Monograph

Theoretical Morphodynamics: Straight Channels

  • Giovanni Seminara,
  • Stefano Lanzoni,
  • Nicoletta Tambroni,

This monograph presents the mechanistic foundations of the theory of Morhodynamics, a discipline that investigates the shape of the erodible boundary of natural water bodies. We focus on the fluvial Morphodynamics of straight erodible channels, providing the basis for subsequent extensions to meandering rivers (treated in the companion monograph 2 of this series) and braided rivers. We present basic notions on the Mechanics of Turbulent Flows and Sediment Transport in straight open channels with mobile beds. We then investigate their morphodynamic equilibrium and its instability, that leads to the formation of a variety of bedforms observed in natural rivers. In particular, fluvial bars will deserve special attention as the fundamental building block of large scale fluvial patterns.

  • Keywords:
  • Morphodynamics,
  • rivers,
  • sediment transport,
  • bedforms,
  • bars,
+ Show more
Purchase

Giovanni Seminara

University of Genoa, Italy - ORCID: 0000-0002-0360-2029

Stefano Lanzoni

Universiyty of Padoa, Italy - ORCID: 0000-0002-6621-2386

Nicoletta Tambroni

University of Genoa, Italy - ORCID: 0000-0002-2952-7290

Giovanni Seminara Master in Civil Engineering (University of Genoa), PhD in Applied Math (Imperial College, London), Professor Emeritus at the University of Genoa and Socio Nazionale of Accademia Nazionale dei Lincei.

Stefano Lanzoni Master in Hydraulic Engineering (University of Padua), PhD in Hydrodynamics (joint program, Universities of Genoa, Florence, Padua and Trent), Professor of Fluid Mechanics at the University of Padua.

Nicoletta Tambroni Master in Civil Engineering (University of Genoa), PhD in Fluid dynamics and Environmental Processes in Engineering (University of Genoa), Associate Professor of Fluid Mechanics at the University of Genoa.
  1. Abbott, J.E. and Francis, R.D. (1977) Saltation and suspension Trajectories of solid grains in a water stream Philos. Trans. R. Soc. London A., 284: 225-254
  2. Abramowitz, M. and I. Stegun (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables https://archive.org/details/handbookofmathe000abra) Abramowitz and Stegun. New York: Dover. ISBN 978-0-486-61272-0., Chapter 5
  3. Adachi, S. (1967) A theory of stability of streams. Proc. 12th Congr. IAHR, Fort Collins, Colorado, 1:338-343
  4. Adami, L. (2016) Multi-decadal morphodynamics of alternate bars in channelized rivers: a multiple perspective. Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Hydrodynamics and Environmental Modeling. University of Trent
  5. Adami, L., W. Bertoldi, and G. Zolezzi (2016). Multidecadal dynamics of alternate bars in the Alpine Rhine River, Water Resour. Res., 52, 8938-8955 DOI: 10.1002/2015WR018228
  6. Allen, J.R.L., (1971a), Transverse erosional marks of mud and rock: Their physical basis and geological significance. Sedimentary Geology, 5, 167-385
  7. Allen, J.R.L., (1971b), Bed forms due to mass transfer in turbulent flows: A kaleidoscope of phenomena. Journal of Fluid Mechanics, 49, 49-63
  8. Amsler, M. A., and García, M. H. (1997). Discussion of sand dune geometry of large rivers during floods by P. Y. Julien and G. J. Klaassen, Journal of Hydraulic Engineering, ASCE, 123(6),582-584
  9. Amsler, M. L., and Schreider, M. I. (1999). Dune height prediction at floods in the Paraná River, Argentina. River Sedimentation: theory and applications, A. W. Jayewardena, J.H.W. Lee and Z. Y. Wang, eds., A. A. Balkema. Rotterdam, pp. 615-620
  10. Ancey, C., Davison, A. C., Bohm, T., Jodeau, M., and Frey, P. (2008). Entrainment and motion of coarse particles in a shallow water stream down a steep slope. Journal of Fluid Mechanics, 595, 83-114 DOI: 10.1017/S0022112007008774
  11. Ancey, C. (2020a). Bedload transport: a walk between randomness and determinism. Part 1. The state of the art. Journal of Hydraulic Research, 58(1), 1-17 DOI: 10.1080/00221686.2019.1702594
  12. Ancey, C. (2020b). Bedload transport : a walk between randomness and determinism. Part 2. Challenges and prospects. Journal of Hydraulic Research, 58(1), 18-33 DOI: 10.1080/00221686.2019.1702595
  13. Anderson, R.S. and Haff, P.K. (1988) Simulation of eolian saltation Science, 241, 820-823
  14. Andrews, E. D. (1980). Effective and bankfull discharges of streams in the Yampa river basin,Colorado and Wyoming. Journal of Hydrology, 46(34):311-330
  15. Aris, R. (1962), Vector, Tensors, and the Basic Equations of Fluid Mechanics, Dover Publications Inc., New York, 300 pp.
