not defined in the study of the central body.

Parâmetros morfométricos da Lagoa Central (Lagoa Santa, Estado de Minas Gerais): comparação de duas metodologias.

The goal of this study was to verify the utility and accuracy of two tools to obtain a bathymetric chart for Lagoa Central (Lagoa Santa, State of Minas Gerais, Brazil) and also to assess the morphometric parameters of the lake and their implications in the ecology of this system. The tested tools were the Biosonics DT-X (Biosonics Inc.) echosounder and the SonarLite (Ohmnex Ltda) bathymeter, both coupled to a Differential Global Positioning System (DGPS) to obtain the geographic coordinates associated with the depth in each point. Lagoa Central is a small, shallow (Zmax < 7.5 m), with low relative depth values (Zr = 0.5%) and concave. This makes the water body less prone to thermal stratification and more susceptible to eutrophication. Both investigated equipments demonstrated to be suitable for the survey, user-friendly, low-cost and with sub-metric accuracy.

Theoretical development on the effects of changing flow hydraulics on incipient bed load motion

Several decades of flume and field measurements have indicated that in rough turbulent flows the critical Shields stress increases with increasing slope and associated decreasing relative depth. This result contradicts the usual consideration of a decreased critical Shields value on very steep slopes because of increased gravitational effects. However, recent studies have demonstrated that these experimental results could be reproduced with a force balance model if the classical logarithmic velocity profile was replaced with a velocity profile that was more compatible with available velocity measurements over gravel beds. These measurements indicate the existence of a roughness layer that is a zone of almost constant velocity close to the bed, whose properties (mean velocity and turbulence) depended on the flow's relative depth. Unfortunately, velocity profile measurements for low relative depth associated with steep slopes are scarce, and it is still difficult to include such flow properties in a force balance model. Flow resistance data (on the basis of depth average velocity measurements) are very common and cover a wide range of slopes and relative depths. In this paper these data are used to fit a velocity profile including a roughness layer. When used in a force balance model for incipient motion, it adequately reproduced a data set composed of 270 critical Shields values measured in a flume with near‐uniform sediments. The relevance of this research to field problems is discussed using a data set composed of 92 critical Shields stresses obtained from field measurements. Finally, a model is proposed for field applications taking into account the slope effect.

Caracterização morfométrica e suas implicações na limnologia de lagoas do Pantanal Norte

The objective of this work is to describe the morphological characteristics of seven Northern Pantanal lakes and discuss their implications on the limnology of these environments. The following morphological parameters were used: area; volume; maximum, mean and relative depths; perimeter; volume and perimeter development indices; maximum length and width. Generally, most lakes are shallow, with low relative depths, suggesting little thermal stratification, as they are more susceptible to mixing of the water column and suspended sediments by wind action. Most lakes have regular banks (few irregularities) and have a concave shape, and thus are less subject to erosion processes. Temporal variations in the morphometry of these lakes are related to the hydrodynamic and limnological patterns of these systems.

Discharge estimation for equatorial natural rivers with overbank flow

The estimation of discharge capacity in river channels is complicated by variations in geometry and boundary roughness. Estimating flood flows is particularly difficult because of compound cross‐sectional geometries and because of the difficulties of flow gauging. Results are presented of a field study including the stage‐discharge relationships and surface roughness in term of the Darcy‐Weisbach friction factor, fa for several frequently flooded equatorial natural rivers. Equations are presented giving the apparent shear force acting on the vertical interface between the main channel and floodplain. The resulted apparent friction factor, fa is shown to increase rapidly for low relative depth. A method for predicting the discharge of overbank flow of natural rivers is then presented, by means of a composite friction, fc , which represents the actual resistance to flow due to the averaged boundary shear force and the apparent shear force. Equations are also presented giving the composite friction factor from easily calculated parameters for overbank flow of natural rivers. The results obtained using the methods proposed show that a significant improvement has been achieved compare to the discharge obtained using traditional methods, with an averaged error of 2.7%.

Avaliação da vulnerabilidade ambiental de reservatórios à eutrofização

Esse trabalho apresenta uma ferramenta de análise da vulnerabilidade de reservatórios à eutrofização, visando subsidiar ações de controle e remediação desse processo. Foram analisadas três subbacias de açudes - Araras, Edson Queiroz e Jaibaras, da bacia do Acaraú, CE, Brasil. A análise multiatributo usada na definição de indicadores ambientais de vulnerabilidade dos açudes à eutrofização, considerou sua sensibilidade e fatores de pressão nas suas sub-bacias que acarretam o transporte de sedimentos e nutrientes para os reservatórios. Foi utilizado um Sistema de Informações Geográficas (SIG) com a ferramenta álgebra de mapas para manipular dados de uso e ocupação do solo, declividade do terreno e erodibilidade do solo. Foi identificada alta vulnerabilidade à eutrofização nos três açudes pelas susceptibilidades à erosão, alta carga poluidora principalmente pela pecuária extensiva na região e baixa profundidade relativa dos reservatórios.

