The applicability of the formulas developed on the Manning-Strickler and Keulegan equations for the calculation of flow resistance for shallow flow in gravel-bed streams - a case study

Applying the mixing layer analogy for flow resistance evaluation in gravel-bed streams

Previous studies about flow resistance in gravel-bed streams mostly use the log-law form and establish the relationship between the friction factor and the relative flow depth based on field data. However, most established relations do not perform very well when applied to shallow water zones with relatively large roughness. In order to clarify the hydraulic variables defined in the single cross-section, and find the reasons that reflect the instability of flow and uneven boundaries of the river, the concepts of hydraulic variables, such as hydraulic radius, are re-defined in the river reach in the paper. The form drag in the river reach is solved based on a reach-averaged flow resistance model which is developed by force balance analyzing of the water body in the given river reach. The reach-averaged form drag relation is then formulated by incorporating the Einstein flow parameter and a newly derived roughness parameter defined in the river reach. A large number of field data (12 datasets, 780 field measurements) is applied to calibrate and validate the form drag relation. The relation is found to give better agreement with the field data in predicting flow velocity in comparison with existing flow resistance equations. A unique feature of the reach-averaged resistance relation is that it can apply to both deep and shallow water zones, which can be treated as a bridge to link the flow hydraulics in plain rivers and mountain streams.

Flow resistance in a natural stream is caused by complex factors, such as the grains on the bed, vegetation, and bed-form, reach profile. Flow resistance in a generally stable gravel bed stream is due to protrudent grains from bed. Therefore, the flow resistance can be calculated by equivalent roughness in gravel bed stream, but estimation of equivalent roughness is difficult because nonuniform size and irregular arrangement of distributed grain on natural stream bed. In previous study, equivalent roughness is empirically estimated using characteristic grain size. However, application of empirical equation have uncertainty in stream that stream bed characteristic differs. In this study, we developed a model using an analytical method considering grain diameter distribution characteristics of grains on the bed and also taking into account flow resistance acting on each grain. Also, the model consider the protrusion height of grain.

Effects of experimental removal of woody debris on the channel morphology of a forest, gravel-bed stream

A data set of 2890 field measurements was used to test the ability of several conventional flow resistance equations to predict mean flow velocity in gravel bed rivers when used with no calibration. The tests were performed using both flow depth and discharge as input since discharge may be a more reliable measure of flow conditions in shallow flows. Generally better predictions are obtained when using flow discharge as input. The results indicate that the Manning‐Strickler and the Keulegan equations show considerable disagreement with observed flow velocities for flow depths smaller than 10 times the characteristic grain diameter. Most equations show some systematic deviation for small relative flow depth. The use of new definitions for dimensionless variables in terms of nondimensional hydraulic geometry equations allows the development of a new flow resistance equation. The best overall performance is obtained by the Ferguson approach, which combines two power law flow resistance equations that are different for deep and shallow flows. To use this approach with flow discharge as input, a logarithmic matching equation in terms of the new dimensionless variables is proposed. For the domains of intermediate and large‐scale roughness, the field data indicate a considerable increase in flow resistance as compared with the domain of small‐scale roughness. The Ferguson approach is used to discuss the importance of flow resistance partitioning for bed load transport calculations at flow conditions with intermediate‐ and large‐scale roughness in natural gravel, cobble, and boulder bed streams.

Stream Restorat Approaches, Anal Geophysical Mon Copyright 2011 b 10.1029/2010GM Bank vegetation substantially influences flow resistance, velocity, shear stress distributions, and geomorphic stability in many natural river settings. We analyze field data from gravel bed streams with typed bank vegetation characteristics and employ three-dimensional computational fluid dynamics (CFD) modeling to examine whether the effects of bank vegetation on channel form and processes are scale dependent. Field data from the United States and United Kingdom indicate that mean bankfull dimensionless shear stresses are significantly higher in channels with thick woody vegetation but only for channel widths less than ~20 m. Because specific mechanisms controlling the apparent scale dependency are difficult to isolate in natural channels, we develop CFD models of streams with coarse beds and bank vegetation to investigate physical processes in channels with variable bed and bank roughness. The CFD models are applied in two sets of simulations to improve mechanistic understanding of patterns in the field data and to examine (1) spatial scale dependency between channel width and vegetation effects and (2) the coevolution of flow hydraulics, channel form, and vegetation establishment. The scale-dependent bank vegetation effects on shear stress distributions in the CFD representations are consistent with field data from gravel bed streams and suggest that the length scale of bank vegetation protrusion relative to channel width is an important factor that could improve shear stress partitioning models. In general, the field data and CFD simulations indicate a significant scale-dependent effect of bank vegetation with important implications for stream restoration designs based on tractive force, regime, and analytical approaches.

Total flow resistance in gravel bed streams with high width/depth ratios and low sinuosities is primarily a result of grain and bar roughnesses. The relative importance of these two roughness elements has not been established. The relative importance of grain and bar resistance is examined for 12 straight and divided gravel bed reaches at bankfull stage by using the Keulegan equation to determine a resistance division of energy slope. The remaining slope is assumed to represent the relative importance of bar resistance. Bar resistance accounts for 50 to 75% of the total resistance in these reaches. Calculated values of reach‐averaged bar slope correlate closely with field measurements of bar magnitude.