  16. Armanini, A. (1995). Non-uniform sediment transport. Dynamics of the active layer. J. Hydr Res., 33(5), 611-622
  17. Armanini, A., and G. Di Silvio (1988). A one-dimensional model for the transport of a sediment mixture in non-equilibrium conditions, J. Hydraul. Res., 26(3), 275-292
  18. Armanini, A. and Di Silvio, G. (1988). A one-dimensional model for the transport of sediment mixture in non-equilibrium condition. J. Hydr. Res., Delft, The Netherlands, 26(3), 275-292
  19. ASCE Task Committee on Hydraulics, Bank Mechanics, and Modeling of River Width Adjustment (1998), River Width Adjustment. I: Processes and Mechanics, Journal of Hydraulic Engineering (ASCE), 124(9), 881-899
  20. Ashida, K. and Michiue, M. (1972) Study on hydraulic resistance and bedload transport rate in alluvial streams Trans., Japanese Society of Civil Engineering, 206, 59-69
  21. Ashida, K. and Shiomi, Y., (1966) Study on the hydraulic behaviours of meander in channels Disaster Prevention Research Institute Annals, Kyoto Univ., 9:457-477
  22. Ashmore, P. E. (1982) Laboratory modelling of gravel bed stream morphology. Earth Surf. Proc Landforms 7, 201-225
  23. Ashmore, P. E. (1991) How do gravel-bed rivers braid? Can. J. Sci. 28, 326-341
  24. Aubert G., V. J. Langlois and P. Allemand (2016), Bedrock incision by bedload: insights from direct numerical simulations, Earth Surf. Dynam., 4, 327-342. DOI: 10.5194/esurf-4-327-2016
  25. Auton, T. R. (1987) The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183:199
  26. Baar, A. W., de Smit, J., Uijttewaal, W. S. J., and Kleinhams, M. G. (2018). Bed Slopes in Rotating Annular Flume Experiments. Water Resources Research, 54, 19-45 DOI: 10.1002/2017WR020604
  27. Bagchi, P. and S. Balachandar (2002). Effect of free rotation on the motion of a solid sphere at moderate Re. Phys. Fluids, 14:2719-2737
  28. Bangold, R.A. (1941) Physics of blown sand (Reprinted 1954) London: Methuen
  29. Bagnold, R.A. (1956) The flow of cohesionless grains in fluids Phil. Trans. Roy. Soc. Lond A225: 49-63
  30. Bagnold, R. A. (1966) An approach to the sediment transport problem from general physics Prof. Paper 422-1, U. S. Geol. Surv
  31. Bagnold, R.A. (1973) The nature of saltation and of â 'bed-load' transport in water Proc. R. Soc London A, 332, 473-504
  32. Balachandar, S. (2009). A scaling analysis for point-particle approaches to turbulent multiphase flows. Int. J. Multiphase Flow 35:801-10
  33. Balachandar, S. and J. K. Eaton (2010). Turbulent Dispersed Multiphase Flow. Annu. Rev. Fluid Mech., 42, 111-33
  34. Bankert, A. R. and Nelson, P. A. (2018) Alternate bar dynamics in response to increases and decreases of sediment supply, Sedimentology 65, 702-720 DOI: 10.1111/sed.12400
  35. Basset, A. B. (1888). A Treatise on Hydrodynamics, Vol. 2, Ch. 22, Deighton, Bell and Co., Cambridge, England
  36. Batchelor G. K. (1967) An Introduction to Fluid Dynamics. Cambridge, UK: Cambridge Univ Press
  37. Batchelor, G. K. (1970). An Introduction to Fluid Dynamics, Cambridge, University Press, Massachusetts
  38. Batchelor, G. K. (1988) A new theory of the instability of a uniform fluidized bed. J. Fluid Mech 193, 75-110
  39. Beer, A. R. and J. M. Turowski (2015) Bedload transport controls bedrock erosion under sediment-starved conditions, Earth Surf. Dynam., 3, 291-309
  40. Bers, A. (1975). Linear waves and instabilities. In Physique des Plasmas, ed. C DeWitt, J Peyraud, pp. 117-215. New York: Gordon & Breach
  41. Bers, A. (1983). Space-time evolution of plasma instabilities-absolute and convective. In Handbook of Plasma Physics, ed. M . N. Rosenbluth, R. Z. Sagdeev, I : 451-517. Amsterdam: North- Holland
  42. Bertagni, M. B. and C. Camporeale (2018) Finite Amplitude of Free Alternate Bars With Suspended Load, Water Resources Research, 54, 9759-9773 DOI: 10.1029/2018WR022819
  43. Bertagni M. B., Perona P., Camporeale C. (2018) Parametric transitions between bare and vegetated states in water-driven patterns. Proceedings of the National Academy of Sciences 115(32): 8125-8130 DOI: 10.1073/pnas.1721765115
  44. Bertoldi, W., A. Siviglia, S. Tettamanti, M. Toffolon, D. Vetsch, and S. Francalanci (2014), Modeling vegetation controls on fluvial morphological trajectories, Geophys. Res. Lett., 41, 7167-7175 DOI: 10.1002/2014GL061666
  45. Best, J. (2005). The fluid dynamics of river dunes: A review and some future research directions Journal of Geophysical Research, 110(F04S02), 1-21. DOI: 10.1029/2004JF000218
  46. Bittner, L. (1994) River bed response to channel width variation: Theory and experiments. Thesis submitted in partial fulfillment of the requirements of the degree of Master of Science Graduate School of Civil Engineering. University of Illinois at Urbana-Champaign
  47. Blom, A., J. S. Ribberink, and G. Parker (2008), Vertical sorting and the morphodynamics of bed form-dominated rivers: A sorting evolution model, J. Geophys. Res., 113, F01019, DOI: 10.1029/2006JF000618
  48. Blondeaux, P. and Seminara, G. (1983) Bed topography and instabilities in sinuous channels. In Proc. ASCE Rivers ’83, New Orleans, pp. 747-758
  49. Blondeaux, P., and G. Seminara (1985), A unified bar-bend theory of river meanders, J. Fluid Mech., 157:449-479
  50. Blondeaux, P. and G. Vittori, (2023), Sea waves and small scale bedforms, Monograph Series on Morphodynamics of Sedimentary Patterns, Ed. Genova University Press
  51. Blondeaux, P., Colombini, M., Seminara, G. and G. Vittori, (2018), Introduction to Morphodynamics of Sedimentary Patterns, Monograph Series on Morphodynamics of Sedimentary Patterns, Ed. Genova University Press
  52. Blondeaux, P., Brocchini, M. and G. Vittori, (2023), Waves, currents and bedforms in the nearshore region, Monograph Series on Morphodynamics of Sedimentary Patterns, Ed Genova University Press
  53. Blumberg, P. N. and R. L. Curl (1974), Experimental and theoretical studies of dissolution roughness. Journal of Fluid Mechanics, 5, 735-742
  54. Bohorquez, P., and Ancey, C. (2015). Stochastic-deterministic modeling of bed load transport in shallow water flow over erodible slope: Linear stability analysis and numerical simulation Advances in Water Resources, 83, 36-54
  55. Bolla Pittaluga, M., and G. Seminara (2003), Depth-integrated modelling of suspended sediment transport, Water Resour. Res., 39(5), 1137 DOI: 10.1029/2002WR001306
  56. Bolla Pittaluga M., Luchi R., Seminara G. (2014a) On the equilibrium profile of river beds. J Geophys. Res. Earth Surf., 119(2), 317-32 DOI: 10.1002/2013JF002806
  57. Bolla Pittaluga M., Tambroni N., Canestrelli A., Slingerland R., Lanzoni S., Seminara G. (2014b) Where river and tide meet: The morphodynamic equilibrium of alluvial estuaries. J. Geophys Res. Earth Surf., 120, 75–94, DOI: 10.1002/2014JF003233
  58. Bonnefille, R. (1963). Essais de synthese des lois de debut d’entrainment des sediments sous l’action d’un courant en regime uniform. Bulletin du Centre de Recherche et d’Essais de Chatou, 5, France (in French)
  59. Borisenko, A.I., Tarapov, I.E. (1968), Vector and Tensors Analysis With Applications, Dover Publications Inc., New York, 257 pp
  60. Bourke, M. and H. Viles (2007) A Photographic Atlas of Rock Breakdown Features in Geomorphic Environments, Edited by Mary Bourke and Heather Viles, Planetary Science Institute
  61. Boussinesq, V. J. (1885). Sur la resistance qu’oppose un liquide indéfini en repos sans pesanteur, au mouvement varié d’une sphère solide qu’il mouille sur toute sa surface, quand les vitesses restent bien continues et assez faibles pour que leurs carrés et produits soitent négligeables., Comptes Rendu, Acad. Sci., 100:935-937
  62. Boussinesq, V. J. (1877) Essai sur la théorie des eaux courantes (Treatise on the theory of flowing water), Mémoires présentés par divers savants à l’Académie des sciences 23 (1877) 1-660 (in French)
