Experimental Studies and Analysis on Mobilization of the Cohesionless Sediments Through Alluvial Channel: A Review
Entrainment of river bed particles by turbulent flow is a core matter of study in river hydrodynamics. It is of great interest to river engineers to evaluate the shear stress for initiating river bed motion. The main objective is to calculate transport rates for bed load, to predict changes in bed level which are scoured or aggraded and to design a stable channel. Forces acting upon the particle especially fluid forces which give a major role in the incipient motion of the particle on the rough boundary. For calculation generally use shield’s diagram but some other modified methods and approaches are discussed. Modeling criteria are discussed for the hydraulically smooth and rough boundary depending on Reynolds number. In the past, experimental studies on tractive shear stress have been done by many researchers but consideration of lift force to analyze the movement of sediment is very limited. For suspended load transport, a detailed analysis of lift force is required. Based on the study it has been observed that shear stress depends on channel slope not only due to gravitational force but also many other factors like drag force, lift force, friction angle, fluctuations, velocity profile, etc. Complete analysis of these factors provides slope dependency over shear stress. To improve past studies, some factors have been discussed, to give a more correct force balance equation. This is very difficult task to analyze more and more variable’s dependency on the slope. Consideration of the possible number of variable holds complete analysis of experimental study. This paper also reviews the effect of particle Reynolds number and relative submergence over critical shield stress.
Full Text: PDF
Sutherland, Alex J. “Proposed Mechanism for Sediment Entrainment by Turbulent Flows.” Journal of Geophysical Research 72, no. 24 (December 15, 1967): 6183–6194. doi:10.1029/jz072i024p06183.
Ninto, Y., and M. H. Garcia. “Experiments on Particle—turbulence Interactions in the Near–wall Region of an Open Channel Flow: Implications for Sediment Transport.” Journal of Fluid Mechanics 326 (November 10, 1996): 285–319. doi:10.1017/s0022112096008324.
Simões, Francisco JM. "Shear velocity criterion for incipient motion of sediment." Water Science and Engineering 7, no. 2 (2014): 183-193. doi:10.3882/j.issn.1674-2370.2014.02.006.
Zanke, U. C. E. "On the influence of turbulence on the initiation of sediment motion." International Journal of Sediment Research 18, no. 1 (2003): 17-31.
Einstein, Hans Albert, and El-Sayed Ahmed El-Samni. “Hydrodynamic Forces on a Rough Wall.” Reviews of Modern Physics 21, no. 3 (July 1, 1949): 520–524. doi:10.1103/revmodphys.21.520.
Southard J. “Introduction to Fluid Motions, Sediment Transport, and Current-Generated Sedimentary Structures.” Massachusetts Inst Technol MIT OpenCourseWare, (2006):260–284.
Miller, M. C., I. N. McCave, and P. D. Komar. “Threshold of Sediment Motion under Unidirectional Currents.” Sedimentology 24, no. 4 (August 1977): 507–527. doi:10.1111/j.1365-3091.1977.tb00136.x.
Yang, Yang, Shu Gao, Ya Ping Wang, Jianjun Jia, Jilian Xiong, and Liang Zhou. “Revisiting the Problem of Sediment Motion Threshold.” Continental Shelf Research 187 (October 2019): 103960. doi:10.1016/j.csr.2019.103960.
Chepil, W. S. “The Use of Spheres to Measure Lift and Drag on Wind-Eroded Soil Grains.” Soil Science Society of America Journal 25, no. 5 (September 1961): 343–345. doi:10.2136/sssaj1961.03615995002500050011x.
Balachandar, Ram, and Faruk Bhuiyan. “Higher-Order Moments of Velocity Fluctuations in an Open-Channel Flow with Large Bottom Roughness.” Journal of Hydraulic Engineering 133, no. 1 (January 2007): 77–87. doi:10.1061/(asce)0733-9429(2007)133:1(77).
Sundborg, Åke. “The River Klarälven a Study of Fluvial Processes.” Geografiska Annaler 38, no. 2–3 (August 1956): 125–316. doi:10.1080/20014422.1956.11880887.
Dey, Subhasish, and Sk Zeeshan Ali. “Review Article: Advances in Modeling of Bed Particle Entrainment Sheared by Turbulent Flow.” Physics of Fluids 30, no. 6 (June 2018): 061301. doi:10.1063/1.5030458.