Bed roughness height (k) is a key parameter for velocity prediction in open‐channel flows. There is not yet a firm consensus about whether characteristic particle size D84 or (standard deviation of the channel thalweg) better describes k in gravel bed streams. A data set of 1,788 flume and 713 field measurements with a wide range of channel morphologies and flow conditions were compiled to test whether D84 or is a better descriptor of k and to explore the influence of several controls on flow resistance variation. Tests were performed using four well‐known flow resistance equations. The results consistently show that outperforms D84 in predicting velocity and the Smart and Jäggi equation, with as k, outperforms other equations. The data set was grouped based on R/k (R is the hydraulic radius), channel morphologies, and study sites. performs better than D84 as a measure of k in all morphologies and much better for channels with large instream wood. The analysis shows R/k is a major control on resistance variation as contains more site‐specific information like bed structure. The topography measurements for step‐pool channels should at least contain measurements on key roughness elements like steps. For gravel‐dune or plane‐bed channels, the proper resolution should be higher than 1/2 dune wavelength and 2D84, respectively. The choice of proper reach length relates to both R/k and roughness type. Further, hydraulic geometry functions with either D84 or as k are proposed, and the relation between the two metrics is discussed.

Pool‐riffle sequences play a central role in providing habitat diversity conditions both in terms of flow and substrate in gravel bed streams. Understanding their capacity to self‐maintain has been the focus of research for many years, starting with the velocity reversal hypothesis. This hypothesis relied only on cross sectional averaged flow information, but its limited success prompted extensions of the hypothesis and alternative explanations for self‐maintenance. Significant advances beyond the velocity reversal hypothesis have been achieved by incorporating more information either on flow or sediment transport characteristics. However, this has been done in a compartmentalized way, with studies either focusing on one or the other aspect. This work bridges the gap between these two aspects by using an approximate methodology that combines observed characteristic stage‐dependent 3‐D flow patterns with time‐varying cross sectional information on bed shear stresses, sediment distribution, and sediment bed changes during a 1 year record of continuous discharges from a real stream. This methodology allows us to track the behavior of different sediment size fractions along flow streamlines over time and identify self‐maintenance conditions due to the combined effect of both flow multidimensionality and sediment transport. We apply this approximate methodology to two contiguous pools and riffles and demonstrate that, unexpectedly, they may rely on different mechanisms for self‐maintenance due to differences in geometry and sediment size distribution. We also demonstrate that our methodology is potentially overarching and integrative of previous partial approaches based on flow multidimensionality or sediment transport, which tend to underestimate the occurrence of self‐maintenance.

Stream-subsurface exchange processes are important because of their role in controlling the transport of contaminants and ecologically relevant substances in streams. Laboratory flume experiments were conducted to examine solute exchange with gravel streambeds. Two morphologies were studied: flat beds and beds covered by dune-shaped bedforms. High rates of exchange were observed with flat beds under a wide range of stream flow conditions, indicating that there was considerable turbulent coupling of stream and pore water flows. The presence of bedforms produced additional exchange under all flow conditions. The exchange with bedforms could be represented well by considering solute flux caused by bedform-induced advective pumping. Pumping exchange was enhanced by inertial effects, including non-Darcy flow and turbulent diffusion. For the flat bed case, dye injections showed that exchange also occurred by a combination of advective pore water flow and turbulent diffusion near the stream-subsurface interface. The relative effects of advective and diffusive transport processes could not be separated due to the complex nature of the induced flows in the gravel bed. However, exchange was found to scale with the square of the stream Reynolds number in all cases. Comparison of these results with those obtained with coarser and finer sediments demonstrated that the exchange rate is also proportional to the square of the characteristic bed sediment size. These scaling relationships can be used to improve interpretation of solute transport observed in natural rivers.

Analytical model of flow velocity in gravel-bed streams under the effect of gravel array with different densities

Review of Fluvial Hydrodynamics: Hydrodynamic and Sediment Transport Phenomena by Subhasish DeyGeoPlanet: Earth and Planetary Sciences Book Series, Springer, Berlin, Heidelberg; 2014; ISBN 978-3-642-19061-2, ISBN 978-3-642-19062-9 (eBook); DOI 10.1007/978-3-642-19062-9; 687 pp.; $139/€107.09/£93.50.

Flow resistance in gravel-bedded streams and torrents

Flow resistance in gravel-bedded streams and torrents

Application of the block ramp technique in steep gradient streams for energy dissipation as well as to maintain river stability finds increasing favor amongst researchers and practitioners in river engineering. This paper dwells on a comprehensive state-of-the-art review of flow resistance, energy dissipation, flow characteristics, stability, and drag force on block ramps by various investigators in the past. The forms and equations for each type are thoroughly discussed with the objective of finding the grey areas and gaps. More research is warranted further to improve the equations, which are essential for design analysis. Block ramps can be a promising simple technique to achieve reasonable attenuation of devastating fluvial forces unleashed in gravel-bed streams during cloud bursts.