  63. Bowen, R. M., (1971) Continuum Physics II, A. C. Eringen, Ed. Academic Press, NY.
  64. Brice, J. C. (1984), Planform properties of meandering rivers, Keynote paper, in River Meandering, Proceedings of the Conference Rivers, ’83 New Orleans, LA, 24-26 October 1983, edited by C. M. Elliott, pp. 1-15, American Society of Civil Engineers, N. Y.
  65. Bridge J. S. and Dominic D. F. (1984) Bed Load Grain Velocities and Sediment Transport Rates, Water Resources Research 20(4):476-490 DOI: 10.1029/WR020i004p00476
  66. Briggs, R. J. (1964). Electron-Stream Interaction With Plasmas. Cambridge, Mass: MIT Press
  67. Brownlie, W.R., (1981) Prediction of flow depth and sediment discharge in open channel. W.M Laboratory Report No KH-R-43A
  68. Brownlie, W. R. (1983). Flow depth in sand-bed channels. Journal of Hydraulic Engineering, 109(7), 959-990
  69. Buffington, J. M. (1999). The legend of A. F. Shields. Journal of Hydraulic Engineering ASCE, 125(4): 376-387 ISSN 0733-9429/99/0004-0376-0387
  70. Callander, R. A. (1969) Instability and river channels. J . Fluid Mech. 36:465
  71. Carling, P. A., Williams, J. J., Golz, E., and Kesley, A. D. (2000) The morphodynamics of fluuvial sand dunes in the River Rhine, near Mainz , Germany. II. Hydrodynamics and sediment transport. Sedimentology, 47, 253-278
  72. Carling, P. A., J. Herget, J. K. Lanz, K. Richardson and A. Pacifici (2009) Channel-scale erosional bedforms in loose granular material and in bedrock: character, processes and implications In: Megaflooding on Earth and Mars, ed. Devon M. Burr, Paul A. Carling and Victor R Baker. Cambridge University Press.
  73. Carrier GF. (1958). Shock waves in a dusty gas. J. Fluid Mech. 4:376-82
  74. Carrier, G. F., Krook M. and C. E. Pearson (2005) Functions of a Complex Variable: Theory and Technique, SIAM
  75. Celik, I. and Rodi, W. (1984). Simulation of free-surface effects in turbulent channel flows Physicochemichal Hydrodynamics, 5, 217-228
  76. Celik, I., and Rodi, W. (1988). Modeling suspended sediment transport in non-equilibrium situations. J. Hydr. Engrg., ASCE, 114(10), 1157-1191
  77. Chang H., Simons, B. D. and Woolhiser, D. A. (1971) Flume experiments on alternate bar formation. J . Waterways, Proc. A.S.C.E. 97 (WW l), 155
  78. Charru, F. (2006) Selection of the ripple length on a granular bed sheared by a liquid flow. Phys Fluids, 18 (12), 121508
  79. Charru, F., Andreotti, B. and Claudin, P. (2013) Sand ripples and dunes. Annu. Rev. Fluid Mech. 45 (1), 469–493
  80. Chatanantavet, P., and G. Parker (2008), Experimental study of bedrock channel alluviation under varied sediment supply and hydraulic conditions, Water Resour. Res., 44, W12446 DOI: 10.1029/2007WR006581
  81. Chatanantavet, P., and G. Parker (2009), Physically based modeling of bedrock incision by abrasion, plucking, and macroabrasion, J. Geophys. Res., 114, F04018 DOI: 10.1029/2008JF001044
  82. Chatanantavet, P., K. X. Whipple, M. Adams, and M. P. Lamb (2013), Experimental study on coarse grain saltation dynamics in bedrock channels, J. Geophys. Res. Earth Surf., 118, 1161-1176, DOI: 10.1002/jgrf.20053
  83. Chavarrías, V., Schielen, R., Ottevanger, W. and A. Blom (2019) Ill posedness in modelling two-dimensional morphodynamic problems: effects of bed slope and secondary flow, J. Fluid Mech., 868, 461-500 DOI: 10.1017/jfm.2019.166
  84. Chézy , A. (1776). Formule pour trouver la vitesse de l’eau conduit dans une rigole donnée Dossier 847(MS 1915) of the manuscript collection of the École National des Ponts et Chaussées, Paris. Reproduced in: Mouret, G. (1921). Antoine Chézy: histoire d’une formule d’hydraulique. Annales des Ponts et Chaussées 61,165-269
  85. Choi, H., Moin, P., and Kim, J. (1993). Direct numerical simulation of turbulent flow over riblets Journal of Fluid Mechanics, 255, 503-539. DOI: 10.1017/S0022112093002575
  86. Church, M., and S. P. Rice (2009), Form and growth of bars in a wandering gravel-bed river, Earth Surf. Processes Landforms, 34(10), 1422-1432 DOI: 10.1002/esp.1831
  87. Clift, R., Grace, J. R. and M. E. Weber (1978). Bubbles, Drops and Particles. Academic, New York
  88. Coddington, E. A. and Levinson, N. (1955) Theory of Ordinary Differential Equations. McGraw- Hill
  89. Coleman N. L. (1967) A theoretical and experimental study of drag and lift forces acting on a sphere resting on a hypothetical stream bed. Proceedings of 12th IAHR Congress, vol 3 Fort Collins, 185-192
  90. Coleman, N. L. (1969). A new examination of sediment suspension in open channels. J. Hydr Res., 7(1), 67-82
  91. Coles, D. (1956). The law of the wake in the turbulent boundary layer. J. Fluid Mech.1, 191-226
  92. Colombini, M. (1993), Turbulence driven secondary flows and the formation of sand ridges, J Fluid Mech., 254, 701-719 DOI: 10.1017/S0022112093002319
  93. Colombini, M. (2004), Revisiting the linear theory of sand dune formation, J. Fluid Mech. vol 502, pp. 1–16
  94. Colombini, M and Parker, G. (1995), Longitudinal streaks, J . Fluid Mech. (1995), 304, 161-183
  95. Colombini, M., and M. Tubino, (1991) Finite-amplitude free bars: A fully nonlinear spectral solution, in Sand Transport in Rivers, Estuaries and the Sea, edited by R. Soulsby and R Bettess, pp. 163-169, A. A. Balkema, Brookfield
  96. Colombini, M., G. Seminara, and M. Tubino (1987), Finite-amplitude alternate bars, J. Fluid Mech., 181:213-232
