Flow resistance in gravel-bed rivers: Progress in research

Earth-Science Reviews

Volumn 136, Issue , 2014, Pages 301-338

  Powell, D Mark ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Boundary layer; Flow resistance; Form drag; Gravel bed rivers; Relative submergence; Skin friction

Indexed keywords

DRAG; FLOW FIELD; FLOW STRUCTURE; FLUID MECHANICS; GRAVEL BED STREAM; HYDRAULICS; OPEN CHANNEL FLOW; PRESSURE GRADIENT; RIVER FLOW; SEDIMENT TRANSPORT; STREAMFLOW; SUBMERGENCE;

EID: 84903440895     PISSN: 00128252     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.earscirev.2014.06.001     Document Type: Review

References (200)

1. Aberle J., Nikora V. Statistical properties of armoured gravel bed surfaces. Water Resour. Res. 2006, 42. 10.1029/2005WR004674.
2. Aberle J., Smart G.M. The influence of roughness structure on flow resistance on steep slopes. J. Hydraul. Res. 2003, 41:259-269.
3. Aberle J., Nikora V., Henning M., Ettmer B., Hentschel B. Statistical characterisation of bed roughness due to bed forms: a field study in the Elbe River at Aken, Germany. Water Resour. Res. 2010, 46. 10.1029/2008WR007406.
4. Abrahams A.D., Li G., Atkinson J.F. Step-pool systems: adjustment to maximum flow resistance. Water Resour. Res. 1995, 31:2593-2602.
5. Aldridge B.N., Garrett J.M. Roughness coefficients for streams channels in Arizona. United States Geological Survey Open File Report 73-3 1973.
6. Anderson J.F. Ludwig Prandtl's boundary layer. Phys. Today 2005, 58:42-48.
7. Arcement G.J., Schneider V.R. Guide for selecting Manning's roughness coefficients for natural channels and floodplains. United States Geological Survey Water Supply Paper 1989, 2339.
8. Barnes H.H. Roughness characteristics of open channels. United States Geological Society Water Supply Paper 1849 1967.
9. Barneveld R.J., Manuel S., Maalen-Johansen I. Assessment of terrestrial laser scanning technology for obtaining high-resolution DEMs of soils. Earth Surf. Process. Landf. 2013, 38. 10.1002/esp.3344.
10. Bathurst J.C. Flow resistance of large-scale roughness. J. Hydraul. Div. ASCE 1978, 104:1587-1603.
11. Bathurst J.C. Theoretical aspects of flow resistance. Gravel-Bed Rivers 1982, 443-462. John Wiley and Sons, Chichester. R.D. Hey, J.C. Bathurst, C.R. Thorne (Eds.).
12. Bathurst J.C. Flow resistance estimation in mountain rivers. J. Hydraul. Eng. 1985, 111:625-643.
13. Bathurst J.C. Flow resistance through the channel network. Channel Network Hydrology 1993, 69-98. John Wiley and Sons, Chichester. K. Bevan, M.J. Kirkby (Eds.).
14. Bathurst J.C. Environmental river flow hydraulics. Applied Fluvial Geomorphology for River Engineering and Management 1997, 69-93. John Wiley and Sons, Chichester. C.R. Thorne, R.D. Hey, M.D. Newson (Eds.).
15. Bathurst J.C. At-a-site variation and minimum flow resistance for mountain rivers. J. Hydrol. 2002, 269:11-26.
16. Bathurst J.C., Li R.-M., Simons D.B. Resistance equation for large-scale roughness. J. Hydraul. Div. ASCE 1981, 107:1593-1613.
17. Benson M.A., Dalrymple T. General field and office procedures for indirect discharge measurements. United States Geological Survey, Techniques of Water Resources Investigations, Applications of Hydraulics (Book 3) 1967, (Chapter A1).
18. Bergeron N.E. Scale-space analysis of stream-bed roughness in coarse gravel-bed streams. Math. Geol. 1996, 28:537-561.
19. Bergeron N.E., Carbonneau P. The effect of sediment concentration on bedload roughness. Hydrol. Process. 1999, 13:2583-2589.
20. Bertrand-Krajewski J.-L. Manning Robert. A Short Historical Dictionary on Urban Hydrology and Drainage (Accessed 05/08/13). http://jlbkpro.free.fr/shduhdfromatoz/manning.pdf.
21. Bjerklie D.M., Dingman S.L., Bolster C.H. Comparison of constitutive flow resistance equations based on the Manning and Chezy equations applied to natural rivers. Water Resour. Res. 2005, 41:W11502. 10.1029/2004WR003776.