Modification of composite hardness models to incorporate indentation size effects in thin films

The indentation hardness of copper films of thickness 25 to 1400 nm on oxidized silicon substrates is determined by nanoindentation. The load-displacement curves are analysed using the Oliver and Pharr method. An indentation size effect is observed at low relative indentation depths for the copper films. Composite hardness models are applied to the data without an indentation size effect and the Korsunksy and Puchi–Cabrera models are found to give very good fits to this data. The Nix and Gao mechanism based strain gradient plasticity (MSG) model is used to account for the indentation size effect. An attempt is made to modify the existing composite hardness models using the MSG model to incorporate indentation size effect. By modification of both the Korsunsky and Puchi-Cabrera models a good fit to the entire range of data is obtained.

Measurement and analysis of alluvial bed roughness

Techniques for measurement and analysis of the physical roughness of alluvial beds are introduced and evaluated. Precise digital elevation models (DEMs) of bed surfaces are developed using laser-scanning technology. Hydraulic roughness is represented by the standard deviation of local bed surface heights, which can be measured by physical profiling, analysis of DEMs or by a simple sand-spreading technique. Results from grain size analyses are compared with these different surface roughness determination techniques. At low relative depths the blocking of flow area by roughness elements is shown to be related to the standard deviation of local bed surface heights. A directional standard deviation is suggested for beds with structural polarization and an inclination index is introduced to identify bed imbrication.

Application and validation of numerical codes in the prediction of compound channel flows

This paper attempts to compare the accuracy of a two-dimensional (2D) depth-averaged code (TELEMAC-2D) and a three-dimensional (3D) code (SSIIM) in the numerical simulation of free surface flows. Assessment was conducted using benchmark data collected from a meandering compound channel at the UK EPSRC Flood Channel Facility. For both codes a standard k–ε turbulence model was employed to simulate the flow field. Assessment of both codes was based on the prediction of depth-averaged velocity traverses around a meander bend, flow features inferred by velocity vectors in the horizontal plane, and water surface elevations for both low and high relative flow depths. In addition, predictions with the 3D code of velocities parallel and perpendicular to the main channel direction are compared with those observed in the experimental programme. Both codes predict the lateral distribution of depth-averaged velocity in the main channel with reasonable accuracy at low relative flow depth, with the 3D code predicting better than the 2D code (maximum percentage errors in depth-averaged velocity are 16% and 22% respectively). At a higher flow depth no extra accuracy in the prediction of depth-averaged velocity is to be gained from the 3D model than from the 2D model, although the 3D model can predict the correct location and direction of secondary currents. For all flow conditions better accuracy was achieved for both codes at the apex section where the mean flow direction is more aligned with the local main channel direction. An accuracy of within 20% can be expected for predictions of depth-averaged velocity magnitude from a 3D model using a standard isotropic representation of turbulence.

Application and validation of numerical codes in the prediction of compound channel flows

This paper attempts to compare the accuracy of a two-dimensional (2D) depth-averaged code (TELEMAC-2D) and a three-dimensional (3D) code (SSIIM) in the numerical simulation of free surface flows. Assessment was conducted using benchmark data collected from a meandering compound channel at the UK EPSRC Flood Channel Facility. For both codes a standard k–ε turbulence model was employed to simulate the flow field. Assessment of both codes was based on the prediction of depth-averaged velocity traverses around a meander bend, flow features inferred by velocity vectors in the horizontal plane, and water surface elevations for both low and high relative flow depths. In addition, predictions with the 3D code of velocities parallel and perpendicular to the main channel direction are compared with those observed in the experimental programme. Both codes predict the lateral distribution of depth-averaged velocity in the main channel with reasonable accuracy at low relative flow depth, with the 3D code predicting better than the 2D code (maximum percentage errors in depth-averaged velocity are 16% and 22% respectively). At a higher flow depth no extra accuracy in the prediction of depth-averaged velocity is to be gained from the 3D model than from the 2D model, although the 3D model can predict the correct location and direction of secondary currents. For all flow conditions better accuracy was achieved for both codes at the apex section where the mean flow direction is more aligned with the local main channel direction. An accuracy of within 20% can be expected for predictions of depth-averaged velocity magnitude from a 3D model using a standard isotropic representation of turbulence.