  97. Copeland, R. R., Biedenharn, D. S., and C., F. J. (2000), Channel forming discharge. Technical Note ERDC/CHL CHETN-VIII-5, U.S. Army Corps of Engineers, Washington D.C., USA
  98. Cordier, F., P. Tassi, N. Claude, A. Crosato, S. Rodrigues, D. Pham Van Bang (2019), Numerical study of alternate bars in alluvial channels with nonuniform sediment, Water Resources Research, 55 (4), 2976-3003, DOI: 10.1029/2017WR022420
  99. Crosato, A., E. Mosselman, F. Beidmariam Desta, and W. S. J. Uijttewaal (2011), Experimental and numerical evidence for intrinsic nonmigrating bars in alluvial channels, Water Resour Res., 47, W03511 DOI: 10.1029/2010WR009714
  100. Crosato, A., F. B. Desta, J. Cornelisse, F. Schuurman, and W. S. J. Uijttewaal (2012), Experimental and numerical findings on the long-term evolution of migrating alternate bars in alluvial channels, Water Resour. Res., 48, W06524 DOI: 10.1029/2011WR011320
  101. Crosby, B. T. (2006) The Transient Response of Bedrock River Networks to Sudden Base Level Fall Submitted to the Department of Earth, Planetary Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Geology at the Massachussets Institute of Technology
  102. Crosby B. and K. X. Whipple (2006). Knickpoint initiation and distribution within fluvial networks: 236 waterfalls in the Waipaoa River, North Island, New Zealand. Geomorphology, 82, 16-38 DOI: 10.1016/j.geomorph.2005.08.023
  103. Crosby, B. T., K. X. Whipple, N. M. Gasparini, and C. W.Wobus (2007), Formation of fluvial hanging valleys: Theory and simulation, J. Geophys. Res., 112, F03S10 DOI: 10.1029/2006JF000566
  104. Crowe C., Sommerfeld M. and Y. Tsuji (2012). Multiphase Flows with Droplets and Particles Boca Raton, FL: CRC Press
  105. Curl, R.L., (1966), Scallops and flutes. Cave Research Group of Great Britain Transactions, 7, 121-160
  106. Darby, S. E., H. Q. Trieu, P. A. Carling, J. Sarkkula, J. Koponen, M. Kummu, I. Conlan, and J. Leyland (2010), A physically based model to predict hydraulic erosion of fine- grained riverbanks: The role of form roughness in limiting erosion, J. Geophys. Res., 115, F04003 DOI: 10.1029/2010JF001708
  107. Dean, R. B. (1974). Aero Rept. 74-11, Imperial College, London
  108. Dean, R. B. (1978). Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. J. Fluids Eng. Trans. ASME 100, 215-223
  109. Defina, A. (2003) Numerical experiments on bar growth. Water Resour. Res. 39, art. no. 1092
  110. Demeter, G. I., L. S. Sklar, and J. R. Davis (2005), The influence of variable sediment supply and bed roughness on the spatial distribution of incision in a laboratory bedrock channel, Eos Trans. AGU, Fall Meet. Suppl., H53D-0519
  111. de Saint-Venant, A. J. C. B. (1871) Théorie du mouvement non-permanent des eaux avec application aux crues des rivières et à l’introduction des marées dans leur lit (Theory of unsteady water flow, with application to river floods and tidal propagation in rivers), C. r hebd. séances Acad. sci. 73, 148-154; 73, 237-240 (in French)
  112. Dey, S. (2001). Bank profile of threshold channels: a simplified approach. Journal of Irrigation and Drainage Engineering, 127(3), 184–187
  113. Dietrich, W. E., (1982) Settling Velocity of Natural Particles, Water Resour. Res., 18(6) 1615-1626
  114. Dietrich, W. E., J. W. Kirchner, H. Ikeda, and F. Iseya (1989), Sediment supply and the development of the coarse surface layer in gravel-bedded rivers, Nature, 340, 215-217 DOI: 10.1038/340215a0
  115. Dietrich, W. E., P. A. Nelson, E. Yager, J. G. Venditti, M. P. Lamb, and L. Collins (2005), Sediment patches, sediment supply, and channel morphology, in River, Coastal and Estuarine Morphodynamics: RCEM 2005, edited by G. Parker and M. H. Garcia, pp. 79-90, Taylor and Francis, London
  116. Dinehart, R. L. (1989). Dune migration in a steep, coarse-bedded stream. Water Resources Research, 25(5), 911-923
  117. Diplas, P. and G. Vigilar (1992) Hydraulic Geometry of Threshold Channels, Journal of Hydraulic Engineering, 118(4), 597-614
  118. Doelman A. (1991) Finite dimensional models of the Ginzburg-Landau equation. Nonlinearity 4, 231-250
  119. Drake, T.G., Shreve, R.L., Dietrich, W.E., Whiting, P.J. and Leopold, L.B. (1988) Bedload transport of fine gravel observed by motionpicture photography J. Fluid Mech., 192, 193-217
  120. Drew, D.A., (1983). Mathematical modeling of two-phase flow. Annual Review of Fluid Mechanics, 15. Annual Reviews, Inc., pp. 261-291
  121. Dunne, K. B. J. and Jerolmack, D. J. (2020). What sets river width? Science Advances, 6(41), 1-9 DOI: 10.1126/sciadv.abc1505
  122. Duran, O., Andreotti, B., and Claudin, P. (2012) Numerical simulation of turbulent sediment transport, from bed load to saltation, Phys. Fluids, 24, 103306, DOI: 10.1063/1.4757662
  123. Durbin, P.A. and Pettersson Reif, B.A. (2011) Statistical theory and modeling for turbulent flows 2nd Edition
  124. Eckelmann, H. (1974) The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow. J. Fluid Mech. 65, 439
  125. Eekhout, J. P. C. (2014) Morphological Processes in Lowland Streams. Implications for Stream Restoration, Thesis submitted in fulfillment of the requirements for the degree of doctor at Wageningen University, the Netherlands
  126. Eekhout, J. P. C., A. J. F. Hoitink, and E. Mosselman (2013), Field experiment on alternate bar development in a straight sand-bed stream, Water Resour. Res., 49, 8357-8369 DOI: 10.1002/2013WR014259