22. Bouratsis P., Diplas P., Dancey C.L., Apsilidis N. High-resolution 3-D monitoring of evolving sediment beds. Water Resour. Res. 2013, 49:977-992.
23. Brasington J., Vericat D., Rychkov I. Modelling river bed morphology, roughness and surface sedimentology using high resolution terrestrial laser scanning. Water Resour. Res. 2012, 48. 10.1029/2012WR012223.
24. Bray D.I. Estimating average velocity in gravel-bed rivers. J. Hydraul. Div. ASCE 1979, 105:1103-1122.
25. Bray D.I. Flow resistance in gravel-bed rivers. Gravel Bed Rivers 1982, 109-137. Wiley, Chichester. R.D. Hey, J.C. Bathurst, C.E. Thorne (Eds.).
26. Bray D.I., Davar K.S. Resistance to flow in gravel-bed rivers. Can. J. Civ. Eng. 1987, 14:77-86.
27. Brown G.O. The history of the Darcy-Weisbach equation for pipe flow resistance. Proceedings of the 150th Anniversary Conference of American Society of Civil Engineers, November 3-6 2002 2002, 34-43. American Society of Civil Engineers, Washington D.C.. A. Fredrich, J. Rogers (Eds.).
28. Burnham M.W., Davis D.W. Effects of data errors in computed steady-flow profiles. J. Hydraul. Eng. 1990, 116:914-929.
29. Butler J.B., Lane S.N., Chandler J.H. Assessment of DEM quality for characterising surface roughness using close range digital photogrammetry. Photogramm. Rec. 1988, 16:271-291.
30. Butler J.B., Lane S.N., Chandler J.H. Characterisation of the structure of river-bed gravels using two dimensional fractal analysis. Math. Geol. 2001, 33:301-330.
31. Butler J.B., Lane S.N., Chandler J.H., Porfiri E. Through-water close range digital photogrammetry in flume and field environments. Photogramm. Rec. 2002, 17:419-439.
32. Byrd T.C., Furbish D.J., Warburton J. Estimating depth-averaged velocities in rough channels. Earth Surf. Process. Landf. 2000, 25:167-173.
33. Cadol D., Wohl E. Variable contribution of wood to the hydraulic resistance of headwater tropical streams. Water Resour. Res. 2013, 49:4711-4723. 10.1002/wrcr.20362.
34. Calomino F., Gaudio R., Miglio A. Effect of bed-load concentration on friction factor in narrow channels. River Flow 2004 2004, 279-285. Taylor and Francis Group, London. M. Greco, A. Carravetta, R. Della Morte (Eds.).
35. Campbell L., McEwan I., Nikora V., Pokrajac D., Gallagher M., Manes C. Bed-load effects on hydrodynamics of rough-bed open-channel flows. J. Hydraul. Eng. 2005, 131:576-585.
36. Canovaro F., Solari L. Dissipative analogies between a schematic macro-roughness arrangement and step-pool morphology. Earth Surf. Process. Landf. 2007, 32:1628-1640.
37. Canovaro F., Paris E., Solari L. Influence of macro-roughness arrangement on flow resistance. River Flow 2004 2004, 287-293. Taylor and Francis Group, London. M. Greco, A. Carravetta, R. Della Morte (Eds.).
38. Carling P.A. The nature of the fluid boundary layer and the selection of parameters for benthic ecology. Freshw. Biol. 1992, 28:273-284.
39. Carson M.A. The Mechanics of Erosion 1971, Pion, London.
40. Carson M.A., Kirkby M.J. Hillslope Form and Processes 1972, Cambridge University Press, Cambridge.
41. Chandler J.H. Effective application of automated digital photogrammetry for geomorphological research. Earth Surf. Process. Landf. 1999, 24:51-63.
42. Chandler J.H., Shiono K., Rameshwaren P., Lane S.N. Measuring flume surfaces for hydraulics research using a Kodak DCS460. Photogramm. Rec. 2001, 17:39-61.
43. Chandler J.H., Ashmore P., Paola C., Gooch M., Varkaris F. Monitoring river channel change using terrestial oblique digital imagery and automated digital photogrammetry. Ann. Assoc. Am. Geogr. 2002, 92:631-644.
44. Charlton F.G., Brown P.M., Benson R.W. The hydraulic geometry of some gravel rivers in Britain. Report No. IT180 1978, Hydraulics Research Station, Wallingford.
45. Cheng N.-S., Nguyen H.T., Zhao K., Tang X. Evaluation of flow resistance in smooth rectangular open channels with modified Prandtl friction law. J. Hydraul. Eng. 2011, 137:441-450.