García, Marcelo H. "Sediment Transport and Morphodynamics." In Sedimentation engineering: Processes, measurements, modeling, and practice, (2008): 21-163.
Valyrakis, Manousos. "Initiation of particle movement in turbulent open channel flow." PhD diss., Virginia Tech, United States, (2011).
Dey, Subhasish, Sankar Sarkar, and Luca Solari. “Near-Bed Turbulence Characteristics at the Entrainment Threshold of Sediment Beds.” Journal of Hydraulic Engineering 137, no. 9 (September 2011): 945–958. doi:10.1061/(asce)hy.1943-7900.0000396.
Dey, Subhasish. “Sediment Threshold.” Fluvial Hydrodynamics (2014): 189–259. doi:10.1007/978-3-642-19062-9_4.
Buffington, John M., and David R. Montgomery. “A Systematic Analysis of Eight Decades of Incipient Motion Studies, with Special Reference to Gravel-Bedded Rivers.” Water Resources Research 33, no. 8 (August 1997): 1993–2029. doi:10.1029/96wr03190..
Iversen, J.D., J.B. Pollack, R. Greeley, and B.R. White. “Saltation Threshold on Mars: The Effect of Interparticle Force, Surface Roughness, and Low Atmospheric Density.” Icarus 29, no. 3 (November 1976): 381–393. doi:10.1016/0019-1035(76)90140-8.
Iversen, James D., Ronald Greeley, John R. Marshall, and James B. Pollack. “Aeolian Saltation Threshold: The Effect of Density Ratio.” Sedimentology 34, no. 4 (August 1987): 699–706. doi:10.1111/j.1365-3091.1987.tb00795.x.
Ward, Bruce D. “Relative Density Effects on Incipient Bed Movement.” Water Resources Research 5, no. 5 (October 1969): 1090–1096. doi:10.1029/wr005i005p01090.
Ali, Sk Zeeshan, and Subhasish Dey. “Hydrodynamics of Sediment Threshold.” Physics of Fluids 28, no. 7 (July 2016): 075103. doi:10.1063/1.4955103.
Salim, Sarik, Charitha Pattiaratchi, Rafael O. Tinoco, and Ravindra Jayaratne. “Sediment Resuspension Due to Near‐Bed Turbulent Effects: A Deep Sea Case Study on the Northwest Continental Slope of Western Australia.” Journal of Geophysical Research: Oceans 123, no. 10 (October 2018): 7102–7119. doi:10.1029/2018jc013819.
C. M. White “The Equilibrium of Grains on the Bed of a Stream.” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 174, no. 958 (February 21, 1940): 322–338. doi:10.1098/rspa.1940.0023.
M. Kurihara. “On the critical tractive force.” Research Institute for Hydraulic Engineering, Japan 4, (1948).
Iwagaki, Yuichi. “(I) Hydrodynamical Study on Critical Tractive Force.” Transactions of the Japan Society of Civil Engineers 1956, no. 41 (1956): 1–21. doi:10.2208/jscej1949.1956.41_1.
Reichardt, H. “Vollständige Darstellung Der Turbulenten Geschwindigkeitsverteilung in Glatten Leitungen.” ZAMM - Zeitschrift Für Angewandte Mathematik Und Mechanik 31, no. 7 (1951): 208–219. doi:10.1002/zamm.19510310704.
Wiberg, Patricia L., and J. Dungan Smith. “Calculations of the Critical Shear Stress for Motion of Uniform and Heterogeneous Sediments.” Water Resources Research 23, no. 8 (August 1987): 1471–1480. doi:10.1029/wr023i008p01471.
Morsi, S. A., and A. J. Alexander. “An Investigation of Particle Trajectories in Two-Phase Flow Systems.” Journal of Fluid Mechanics 55, no. 02 (September 1972): 193-208. doi:10.1017/s0022112072001806.
Lamb, Michael P., William E. Dietrich, and Jeremy G. Venditti. “Is the Critical Shields Stress for Incipient Sediment Motion Dependent on Channel-Bed Slope?” Journal of Geophysical Research 113, no. F2 (May 1, 2008). doi:10.1029/2007jf000831.
Armanini, Aronne, and Carlo Gregoretti. “Incipient Sediment Motion at High Slopes in Uniform Flow Condition.” Water Resources Research 41, no. 12 (December 2005): 1-8. doi:10.1029/2005wr004001.
Tipper, J.C. “The Equilibrium and Entrainment of a Sediment Grain.” Sedimentary Geology 64, no. 1–3 (August 1989): 167–174. doi:10.1016/0037-0738(89)90090-0.