  127. Egiazaroff, I. V. (1965) Calculation of nonuniform sediment concentrations, Journal of Hydraulic Engineering, 91(4), 225-247
  128. Einstein, A. (1926). Die Ursache der Mäanderbildung der Flussläufe und des sogenannten Baerschen Gesetzes Die Naturwissenschaften, 14 (11), 223-224 DOI: 10.1007/BF01510300
  129. Einstein, H. (1937). Der Geschiebetrieb als Wahrscheinlichkeit problem (Bedload transport as a probability problem) (English translation by W.W. Sayre, in Sedimentation (Symposium to honor H. A. Einstein), edited by H. W. Shen, Fort Collins, Colorado, 1972, C1-C105) Zurich: ETHZ
  130. Einstein, H. A. (1950). The Bedload function for sediment transportation in open channel flows Technical Bulletin 1026, U.S. Dept. of the Army, Soil Conservation Service, 1-71
  131. Einstein, H. A., and Chien, N. (1955). Effects of heavy sediment concentration near the bed on velocity and sediment distribution. MRD Series No. 8, Univ. of California/Missouri River Div., Corps of Engrs., Omaha, Neb
  132. Elghobashi, S. (1991). Particle-laden turbulent flows: direct simulation and closure models. Appl Sci. Res. 48:301-14
  133. Elghobashi, S. (1994). On predicting particle-laden turbulent flows. Appl. Sci. Res. 52:309-29
  134. Elghobashi S. and Truesdell G.C. (1993). On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Phys. Fluids A 5:1790-801
  135. Engelund, F. (1964). A practical approach to self-preserving turbulent flows. Acta Polytechnica Scandinavica
  136. Engelund, F. (1974), Flow and bed topography in channel bends, J. Hydraul. Div., 574 100 (11), 1631-1648
  137. Engelund, F. and Fredsøe, J. (1976) A Sediment Transport Model for Straight Alluvial Channels, Nordic Hydrology, 7: 293-306
  138. Engelund F. and Fredsøe J. (1982). Sediment ripples and dunes. Annu. Rev. Fluid Mech 14:13-37
  139. Engelund, F. and Hansen, E., (1966), Hydraulic resistance in alluvial streams, Acta Polytechnica Scandanavica, V. Ci-35
  140. Engelund, F., and Hansen, E. (1967). A Monograph on Sediment Transport in Alluvial Streams Teknisk Vorlag, Copenhagen, Denmark
  141. Engelund, F. and Skovgaard, O. (1973) On the origin of meandering and braiding in alluvial streams. J. Fluid Mech. 57, 289
  142. Engle, P. A. (1978), Impact Wear of Materials, Elsevier Sci., New York
  143. Exner, F. M. (1925) ¨U ber die Wechselwirkung zwischen Wasser und geschiebe in Fl¨ussen. Sitzer Akad. Wiss. Wien 165-180
  144. Fadlun, E., Verzicco, R., Orlandi, P., Mohd-Yusof, J. (2000) Combined immersed-boundary finite-difference methods for threedimensional complex flow simulations, J. Comput. Phys 161, 35–60
  145. Federici, B., and G. Seminara (2003), On the convective nature of bar instability, J. Fluid Mech., 487, 125-145
  146. Federici, B., and G. Seminara (2006), Effect of suspended load on sandbar instability, Water Resour. Res., 42, W07407 DOI: 10.1029/2005WR004399
  147. Fenton, J.D. and Abbott, J.E. (1977) Initial movement of grains on a stream bed: the effect of relative protrusion Proc. Roy. Soc. London.A 352: 523-537
  148. Ferguson, R.I., Prestegaard, K. and Ashworth, P.J. (1989): Influence of sand on hydraulics and gravel transport in a braided, gravel-bed river. Water Resources Research 25, 635-43
  149. Fernandez Luque, R., and R. van Beek (1976), Erosion and transport of bed-load sediment, J Hydraul. Res., 14, 127-144
  150. Ferrante A, Elghobashi S. (2003). On the physical mechanism of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15:315-29
  151. Ferry J, Rani SL, Balachandar S. (2003). A locally implicit improvement of the equilibrium Eulerian method. Int. J. Multiphase Flow 29:869-91
  152. Ferry, J. and S. Balachandar (2001). A fast Eulerian method for disperse two-phase flow. Int. J Multiphase Flow 27:1199-1226
  153. Fick, A. (1855) Ann. der Phys. 94: 59
  154. Finnegan N. J. (2007) Channel morphology and bedrock river incision: Theory, experiments, and application to the eastern Himalaya, Ph D Dissertation, University of Washington, USA
  155. Finnegan, N. J., Roe, G., Montgomery, D. R., and Hallet, B. (2005). Controls on the channel width of rivers: Implications for modeling fluvial incision of bedrock. Geology, 33(3), 229-232 DOI: 10.1130/G21171.1
  156. Finnegan, N. J., L. S. Sklar, and T. K. Fuller (2007), Interplay of sediment supply, river incision, and channel morphology revealed by the transient evolution of an experimental bedrock channel, J. Geophys. Res., 112, F03S11 DOI: 10.1029/2006JF000569
  157. Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in Inland and Coastal Waters. New York: Academic Press
  158. Fletcher, C. A. J. (1991). Computational Techniques for Fluid Dynamics. 1, CSpringer-Verlag, Berlin, Heidelberg
  159. Francalanci S. (2005) Sediment transport processes and local scale effects on river morphodynamic Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in in Hydrodynamics and Environmental Modeling. University of Florence
  160. Francalanci, S., and Solari, L. (2007). Gravitational effects on bed load transport at low shields stress: Experimental observations, Water Resour. Res., 43, W03424
  161. Francalanci, S., and Solari, L. (2008). Bed-Load Transport Equation on Arbitrarily Sloping Beds Journal of Hydraulic Engineering, Vol. 134, No. 1. ISSN 0733-9429/2008/1- 110-115