46. Chin A. The geomorphic significance of step-pools in mountain streams. Geomorphology 2003, 55:125-137.
47. Chow V.T. Open Channel Hydraulics 1959, McGraw-Hill, New York.
48. Church M., Zimmermann A. Form and stability of step-pool channels: research progress. Water Resour. Res. 2007, 43. 10.1029/2006WR005037.
49. Clifford N.J., Robert A., Richards K.S. Estimation of flow resistance in gravel-bed rivers: a physical explanation of the multiplier of roughness length. Earth Surf. Process. Landf. 1992, 17:111-126.
50. Colebrook C.F. Turbulent flow in pipes, with particular reference to the transition region between smooth and rough pipe laws. J. Inst. Civ. Eng. 1939, 11:133-156.
51. Colosimo C., Copertino V.A., Veltri M. Friction factor evaluation on gravel bed rivers. J. Hydraul. Eng. 1988, 114:861-869.
52. Comiti F., Mao L. Recent advances in the dynamics of steep channels. Gravel-Bed Rivers: Processes, Tools, Environments 2012, 353-377. Wiley-Blackwell, Chichester. M. Church, P.M. Biron, A.G. Roy (Eds.).
53. Comiti F., Mao L., Wilcox A., Wohl E.E., Lenzi M.A. Field-derived relationships for flow velocity and resistance in high-gradient streams. J. Hydrol. 2007, 340:48-62.
54. Comiti F., Cadol D., Wohl E. Flow regimes, bed morphology, and flow resistance in self-formed step-pool channels. Water Resour. Res. 2009, 45. 10.1029/2008WR007259.
55. Coon W.F. Estimation of roughness coefficients for natural stream channels with vegetated banks. United States Geological Survey Water Supply Paper 1998, 2441.
56. Cowan W.L. Estimating hydraulic roughness coefficients. Agric. Eng. 1956, 37:473-475.
57. Croft H., Anderson K., Brazier R.E., Kuhn N.J. Modeling fine-scale soil surface structure using geostatistics. Water Resour. Res. 2013, 49. 10.1002/wrcr.20172.
58. Curran J.H., Wohl E.E. Large woody debris and flow resistance in step-pool channels, Cascade Range, Washington. Geomorphology 2003, 51:141-157.
59. Dalrymple T., Benson M.A. Measurement of peak discharge by the slope-area method. United States Geological Survey, Techniques of Water Resources Investigations, Applications of Hydraulics (Book 3) 1968, (Chapter A2).
60. Dartevelle S. Numerical and granulometric approaches to geophysical granular flows 2003, (Ph.D. Thesis), Michigan Technological University, Department of Geological and Mining Engineering, Houghton, Michigan.
61. David G.C.L., Wohl E., Yochum S.E., Bledsoe B.P. Controls on spatial variations in flow resistance along steep mountain streams. Water Resour. Res. 2010, 46. 10.1029/2009WR008134.
62. Dingman S.L. Fluvial Hydrology 1984, W.H. Freeman and Company, New York.
63. Duncan W.J., Thom A.S., Young A.D. Mechanics of Fluids 1970, Edward Arnold, London. 2nd edition.
64. Dust D., Wohl E.E. Characterisation of the hydraulics at natural steps crests in step-pool streams via weir flow concepts. Water Resour. Res. 2012, 48. 10.1029/2011WR11724.
65. Ferguson R. Flow resistance equations for gravel- and boulder-bed streams. Water Resour. Res. 2007, 43. 10.1029/2006WR005422.
66. Ferguson R. Time to abandon the Manning equation?. Earth Surf. Process. Landf. 2010, 35. 10.1002/esp.2091.
67. Ferguson R. River channel slope, flow resistance and gravel entrainment thresholds. Water Resour. Res. 2012, 48. 10.1029/2011WR010850.
68. Ferguson R. Reach-scale flow resistance. Treatise on Geomorphology, Fluvial Geomorphology 2013, vol. 9. Elsevier, New York, (Chapter 9.5). J. Schroder, W. Wohl (Eds.).
69. Ferro V., Baiamonte G. Flow velocity profiles in gravel-bed rivers. J. Hydraul. Eng. 1994, 120:60-80.
70. Ferro V., Pecoraro R. Incomplete self-similarity and flow velocity in gravel bed channels. Water Resour. Res. 2000, 36:2761-2769.
71. Finnigan J.J. Turbulent transport in flexible plant canopies. The Forest-Atmosphere Interaction 1985, 443-480. D Reidel Publishing Company, Dordrecht. B.A. Hutchinson, B.B. Hicks (Eds.).