Bridge, John S., and Sean J. Bennett. “A Model for the Entrainment and Transport of Sediment Grains of Mixed Sizes, Shapes, and Densities.” Water Resources Research 28, no. 2 (February 1992): 337–363. doi:10.1029/91wr02570.
Komar, Paul D., and Paul A. Carling. “Grain Sorting in Gravel-Bed Streams and the Choice of Particle Sizes for Flow-Competence Evaluations.” Sedimentology 38, no. 3 (June 1991): 489–502. doi:10.1111/j.1365-3091.1991.tb00363.x.
Kirchner, James W., William E. Dietrich, Fujiko Iseya, and Hiroshi Ikeda. “The Variability of Critical Shear Stress, Friction Angle, and Grain Protrusion in Water-Worked Sediments.” Sedimentology 37, no. 4 (August 1990): 647–672. doi:10.1111/j.1365-3091.1990.tb00627.x.
Ferguson, Robert I. "Emergence of abrupt gravel to sand transitions along rivers through sorting processes." Geology 31, no. 2 (2003): 159-162. doi:10.1130/0091-7613(2003)031<0159:EOAGTS>2.0.CO;2.
Lisle, T. E. "Overview: channel morphology and sediment transport in steepland streams." Erosion and Sedimentation in the Pacific Rim (Proceedings of the Corvallis Symposium, August 1987). International Association of Hydrological Sciences Pub. No. 165, (1987): 287-297.
Aminoroayaie Yamini, O., S. Hooman Mousavi, M. R. Kavianpour, and Azin Movahedi. “Numerical Modeling of Sediment Scouring Phenomenon Around the Offshore Wind Turbine Pile in Marine Environment.” Environmental Earth Sciences 77, no. 23 (November 24, 2018). doi:10.1007/s12665-018-7967-4.
Buffington, John M., and David R. Montgomery. “Effects of Hydraulic Roughness on Surface Textures of Gravel-Bed Rivers.” Water Resources Research 35, no. 11 (November 1999): 3507–3521. doi:10.1029/1999wr900138.
Gordon RJ. “Boundary Layer Theory.” AIChEMI Modul Instr Ser C Series C: TRANSPORT, Volume 7: Calculation and Measurement Techniques for Momentum, Energy and Mass Transfer, (1983): 23–27.
Wilcock, Peter R., and Brian W. McArdell. “Surface-Based Fractional Transport Rates: Mobilization Thresholds and Partial Transport of a Sand-Gravel Sediment.” Water Resources Research 29, no. 4 (April 1993): 1297–1312. doi:10.1029/92wr02748.
Komar, Paul D. “Selective Gravel Entrainment and the Empirical Evaluation of Flow Competence.” Sedimentology 34, no. 6 (December 1987): 1165–1176. doi:10.1111/j.1365-3091.1987.tb00599.x.
Hammond, F. D. C., A. D. Heathershaw, and D. N. Langhorne. "A comparison between Shields' threshold criterion and the movement of loosely packed gravel in a tidal channel." Sedimentology 31, no. 1 (1984): 51-62. doi:10.1111/j.1365-3091.1984.tb00722.x.
Shvidchenko, Andrey B., and Gareth Pender. “Flume Study of the Effect of Relative Depth on the Incipient Motion of Coarse Uniform Sediments.” Water Resources Research 36, no. 2 (February 2000): 619–628. doi:10.1029/1999wr900312.
Wilcock, Peter R. “Methods for Estimating the Critical Shear Stress of Individual Fractions in Mixed-Size Sediment.” Water Resources Research 24, no. 7 (July 1988): 1127–1135. doi:10.1029/wr024i007p01127.
Tsujimoto, Tetsuro. “Bed-Load Transport in Steep Channels.” Lecture Notes in Earth Sciences (1991): 89–102. doi:10.1007/bfb0011185.
Chiew, Yee-Meng, and Gary Parker. “Incipient Sediment Motion on Non-Horizontal Slopes.” Journal of Hydraulic Research 32, no. 5 (September 1994): 649–660. doi:10.1080/00221689409498706.
McLean, S. R., and V. I. Nikora. “Characteristics of Turbulent Unidirectional Flow over Rough Beds: Double-Averaging Perspective with Particular Focus on Sand Dunes and Gravel Beds.” Water Resources Research 42, no. 10 (October 2006): 1-19. doi:10.1029/2005wr004708.