  162. Francalanci, S., Lanzoni, S., Solari, L. and Papanicolaou, A. N. (2020). Equilibrium cross section of river channels with cohesive erodible banks. Journal of Geophysical Research: Earth Surface, 125, e2019JF005286 DOI: 10.1029/2019JF005286
  163. Francis, J.R.D. (1973) Experiments on the motion of solitary grains along the bed of a water stream. Proc. R. Soc. London A, 332, 443-471
  164. Fredsòe, J. (1978) Meandering and braiding of rivers. J. Fluid Mech. 84, 609-624
  165. Fredsòe, J. (1982). Shape and dimensions of stationary dunes in rivers. Journal of the Hydraulics Division , ASCE , 108(8), 932-947
  166. Fredsòe, J., and R. Deigaard (1992). Mechanics of Coastal Sediment Transport. World Scientific
  167. Frisch, U. (1995) Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press
  168. Fujita, Y. and Y. Muramoto: Experimental study on stream channel processes in alluvial rivers, Bull., Disast. Prey. Res. Inst., Kyoto Univ., 32(1), 49-96
  169. Fujita, Y., and Y. Muramoto, (1985) Studies on the process of development of alternate bars, Bull. Disaster Prev. Res. Inst. Kyoto Univ., 35: 55-86
  170. Furbish, D. J., Haff, P. K., Roseberry, J. C., and Schmeeckle, M. W. (2012). A probabilistic description of the bed load sediment flux: 1. Theory. Journal of Geophysical Research, 117(F03031) DOI: 10.1029/2012JF002352
  171. Furbish, D. J., Fathel, S. L., Schmeeckle, M. W., Jerolmack, D. J., and Schumer, R. (2017). The elements and richness of particle diffusion during sediment transport at small timescales Earth Surface Processes and Landforms, 42, 214-237 DOI: 10.1002/esp.4084
  172. Galappatti, R., (1983) A depth-integrated model for suspended transport, Delft University of Technology, Faculty of Civil Eng., Report No.83-7
  173. Galappatti, R. and Vreugdenhil, C.B. (1985) A depth-integrated model for suspended sediment transport, J. Hydr. Res., 23(4):359-377
  174. Garcia, M.H. (2008) Sedimentation engineering: processes, measurements, modeling and practice, ASCE manuals and reports on engineering practice, 110. ASCE: Reston. ISBN: 978-0-7844- 0814-8. xx, 1132 pp.
  175. Garcia, M. H. and G. Parker, (1991) Entrainment of Bed Sediment Into Suspension. Journal of Hydraulic Engineering, 117(4), 414-435
  176. Gatignol R. (1983). The Faxén formulae for a rigid particle in an unsteady non-uniform Stokes flow. J Mecanique Theorique et Appliquè 1(2):143-160
  177. Gelfenbaum, G., and J. D. Smith (1986), Experimental evaluation of a generalized suspendedsediment transport theory, in Shelf Sands and Sandstones, edited by R. J. Knight and J. R
  178. Mclean, pp. 133-144, Canadian Society of Petroleum Geologists Memoir II, Calgary, Alberta, Canada
  179. Gilbert, G. K. (1877), Report on the Geology of the Henry Mountains: Geographical and Geological Survey of the Rocky Mountain Region, 160 pp., U.S. Gov. Print. Off., Washington, D. C.
  180. Gilbert, G.K., (1914a) Transportation of Debris by Running Water Professional Paper No. 86, United States Geological Survey
  181. Gilbert, G. K. (1914b), The transport of debris by running water, U.S. Geol. Survey Prof. Paper 86, 263 p.
  182. Ginzburg, V.L. and L.D. Landau, (1950) On the theory of superconductivity, Zh. Eksper. Teor Fiz., 20, 1064-1082 (In Russian) (English transl.: Men of Physics: L.D. Landau (D. ter Haar, ed.), Pergamon, 1965,138-167 )
  183. Glover, R. E. and Q. L. Florey (1951) Stable channel profiles, Bureau of Reclamation Hydraulic Lab. Rep., n. 325
  184. Goldstein, D., Handler, R. and Sirovich, L. (1993) Modeling a no-slip boundary with an external force field, J. Comput. Phys. 105, 354–366
  185. Gomez, B., R. L. Naff, and D. W. Hubbell (1989), Temporal variations in bedload transport rates associated with the migration of bedforms, Earth Surf. Processes Landforms, 14, 135-156 DOI: 10.1002/esp.3290140205
  186. Graf, W. H. (1971). Hydraulics of sediment transport. McGraw-Hill Book Co., Inc., New York, N.Y.
  187. Green, M. A., Rowley, C. W. and Haller, G. (2007) Detection of Lagrangian coherent structures in three-dimensional turbulence, Journal of Fluid Mechanics, 572, 111-120
  188. Gresho, P. M. (1991). Incompressible Fluid Dynamics: Some Fundamental Formulation Issues, Annu. Rev. Fluid Mech., 23, 413-453
  189. Griffiths, G. A. (1981) Stable-channel design in gravel-bed rivers Journal of Hydrology, 52(3-4), 291-305
  190. Guy, H.P., Simmons, D.B and Richardson, E.V. (1966) Summary of Alluvial Channel Data from Fume Experiments, 1956-61 Professional Paper 462-I, United States Geological Survey
  191. Hack J. T. (1957). Studies of longitudinal stream profiles in Virginia Maryland. U.S. Geol. Surv Prof. Pap, 294-B:97
  192. Hadamard, J. S. (1923) Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale University Press
  193. Hager, W. H., and Castro-Orgaz, O. and Hutter, K. (2019) Correspondence between de Saint- Venant and Boussinesq. 1: Birth of the ShallowWater Equations, Comptes Rendus Mécanique 347 (9), 632-662
  194. Hall, P. (2007) A note on bar instabilities in very wide rivers. Int. J. of Computing Science and Mathematics 1, 147-156
  195. Hansen, E. (1967) The formation of meanders as a stability problem. Hydraul. Lab., Tech. Univ Denmark Basic Res. Prog. Rep. no. 13
  196. Happel, J. and H. Brenner (1965). Low Reynolds number hydrodynamics: With special applications to particulate media. Prentice-Hall (Englewood Cliffs, N.J.)