72. Fischenich C. Robert Manning, A Historical Perspective. EMRRP Technical Notes Collection, ERDC TN-EMRRP-SR-10 2000, United States Army Engineer Research and Development Centre, Vicksberg, MS.
73. Flammer G.H., Tullis P., Mason E.S. Free surface, velocity gradient flow past hemisphere. J. Hydraul. Div. ASCE 1970, 96:1485-1502.
74. Francalanci S., Solari L., Toffolon M., Parker G. Do alternate bars affect sediment transport and flow resistance in gravel-bed rivers?. Earth Surf. Process. Landf. 2012, 37. 10.1002/esp.3217.
75. Gao P., Abrahams A. Bedload transport resistance in rough open-channel flows. Earth Surf. Process. Landf. 2004, 29. 10.1002/esp.1038.
76. Giménez-Curto L.A., Corniero Lera M.A. Oscillating turbulent flow over very rough surfaces. J. Geophys. Res. 1996, 101(C9):20,745-20,785.
77. Gomez B. Roughness of stable armoured gravel beds. Water Resour. Res. 1993, 29:3631-3642.
78. Gordon N.D., McMahon T.A., Finlayson B.L. Stream Hydrology: An Introduction for Ecologists 1992, John Wiley and Sons, Chichester.
79. Green J.C. Modelling flow resistance in vegetated streams: a review and development of new theory. Hydrol. Process. 2005, 19:1245-1259.
80. Green J.C. Choice of percentiles and axes to determine grain resistance. J. Hydraul. Eng. 2005, 131:1007-1010.
81. Griffiths G.A. Flow resistance in coarse-gravel bed rivers. J. Hydraul. Div. ASCE 1981, 107:899-918.
82. Hendrick R.R., Ely L.L., Papanicolaou A.N. The role of hydrologic processes and geomorphology on the morphology and evolution of sediment clusters in gravel-bed rivers. Geomorphology 2010, 114:483-496.
83. Heritage G.L., Milan D.J. Terrestrial laser scanning of grain roughness in a gravel-bed river. Geomorphology 2009, 113:4-11.
84. Hey R.D. Flow resistance in gravel-bed rivers. J. Hydraul. Div. ASCE 1979, 105:365-379.
85. Hey R.D. Bar form resistance in gravel-bed rivers. J. Hydraul. Eng. 1988, 114:1498-1508.
86. Hicks D.M., Mason P.D. Roughness characteristics of New Zealand Rivers 1991, DSIR Water Resources Survey, Wellington.
87. Hodge, R.A., 2007. Grain scale approaches to modelling and measuring fluvial sedimentology and bedload transport. Unpublished PhD Thesis, University of Cambridge.
88. Hodge R.A. Using simulated Terrestrial Laser Scanning to analyse errors in high-resolution scan data of irregular surfaces. ISPRS J. Photogramm. Remote Sens. 2010, 65:227-240.
89. Hodge R.A., Brasington J., Richards K. In situ characterization of grain-scale fluvial morphology using Terrestrial Laser Scanning. Earth Surf. Process. Landf. 2009, 34:954-968.
90. Hodge R.A., Brasington J., Richards K. Analysing laser-scanned digital terrain models of gravel bed surfaces: linking morphology to sediment transport processes and hydraulics. Sedimentology 2009, 56:2024-2043.
91. Jarrett R.D. Hydraulics of high-gradient streams. J. Hydraul. Eng. 1984, 110:1519-1539.
92. Jarrett R.D. Errors in slope-area computations of peak discharges in mountain streams. J. Hydrol. 1987, 96:53-67.
93. Jarrett R.D. Hydrologic and hydraulic research in mountain rivers. Water Resour. Bull. 1990, 26:419-429.
94. Järvelä J. Flow resistance in environmental channels: Focus on vegetation 2004, (PhD Thesis), Helsinki University of Technology Water Resources Publications, Helsinki, (TKK-VTR-10).
95. Johnson P.A. Uncertainty of hydraulic parameters. J. Hydraul. Eng. 1996, 122:112-114.
96. Judd H.E., Peterson D.F. Hydraulics of large bed element channels. Report PRWG 17-6 1969, Utah Water Research Laboratory, Utah State University, Logan.
97. Katul G., Wiberg P., Albertson J., Hornberger G. A mixing layer theory for flow resistance in shallow streams. Water Resour. Res. 2002, 38. 10.1029/2001WR000817.
98. Kay M. Practical Hydraulics 1998, Routledge, London.
99. Kean J.W., Smith J.D. Generation and verification of theoretical rating curves in the Whitewater River Basin, Kansas. J. Geophys. Res. 2005, 110. 10.1029/2004JF000250.