Vanoni, Vito A., and Norman H. Brooks. “Laboratory studies of the roughness and suspended load of alluvial streams.” No. 11. US Army Engineer Division, Missouri River, (1957).
Parker, Gary, Peter R. Wilcock, Chris Paola, William E. Dietrich, and John Pitlick. “Physical Basis for Quasi-Universal Relations Describing Bankfull Hydraulic Geometry of Single-Thread Gravel Bed Rivers.” Journal of Geophysical Research 112, no. F4 (November 2, 2007). doi:10.1029/2006jf000549.
Mueller, Erich R. “Morphologically Based Model of Bed Load Transport Capacity in a Headwater Stream.” Journal of Geophysical Research 110, no. F2 (2005): 1-14. doi:10.1029/2003jf000117.
Aristide Lenzi, Mario, Luca Mao, and Francesco Comiti. “When Does Bedload Transport Begin in Steep Boulder-Bed Streams?” Hydrological Processes 20, no. 16 (2006): 3517–3533. doi:10.1002/hyp.6168.
Braudrick, Christian A., and Gordon E. Grant. “When Do Logs Move in Rivers?” Water Resources Research 36, no. 2 (February 2000): 571–583. doi:10.1029/1999wr900290.
Yager, E. M., J. W. Kirchner, and W. E. Dietrich. “Calculating Bed Load Transport in Steep Boulder Bed Channels.” Water Resources Research 43, no. 7 (July 2007). doi:10.1029/2006wr005432.
Wilcox, Andrew C., Jonathan M. Nelson, and Ellen E. Wohl. “Flow Resistance Dynamics in Step-Pool Channels: 2. Partitioning Between Grain, Spill, and Woody Debris Resistance.” Water Resources Research 42, no. 5 (May 2006). doi:10.1029/2005wr004278.
Chanson, H. “Drag Reduction in Skimming Flow on Stepped Spillways by Aeration.” Journal of Hydraulic Research 42, no. 3 (January 2004): 316–322. doi:10.1080/00221686.2004.9728397.
Schmeeckle, Mark W., Jonathan M. Nelson, and Ronald L. Shreve. “Forces on Stationary Particles in Near-Bed Turbulent Flows.” Journal of Geophysical Research 112, no. F2 (April 11, 2007). doi:10.1029/2006jf000536.
Lawrence, D. S. L. “Hydraulic Resistance in Overland Flow during Partial and Marginal Surface Inundation: Experimental Observations and Modeling.” Water Resources Research 36, no. 8 (August 2000): 2381–2393. doi:10.1029/2000wr900095.
Schwendel, Arved C., Russell G. Death, and Ian C. Fuller. “The Assessment of Shear Stress and Bed Stability in Stream Ecology.” Freshwater Biology 55, no. 2 (February 2010): 261–281. doi:10.1111/j.1365-2427.2009.02293.x.
Nikora, Vladimir, Derek Goring, Ian McEwan, and George Griffiths. “Spatially Averaged Open-Channel Flow over Rough Bed.” Journal of Hydraulic Engineering 127, no. 2 (February 2001): 123–133. doi:10.1061/(asce)0733-9429(2001)127:2(123).
Defina, Andrea, and Anna Chiara Bixio. “Mean Flow and Turbulence in Vegetated Open Channel Flow.” Water Resources Research 41, no. 7 (July 2005). doi:10.1029/2004wr003475.
Hofland, Bas, Jurjen A. Battjes, and Robert Booij. “Measurement of Fluctuating Pressures on Coarse Bed Material.” Journal of Hydraulic Engineering 131, no. 9 (September 2005): 770–781. doi:10.1061/(asce)0733-9429(2005)131:9(770).
Neill C.R. “Mean-velocity criterion for scour of coarse uniform bed-material.” Twelfth Congress of the International Association for Hydraulic Research, Fort Collins: Colorado State University 3, (1967): 46–54.
Meyer-Peter E, Müller R. “Formulas for Bed-Load Transport.” Proceedings of the 2nd Meeting of the International Association of Hydraulic Research, IAHR, (1948):39–64.
Mueller, Erich R., John Pitlick, and Jonathan M. Nelson. “Variation in the Reference Shields Stress for Bed Load Transport in Gravel-Bed Streams and Rivers.” Water Resources Research 41, no. 4 (April 2005). doi:10.1029/2004wr003692.