  197. Hasegawa, K., (1981) Bank-erosion discharge based on a non-equilibrium theory (in Japanese), Trans Jpn. Soc. Civil Eng., 316, 37-52
  198. Hashin, Z. (1964) Theory of mechanical behaviour of heterogeneous media. Appl. Mech. Rev. 17, 1-9
  199. Hassan, M. A., and Church, M. (1994). Vertical mixing of coarse particles in gravel-bed rivers: A kinematic model, Water Resour. Res., 30(4), 1173-1185
  200. Hayashi, T. (1971) Study on the cause of meandering of rivers. Trans. JSCE 2:235
  201. Hayashi, T. and Ozaki, S. (1980) Alluvial bed form analysis - formation of alternating bars and braids. In Application of Stochastic Processes in Sediment Transport (ed. T. Kishi & M Kuroki) Water Resources Publ., Littleton, Colorado, pp. 7.1-7.40
  202. Head, M. R. and Bandyopadhyay, P. (1981) New aspects of turbulent boundary-layer structure. J Fluid Mech. 107, 297-337
  203. Head, W. J., and M. E. Harr (1970), The development of a model to predict the erosion of materials by natural contaminants, Wear, 15, 1-46
  204. Heathershaw, A.D. and Thorne, P.D. (1985) Sea-bed noises reveal role of turbulent bursting phenomenon in sediment transport by tidal currents. Nature 316, 339-432
  205. Henshaw, A. J., A. M. Gurnell, W. Bertoldi, and N. A. Drake (2013), An assessment of the degree to which Landsat TM data can support the assessment of fluvial dynamics, as revealed by changes in vegetation extent and channel position, along a large river, Geomorphology, 202, 74-85, DOI: 10.1016/j.geomorph.2013.01.011
  206. Hersen, P. (2005), Flow effects on the morphology and dynamics of aeolian and subaqueous barchan dunes, J. Geophys. Res., 110, F04S07 DOI: 10.1029/2004JF000185
  207. Hey, R. and Thorne, C. (1986) Stable Channels with Mobile Gravel Beds, Journal of Hydraulic Engineering, 112(8), 671-689
  208. Heywood, J. G., Rannacher, R., Turek, S. (1994). Artificial boundaries and flux and pressure conditions for Navier-Stokes Equations Int. J. Comput. Fluid Mech., 22, 325-352
  209. Hibma, A., Schuttelaars, H. M., and Wang, Z. B. (2003). Comparison of longitudinal equilibrium profiles of estuaries in idealized and process-based models. Ocean Dynamics, 53, 252-269 DOI: 10.1007/s10236-003-0046-7
  210. Hirano, M. (1971), River bed degradation with armouring (in Japanese), Trans. Jpn. Soc. Civ Eng., 3, 194-195
  211. Hirano, M. (1973), River-bed variation with bank-erosion, Trans. Jpn. Soc. Civ. Eng., 210:13-20 (in Japanese)
  212. Hirsch, C. (2007). Numerical Computation of Internal and External Flows, 2nd Edition Butterworth- Heinemann, Elsevier, Oxford. ISBN: 978-0-7506-6594-0
  213. Hodge, R. A., and T. B. Hoey (2012), Upscaling from grain-scale processes to alluviation in bedrock channels using a cellular automaton model, J. Geophys. Res., 117, F01017 DOI: 10.1029/2011JF002145
  214. Hodge, R. A., T. B. Hoey, and L. S. Sklar (2011), Bed load transport in bedrock rivers: The role of sediment cover in grain entrainment, translation, and deposition, J. Geophys. Res., 116, F04028, DOI: 10.1029/2011JF002032
  215. Hodge, R., T. Hoey, G. Maniatis and E. Leprˇetre (2016) Formation and erosion of sediment cover in an experimental bedrock-alluvial channel Earth Surf. Process. Landforms DOI: 10.1002/esp.3924
  216. Hopson, T. M. (1999), The form drag of large natural vegetation along the banks of open channels, M. S. thesis, 114 pp., Univ. of Colorado at Boulder
  217. Houjou, K., Shimizu, Y., and Ishii, C. (1990). Calculation of boundary shear stress in open channel flow. J. Hydrosci. Hydr. Eng., 8, 21-37
  218. Howard, A. D. (1980), Thresholds in fiver regimes, in Thresholds in Geomorphology edited by D.R. Coates and J.D. Vitek, pp. 227-258, Allen and Unwin, Winchester, Mass., 1980
  219. Howard, A. D. (1987), Modelling fluvial systems: Rock, gravel and sand bed channels, in River Channels, edited by K. S. Richards, pp. 69-94, Basil Blackwell, Oxford
  220. Howard A. D. and G. Kerby (1983). Channel changes in badlands. Geological Society of America Bulletin, 94, 739-752
  221. Howard, A. D., W. E. Dietrich, and M. A. Seidl (1994), Modeling fluvial erosion on regional to continental scales, J. Geophys. Res., 99, 13, 971-13,986
  222. Huda, S. A. (2013) Modeling the Effects of Bed Topography on Fluvial Erosion by Saltating Bed Load, A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science
  223. Huda, S. A. and Small, E. E. (2014) Modeling the Effects of Bed Topography on Fluvial Bedrock Erosion by Saltating Bed Load, J. Geophys. Res.Earth, 119, 1222-1239 DOI: 10.1002/2013JF002872
  224. Huerre, P. and P. Monkewitz (1990) Local and global instabilities in spatially developing flows, Annual Review of Fluid Mechanics 22, 473-537
  225. Hunziker, R. P. and Jäggi, M. N. R. (2002). Grain sorting processes. J. Hydraul. Eng., ASCE, 128(12): 1060-1068
  226. Ikeda, S. (1971) Some studies on the mechanics of bed load transport. Proc. of JSCE, 185: 61-70
  227. Ikeda, S. (1982a) Incipient motion of sand particles on side slopes Hydraul. Div. Am. Soc. Civ Eng., 108(HY1), 95-114
  228. Ikeda, S. (1982b) Prediction of alternate bar wavelength and height. Rep. Dept. Found. Engng and Const. Engng, Saitama Univ., 12:23-45
  229. Ikeda, S. and N. Izumi (1991) Stable Channel Cross Sections of Straight Sand Rivers, Water Resources Research, 27(9), 2429-2438 DOI: 10.1029/91WR01220
  230. Ikeda S, Parker G, Sawai K. (1981). Bend theory of river meanders. Part 1. Linear development J. Fluid Mech., 112:363-77
  231. Jaeggi, M. (1983) Alternierende Kiesbänke. Mitteilungen der Versuchanstalt für Wasserbau, Hydrologie und Glaziologie. Zurich: E.T.H
  232. Jaeggi, M. (1984) Formation and effects of alternate bars. J. Hydraul. Eng., ASCE 110:142-156