100. Kean J.W., Smith J.D. Form drag in rivers due to small-scale natural topographic features: 1. Regular sequences. J. Geophys. Res. 2006, 111. 10.1029/2006JF000467.
101. Kean J.W., Smith J.D. Form drag in rivers due to small-scale natural topographic features: 2. Irregular sequences. J. Geophys. Res. 2006, 111. 10.1029/2006JF000490.
102. Keulegan G.H. Laws of turbulent flow in open channels. J. Res. Nat. Bur. Stand. 1938, 21:707-741.
103. Kidson R., Richards K.S., Carling P.A. Reconstructing the ca. 100year flood in Northern Thailand. Geomorphology 2005, 70:279-295.
104. King J., Nickling W.G., Gillies J.A. Investigations of the law-of-the-wall over sparse roughness elements. J. Geophys. Res. 2008, 113. 10.1029/2007JF000804.
105. Kironoto B.A., Graf W.H. Turbulence characteristics in rough uniform open channel flow. Proceedings Institute Civil Engineers: Water, Maritime and, Energy 1994, 106:333-344.
106. Koloseus H.K., Davidian J. Roughness-concentration effects on flow over hydrodynamically rough surfaces. United States Geological Survey Water-Supply Paper 1592D 1966.
107. Lane S.N. Roughness-time for a re-evaluation?. Earth Surf. Process. Landf. 2005, 30:251-253.
108. Lang S., Ladson T., Anderson B. A review of empirical equations for estimating stream roughness and their application to four streams in Victoria. Aust. J. Water Resour. 2004, 8:69-82.
109. Laronne J.B., Carson M.A. Interrelationships between bed norphology and bed-material transport for a small, gravel-bed channel. Sedimentology 1976, 23:67-85.
110. Lawrence D.S.L. Macroscale surface roughness and frictional resistance in overland flow. Earth Surf. Process. Landf. 1997, 22:365-382.
111. Lawrence D.S.L. Hydraulic resistance in overland flow during partial and marginal surface inundation: experimental observations and modelling. Water Resour. Res. 2000, 36:2381-2393.
112. Lee A.J., Ferguson R.I. Velocity and flow resistance in step-pool streams. Geomorphology 2002, 46:59-71.
113. Leopold L.B., Wolman M.G. River channel patterns-braided, meandering and straight. United States Geological Survey Professional Paper, 292B 1957.
114. Leopold L.B., Bagnold R.A., Wolman M.G., Brush L.M.Jr Flow resistance in sinuous or irregular channels. United States Geological Survey Professional Paper 282D 1960.
115. Leopold L.B., Wolman M.G., Millar J.P. Fluvial Processes in Geomorphology 1964, W.H. Freeman and Company, San Francisco.
116. Limerinos J.T. Determination of the Manning coefficient from measured bed roughness in natural channels. United States Geological Survey Water Supply Paper 1898B 1970.
117. López R., Barragán J. Equivalent roughness of gravel-bed rivers. J. Hydraul. Eng. 2008, 134:847-851.
118. López R., Barragán J., Colomer M.A. Flow resistance equations without explicit estimation of the resistance coefficient for coarse-grained rivers. J. Hydrol. 2007, 338:113-121.
119. Manga M., Kirchner J.W. Stress partitioning in streams with large woody debris. Water Resour. Res. 2000, 36:2373-2379.
120. Mao L., Cooper J.R., Frostick L.E. Grain size and topographical differences between static and mobile armoured layers. Earth Surf. Process. Landf. 2011, 36:1321-1334.
121. Marchand J.P., Jarrett R.D., Jones L.L. Velocity profile, water-surface slope, and bed material size for selected streams in Colorado. United States Geological Survey Open-File Report 84-733 1984.
122. Marcus W.A., Roberts K., Harvey L., Tackman G. An evaluation of methods for estimating Manning's n in small mountain streams. Mt. Res. Dev. 1992, 12:227-239.
123. Marion A., Tait S.J., McEwan I.K. Analysis of small-scale gravel-bed topography during armouring. Water Resour. Res. 2003, 39. 10.1029/2003WR002367.
124. Marusic I., McKeon B.J., Monkewitz P.A., Nagib H.M., Smits A.J., Sreenivasan K.R. Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 2010, 22. 10.1063/1.3453711.
125. Massey B.S. Mechanics of Fluids 1983, Van Nostrand Reinhold (UK), Wokingham. 5th edition.
126. McCuen R.H., Knight Z. Fuzzy analysis of slope-area discharge estimates. J. Irrig. Drain. Eng. 2006, 132:64-69.
127. Middleton G.V., Southard J.B. Mechanics of Sediment Movement. Lecture notes for Short Course No. 3. Eastern Section of the Society of Economic Paleontologists and Mineralogsists, Binghampton, New York 1984, 10.2110/scn.84.03.