Roušar, Ladislav, Zbyněk Zachoval, and Pierre Julien. “Incipient Motion of Coarse Uniform Gravel.” Journal of Hydraulic Research 54, no. 6 (August 16, 2016): 615–630. doi:10.1080/00221686.2016.1212286.
Gregoretti, Carlo. “The Initiation of Debris Flow at High Slopes: Experimental Results.” Journal of Hydraulic Research 38, no. 2 (March 2000): 83–88. doi:10.1080/00221680009498343.
Dey, Subhasish, and Uddaraju V. Raju. “Incipient Motion of Gravel and Coal Beds.” Sadhana 27, no. 5 (October 2002): 559–568. doi:10.1007/bf02703294.
Asheghi, Reza, and Seyed Abbas Hosseini. “Prediction of Bed Load Sediments Using Different Artificial Neural Network Models.” Frontiers of Structural and Civil Engineering 14, no. 2 (March 16, 2020): 374–386. doi:10.1007/s11709-019-0600-0.
Kališ J. “Hydraulic research of boulder chutes.” In Brno University of Technology, (1970).
Neill CR. “Stability of coarse bed-material in open-channel flow.” Res Counc Alberta, (1967).
Pokrajac, Dubravka, and Costantino Manes. “Velocity Measurements of a Free-Surface Turbulent Flow Penetrating a Porous Medium Composed of Uniform-Size Spheres.” Transport in Porous Media 78, no. 3 (February 7, 2009): 367–383. doi:10.1007/s11242-009-9339-8.
Nikora, Vladimir, Katinka Koll, Ian McEwan, Stephen McLean, and Andreas Dittrich. “Velocity Distribution in the Roughness Layer of Rough-Bed Flows.” Journal of Hydraulic Engineering 130, no. 10 (October 2004): 1036–1042. doi:10.1061/(asce)0733-9429(2004)130:10(1036).
Shimizu, Yoshihiko, Tetsuro Tsujimoto, and Hiroji Nakagawa. "Experiment and macroscopic modelling of flow in highly permeable porous medium under free-surface flow." J. Hydrosci. Hydraul. Eng 8, no. 1 (1990): 69-78.
Fenton, J. D. and J. E. Abbott “Initial Movement of Grains on a Stream Bed: The Effect of Relative Protrusion.” Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 352, no. 1671 (February 4, 1977): 523–537. doi:10.1098/rspa.1977.0014.
Dey, Subhasish, and Koustuv Debnath. “Influence of Streamwise Bed Slope on Sediment Threshold under Stream Flow.” Journal of Irrigation and Drainage Engineering 126, no. 4 (July 2000): 255–263. doi:10.1061/(asce)0733-9437(2000)126:4(255).
Fernandez Luque, R., and R. Van Beek. “Erosion And Transport Of Bed-Load Sediment.” Journal of Hydraulic Research 14, no. 2 (April 1976): 127–144. doi:10.1080/00221687609499677.
Graf, Walter Hans. "Sediment transport in steep channel." Jour. Hydroscience and Hydr. Eng., JSCE. 5, no. 1 (1987): 11-26.
Cao, Zhixian, Gareth Pender, and Jian Meng. “Explicit Formulation of the Shields Diagram for Incipient Motion of Sediment.” Journal of Hydraulic Engineering 132, no. 10 (October 2006): 1097–1099. doi:10.1061/(asce)0733-9429(2006)132:10(1097).
Guo, Junke. “Logarithmic Matching and Its Applications in Computational Hydraulics and Sediment Transport.” Journal of Hydraulic Research 40, no. 5 (September 2002): 555–565. doi:10.1080/00221680209499900.
Yalin MS. “Mechanics of sediment transport.” 2nd ed. University of Brighten, Oxford, (1977).
Yalin, M. S. and da Silva AMF. “Fluvial Processes.” IAHR International Association of Hydraulic Engineering, and Research, Delft, The Netherlands, (2001).
Bravo, R., P. Ortiz, and J.L. Pérez-Aparicio. “Incipient Sediment Transport for Non-Cohesive Landforms by the Discrete Element Method (DEM).” Applied Mathematical Modelling 38, no. 4 (February 2014): 1326–1337. doi:10.1016/j.apm.2013.08.010.
Ikeda, Syunsuke. “Incipient Motion of Sand Particles on Side Slopes.” Journal of the Hydraulics Division 108, no. 1 (January 1982): 95–114. doi:10.1061/jyceaj.0005812.
Coleman, Neil L. "A theoretical and experimental study of drag and lift forces acting on a sphere resting on a hypothetical streambed." (1967).
Nelson, Jonathan M., Mark W. Schmeeckle, and Ronald L. Shreve. "Turbulence and particle entrainment." Gravel Bed Rivers V (2001): 221-248.
Parker, Gary, and Marcelo H. Garcia, eds. “River, Coastal and Estuarine Morphodynamics” Proceedings of the 4th IAHR Symposium on River, Coastal and Estuarine Morphodynamics, London, Taylor and Francis, First Edition, (September 29, 2005): 65-69. doi:10.1201/9781439833896.
Vollmer, Stefan, and Maarten G. Kleinhans. “Predicting Incipient Motion, Including the Effect of Turbulent Pressure Fluctuations in the Bed.” Water Resources Research 43, no. 5 (May 2007). doi:10.1029/2006wr004919.
Mizuyama, T. “Bedload transport in steep channels” (PhD dissertation), Kyoto University, Kyoto, (1977).
Vanoni, Vito A., ed. “Sedimentation Engineering” American Society of Civil Engineers, Manuals and Reports on Engineering Practice 54 (March 29, 2006). doi:10.1061/9780784408230.
Ahmad, Muhammad, Usman Ghani, Naveed Anjum, Ghufran Ahmed Pasha, Muhammad Kaleem Ullah, and Afzal Ahmed. “Investigating the Flow Hydrodynamics in a Compound Channel with Layered Vegetated Floodplains.” Civil Engineering Journal 6, no. 5 (May 1, 2020): 860–876. doi:10.28991/cej-2020-03091513.
Sun, Zhilin, Haolei Zheng, Dan Xu, Chunhong Hu, and Chaofan Zhang. “Vertical Concentration Profile of Nonuniform Sediment.” International Journal of Sediment Research 36, no. 1 (February 2021): 120–126. doi:10.1016/j.ijsrc.2020.06.008.
Unal, Necati. “Shear Stress-Based Analysis of Sediment Incipient Deposition in Rigid Boundary Open Channels.” Water 10, no. 10 (October 9, 2018): 1399. doi:10.3390/w10101399.
Singh, Umesh K., Z. Ahmad, Ashish Kumar, and Manish Pandey. “Incipient Motion for Gravel Particles in Cohesionless Sediment Mixtures.” Iranian Journal of Science and Technology, Transactions of Civil Engineering 43, no. 2 (July 30, 2018): 253–262. doi:10.1007/s40996-018-0136-x.
Carrillo, Veronica, John Petrie, Luis Timbe, Esteban Pacheco, Washington Astudillo, Carlos Padilla, and Felipe Cisneros. “Validation of an Experimental Procedure to Determine Bedload Transport Rates in Steep Channels with Coarse Sediment.” Water 13, no. 5 (March 2, 2021): 672. doi:10.3390/w13050672.
Phillips, C. B., and D. J. Jerolmack. “Bankfull Transport Capacity and the Threshold of Motion in Coarse‐Grained Rivers.” Water Resources Research 55, no. 12 (December 2019): 11316–11330. doi:10.1029/2019wr025455.
Bathurst, J. C., Li, R. M., & Simons, D. B. “Hydraulics of mountain rivers.” Fort Collins, CO: Colorado State University, (1979).
Cao, H. H. “Resistance hydraulique d’un lit de gravier mobile a pente raide: etude experimentale.”, Thesis. EPFL (1985). doi: 10.5075/epfl-thesis-589
Bathurst, J. C., Graf, W. H., Cao, H. H. “Bed load discharge equations for steep mountain rivers.” Sediment transport in gravel-bed rivers (1987):453-491.
Suszka, Lechostaw. “Modification of Transport Rate Formula for Steep Channels.” Lecture Notes in Earth Sciences (1991): 59–70. doi:10.1007/bfb0011182.
Papanicolaou, Athanasios N. "The role of turbulence on the initiation of sediment motion." PhD diss., Virginia Tech, United States, (1997).
Recking, Alain. "An experimental study of grain sorting effects on bedload." Institut National des Sciences Appliquees de Lyon, Lyon, France, (2006).
- There are currently no refbacks.
Copyright (c) 2021 AKASH ANAND, Mubeen Beg, Neeraj Kumar
This work is licensed under a Creative Commons Attribution 4.0 International License.