128. Middleton G.V., Wilcock P.R. Mechanics in the Earth and Environmental Sciences 1994, Cambridge University Press, Cambridge.
129. Millar R.G. Grain and form resistance in gravel-bed rivers. J. Hydraul. Res. 1999, 37:303-312.
130. Montgomery D.R., Buffington J.M. Channel reach morphology in mountain drainage basins. Bull. Geol. Soc. Am. 1997, 109:596-611.
131. Moody L.F. Friction factors for pipe flow. Trans. Am. Soc. Mech. Eng. 1944, 66:671-684.
132. Morris H.M. A new concept of flow in rough conduits. Trans. Am. Soc. Civ. Eng. 1955, 120:373-410.
133. Munson B.R., Young D.F., Okiishi T.H., Huebsch W.W. Fundamentals of Fluid Mechanics 2009, John Wiley and Sons, Chichester. Sixth edition.
134. Naden P., Brayshaw A.C. Bedforms in gravel-bed rivers. IBG Special Publication 18 1987, 249-271. Blackwell, Oxford. K.S. Richards (Ed.).
135. Nelson J.M., Emmett W.W., Smith J.D. Flow and sediment transport in rough channels. Proceedings of the Fifth Federal Interagency Sedimentation Conference 1991, (Chapter R: 55-62). S. Fan, Y. Kuo (Eds.).
136. Nezu I., Nakagawa H. Turbulence in Open-Channel Flows 1993, Balkema, Rotterdam.
137. Nikora V. Hydrodynamics of gravel-bed rivers: scale issues. Gravel-Bed Rivers VI: From Process Understanding to River Restoration 2008, 61-81. Elsevier Science, London. H. Habersack, H. Piegay, M. Rinaldi (Eds.).
138. Nikora V., Walsh J. Water-worked gravel-surfaces: high-order structure functions at the particle scale. Water Resour. Res. 2004, 40. 10.1029/2004WR003346.
139. Nikora V., Goring D., Biggs B.J.F. On gravel-bed roughness characterisation. Water Resour. Res. 1998, 34:517-527.
140. Nikora V., Goring D., McEwan I., Griffiths G. Spatially averaged open-channel flow over rough bed. J. Hydraul. Eng. 2001, 127:123-133.
141. Nikora V., McEwan I., Mclean S., Coleman S., Pokrajac D., Walters R. Double averaging concept for rough bed open-channel and overland flows: theoretical background. J. Hydraul. Eng. 2007, 133:873-883.
142. Nikora V., Mclean S., Coleman S., Pokrajac D., McEwan I., Campbell L., Aberle J., Clunie D., Koll K. Double averaging concept for rough bed open-channel and overland flows: applications. J. Hydraul. Eng. 2007, 133:884-895.
143. Nikuradse J. Stromungsgesetz in rauhren rohren, vDI Forschungshefte361 (English translation: Laws of flow in rough pipes). Tech. Rep. NACA Technical Memorandum 1292 1933, National Advisory Commission for Aeronautics, Washington, DC, USA, (1950).
144. Nitsche M., Rickenmann D., Kirchner J.W., Turowski J.M., Badoux A. Macroroughness and variations in reach-averaged flow resistance in steep mountain streams. Water Resour. Res. 2012, 48:W12518. 10.1029/2012WR012091.
145. Nyander A., Addison P.S., McEwan I., Pender G. Analysis of river bed surface roughnesses using 2D wavelet transform-based methods. Arab. J. Sci. Eng. 2003, 28:107-122.
146. O'day C.M., Phillips J.V. Computed roughness coefficients for Skunk Creek above Interstate 17, Maricopa County, Arizona. United States Geological Survey, Water Resources Investigations Report 99-4248 2000.
147. Papanicolaou A.N., Tsakiris A.G., Strom K.B. The use of fractals to quantify the morphology of cluster microforms. Geomorphology 2012, 139:91-108.
148. Parker G. Transport of gravel and sediment mixtures. Sedimentation Engineering: Processes, Measurements, Modelling and Practice 2008, 165-252. American Society of Civil Engineers, Reston, Virginia. M.H. Garcia (Ed.).
149. Parker G., Peterson A.W. Bar resistance of gravel-bed streams. J. Hydraul. Div. ASCE 1980, 106:1559-1575.
150. Partridge J., Baker V.R. Palaeoflood hydrology of the Salt River, Arizona. Earth Surf. Process. Landf. 1987, 12:109-125.
151. Phillips J.V., Ingersoll T.L. Verification of roughness coefficients for selected natural and constructed stream channels in Arizona. United States Geological Survey Professional Paper 1584 1998.
152. Phillips J.V., McDoniel D., Capesius J.P., Asquith W. Method to estimate effects of flow-induced vegetation changes on channel conveyance of streams in central Arizona. USGS Water-Resources Investigations Report 98-4040 1998.
153. Prestegaard K. Bar resistance in gravel bed streams at bankfull stage. Water Resour. Res. 1983, 19:472-476.
154. Qin J., Zhong D., Wang G., Ng S.L. On characterisation of the imbrication of armoured gravel surfaces. Geomorphology 2012, 159:116-124.
155. Quick M.C. Reliability of flood discharge estimates. Can. J. Civ. Eng. 1991, 18:624-630.
156. Raupach M.R., Shaw R.H. Averaging procedures for flow within vegetation canopies. Bound.-Layer Meteorol. 1982, 22:79-90.
157. Raupach M.R., Finnigan J.J., Brunet Y. Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Bound.-Layer Meteorol. 1996, 78:351-382.
158. Recking A., Frey P., Paquier A., Belleudy P., Champagne J.Y. Feedback between bed load transport and flow resistance in gavel and cobble bed rivers. Water Resour. Res. 2008, 44. 10.1029/2007WR006219.
159. Recking A., Frey P., Paquier A., Belleudy P., Champagne J.Y. Bed-load transport flume experiments on steep slopes. J. Hydraul. Eng. 2008, 134. 10.1061/(ASCE)0733-9429(2008)134:9(1302).
160. Richards K.S. Rivers: Form and Process in Alluvial Channels 1982, Methuen, London.
161. Richards K.S., Clifford N. Fluvial geomorphology: structured beds in gravelly rivers. Prog. Phys. Geogr. 1991, 15:407-422.
162. Rickenmann D. Hyperconcentrated flow and sediment transport at steep slopes. J. Hydraul. Eng. 1991, 117:1419-1439.
163. Rickenmann D., Recking A. Evaluation of flow resistance in gravel-bed rivers though a large field data set. Water Resour. Res. 2011, 47. 10.1029/2010WR009793.
164. Robert A. Statistical properties of sediment bed profiles in alluvial channels. Math. Geol. 1988, 20:205-225.
165. Robert A. Boundary roughness in coarse-grained channels. Prog. Phys. Geogr. 1990, 14:42-70.
166. Robert A. Fractal properties of simulated bed profiles in coarse-grained channels. Math. Geol. 1991, 23:367-382.
167. Rouse H. Critical analysis of open-channel flow resistance. J. Hydraul. Div. ASCE 1965, 91:1-25.
168. Rupp D.E., Smart G.M. Comment on "Flow resistance equations without explicit estimation of the resistance coefficient for coarse-grained rivers" by Raúl López, Javier Barragán, and M. Àngels. J. Hydrol. 2007, 346:174-178. 10.1016/j.jhydrol.2007.08.024.
169. Sayre W.W., Albertson M.L. Roughness spacing in rigid open channels. Trans. Am. Soc. Civ. Eng. 1963, 128:343-372.
170. Simmons C.T. Henry Darcy (1803-1858): immortalised by his scientific legacy. Hydrogeol. J. 2008, 16:1023-1038.
171. Slattery M. Geomorphology: A Collection of Images. CD-Rom published by the International Association of Geomorphologists 2000.
172. Smart G.M., Duncan M.J., Walsh J.M. Relatively rough flow resistance equations. J. Hydraul. Eng. 2002, 128:568-577.
173. Song T., Chiew Y.M., Chin C.O. Effect of bed-load movement on flow friction factor. J. Hydraul. Eng. 1998, 124:165-175.
174. Strickler A. Contributions to the question of a velocity formula and roughness data for streams, channels and closed pipelines. W. M. Keck Lab of Hydraulics and Water Resources, Calif. Inst. Tech., Pasadena, Calif. January 1981 1923, 16. Mitteilungen des Eidgenossischen Amtes fur Wasserwirtschaft, Bern, Switzerland, (Translation T-10). T. Roesgan, W.R. Brownie (Eds.).
175. Thompson S.M., Campbell P.L. Hydraulics of a large channel paved with boulders. J. Hydraul. Eng. 1979, 17:341-354.
176. Thorne C.R., Zevenbergen L.W. Estimating mean velocity in mountain rivers. J. Hydraul. Eng. 1985, 111:612-624.
177. Tillery A.C., Phillips J.V., Capesius J.P. Potential errors associated with stage-discharge relations for selected stream-flow gauging stations, Maricopa County, Arizona. USGS Water-Resources Investigations Report 00-4224 2001.
178. van Rijn L.C. Equivalent roughness of alluvial bed. J. Hydraul. Div. ASCE 1982, 108:1215-1218.
179. Vogel S. Life in Moving Fluids: The Physical Biology of Flow 1981, Princeton University Press, New Jersey.
180. Wahl K.L. Bias in regression estimate of Manning's n. Proceedings ASCE Hydraulic Engineering '94 Conference, August 1-5, Buffalo, New York 1994, 727-731. American Society of Civil Engineers, New York. G.V. Cotroneo, R.R. Rumer (Eds.).
181. Warner J.C., Brunner G.W., Wolfe B.C., Piper S.S. HEC-RAS River Analysis System Applications Guide. Report CPD-70 2009, 29. US Army Corps of Engineers, Davis, CA.
182. Webb R.H., Jarrett R.D. One dimensional estimation techniques for discharges of palaeofloods and historical floods. Ancient Floods, Modern Hazards: Principles and Applications of Paleoflood Hydrology 2002, 111-125. American Geophysical Union, Washington DC. P.K. House (Ed.).
183. Whatmore S.J., Landstrom C. Mannning's n-putting roughness to work. How Well Do Facts travel?: The Dissemination of Reliable Knowledge 2011, 111-135. Cambridge University Press, Cambridge. P. Howlett, M.S. Morgan (Eds.).
184. Whitaker S. Introduction to Fluid Mechanics 1968, Prentice Hall, Englewood Cliffs, New Jersey, (457pp.).
185. White F.M. Fluid Mechanics 1994, McGraw-Hill, New York. 3rd edition.
186. Whiting P.J., Dietrich W.E. Convective accelerations and boundary shear stress over a channel bar. Water Resour. Res. 1991, 27:783-796.
187. Wiberg P., Smith J.D. Velocity distribution and bed roughness in high gradient streams. Water Resour. Res. 1991, 27:825-838.
188. Wilcock P., Pitlick J., Cui Y. Sediment Transport Primer: Estimating Bed-Material Transport in Gravel-bed Rivers. United States Department of Agriculture Forest Service, Rocky Mountain Research Station, General Technical Report, RMRS-GTR-226 2009.
189. Wilcox A.C., Wohl E.E. Flow resistance dynamics in step-pool channels: 1. Large woody debris and controls on total resistance. Water Resour. Res. 2006, 42. 10.1029/2005WR004277.
190. Wilcox A.C., Wohl E.E. Field measurements of three-dimensional hydraulics in a step-pool channel. Geomorphology 2007, 83:215-231.
191. Wilcox A.C., Nelson J.M., Wohl E.E. Flow resistance dynamics in step-;pool channels: 2. Partitioning between grain, spill and woody debris resistance. Water Resour. Res. 2006, 42. 10.1029/2005WR004278.
192. Wilcox A.C., Wohl E., Comiti F., Mao L. Hydraulics, morphology and energy dissipation in an alpine step-pool channel. Water Resour. Res. 2011, 47. 10.1029/2010WR010192.
193. Wilson N.R., Shaw R.H. A higher-order closure model for canopy flow. J. Appl. Meteorol. 1977, 16:1198-1205.
194. Wohl E.E., Ikeda H. The effect of roughness configuration on velocity profiles in an artificial channel. Earth Surf. Process. Landf. 1998, 23:159-169.
195. Wohl E.E., Thompson D.M. Velocity characteristics along a small step-pool channel. Earth Surf. Process. Landf. 2000, 25:353-367.
196. Yager E.M., Dietrich W.E., Kirchner J.W., McArdell B.W. Prediction of sediment transport in step-pool channels. Water Resour. Res. 2012, 48. 10.1029/2011WR010829.
197. Yen B.C. Hydraulic resistance in open channels. Channel Flow Resistance: Centennial of Manning's Formula 1991, 1-135. Water Resource Publications, Highlands Ranch, Colorado. B.C. Yen (Ed.).
198. Yochum S.E., Bledsoe B.P., David G.C.L., Wohl E. Velocity prediction in high-gradient channels. J. Hydrol. 2012, 424:94-98. 10.1016/j.jhydrol.2011.12.031.
199. Zimmermann A. Flow resistance in steep streams: an experimental study. Water Resour. Res. 2010, 46. 10.1029/2009WR007913.
200. Zimmermann A., Church M. Channel morphology, gradient profiles and bed stresses during flood in a step-pool channel. Geomorphology 2001, 40:311-327. 10.1016/S0169-555X(01)00057-5.