  233. Jimenez, J. (2004). Turbulent flows over rough walls. Annu. Rev. Fluid Mech. Vol 36:173-196 DOI: 10.1146/annurev.fluid.36.050802.122103
  234. Inoue, T., and Nelson, J. M. (2020). An experimental study of longitudinal incisional grooves in a mixed bedrock-alluvial channel. Water Resources Research, 56, e2019WR025410 DOI: 10.1029/2019WR025410
  235. Inoue, T., Izumi, N., Shimizu, Y., Parker, G., (2014). Interaction among alluvial cover, bed roughness and incision rate in purely bedrock and alluvial-bedrock channel. J. Geophys. Res Earth Surf., 119, 2123-2146 DOI: 10.1002/2014JF003133
  236. Inoue, T., Iwasaki, T., Parker, G., Shimizu, Y., Izumi, N., Stark, C. P., and Funaki, J. (2016) Numerical simulation of effects of sediment supply on bedrock channel morphology, J. Hydr Eng., 142, 04016014
  237. Inoue, T., S. Yamaguchi and J. M. Nelson (2017), The effect of wet-dry weathering on the rate of bedrock river channel erosion by saltating gravel, Geomorphology, DOI: 10.1016/j.geomorph.2017.02.018
  238. Izumi, N., Yokokawa, M. and Parker, G. (2017) Incisional cyclic steps of permanent form in mixed bedrock-alluvial rivers, J. Geophys. Res. Earth Surf., 122, 130-152
  239. John, V. (2016) Finite Element Methods for Incompressible Flow Problems. Springer Series in Computational Mathematics. Springer International Publishing
  240. Johnson, J. P. L., and K. X. Whipple (2010), Evaluating the controls of shear stress, sediment supply, alluvial cover, and channel morphology on experimental bedrock incision rate, J Geophys. Res., 115, F02018 DOI: 10.1029/2009JF001335
  241. Johnson, J. P., and K. X. Whipple (2007), Feedbacks between erosion and sediment transport in experimental bedrock channels, Earth Surf. Processes Landforms, 32, 1048-1062
  242. Johnson, J. P. L., K. X. Whipple, L. S. Sklar, and T. C. Hanks (2009), Transport slopes, sediment cover, and bedrock channel incision in the Henry Mountains, Utah, J. Geophys. Res., 114 , F02014 DOI: 10.1029/2007JF000862
  243. Joseph, G. G., and M. L. Hunt (2004), Oblique particle-wall collisions in a liquid, J. Fluid Mech., 510, 71-93 DOI: 10.1017/S002211200400919X
  244. Joseph, D, D. and Lundgren, T. S. (1990) Ensemble averaged and mixture theory equations for incompressible fluid-particle suspensions. Int. J. Multiphase Flow 16, 3542
  245. Jourdain, C., Claude, N., Tassi, P., Cordier, F. and Germain A. (2020) Morphodynamics of alternate bars in the presence of riparian vegetation, Earth Surf. Process. Landforms 45, 1100-1122
  246. Julien, P. Y. and Klaassen, G. J. (1995). Sand-dune geometry of large rivers during floods Journal of Hydraulic Engineering, ASCE, 121, 657-663
  247. Kean, J. W. (2003) Computation of flow and boundary shear stress near the banks of streams and rivers. A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirement for the degree of Doctor of Philosophy
  248. Kean, J. W., and Smith, J. D. (2004). Flow and boundary shear stress in channels with woody bank vegetation. Riparian vegetation and fluvial geomorphology, AGU Water Science and Application Series 8, S. J. Bennett and A. Simon, eds., AGU, Washington, D.C., 237-252
  249. Kean, J. W., and J. D. Smith (2006a), Form drag in rivers due to small-scale natural topographic features: 1. Regular sequences, J. Geophys. Res., 111, F04009 DOI: 10.1029/2006JF000467
  250. Kean, J. W., and J. D. Smith (2006b), Form drag in rivers due to small-scale natural topographic features: 2. Irregular sequences, J. Geophys. Res., 111, F04010 DOI: 10.1029/2006JF000490
  251. Kean, J. W., Kuhnle, R. A., Dungan Smith, J., Alonso, C. V. and Langendoen, E. J. (2009) Test of a Method to Calculate Near-Bank Velocity and Boundary Shear Stress Journal of Hydraulic Engineering, 135(7), ASCE, ISSN 0733-9429/2009/7-588-601
  252. Keefe L. R. (1985) Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation Stud. Appl. Maths. 73, 91-153
  253. Kennedy, J. F. (1995). The Albert Shields story. J. Hydr. Engrg., ASCE, 121(11): 766-772
  254. Kevorkian, J. and Cole, J. D. (1981) Perturbation Methods in Applied Mathematics. Springer
  255. Keylock, C.J., Constantinescu, G. and Hardy, R.J. (2012) The application of computational fluid dynamics to natural river channels: Eddy resolving versus mean flow approaches
  256. Geomorphology, 179. 1-20. ISSN 0169-555X Kidanemariam A. G. and Uhlmann, M. (2014a) Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2
  257. Kidanemariam A. G. and Uhlmann, M. (2014b) Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar channel flow. Intl J. Multiphase Flow 1-27
  258. Kidanemariam A. G. and Uhlmann, M. (2017) Formation of sediment patterns in channel flow: minimal unstable systems and their temporal evolution. J. Fluid Mech., vol. 818, pp 716-743
  259. Kidanemariam A. G., Scherer, M. and Uhlmann, M. (2022) Open-channel flow over evolving subaqueous ripples J. Fluid Mech., vol. 937, A26 DOI: 10.1017/jfm.2022.113
  260. Kim, J., Kline, S. J. and Reynolds, W. C. 1971. The production of turbulence near a smooth wall in a turbulent boundary layer. J . Fluid Mech. 50, 133
  261. Kim, J., Moin, P. & Moser, R. (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, pp. 133-166
  262. Kinoshita, R. (1961) An investigation of channel deformation of the Ishikari River. Tech. Rep., Natural Resources Division, Ministry of Science and Technology of Japan, Tokio, 36 , pp 1-174
  263. Kinoshita, R. and Miwa, H. (1974) River channel formation which prevents downstream translation of transverse bars. Shinsabo 94, 12-17 (in Japanese)
  264. Kirchner, J.W.,W. E. Dietrich, F. Iseya, and H. Ikeda (1990), The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments, Sedimentology, 37(4), 647-672 DOI: 10.1111/j.1365-3091.1990. tb00627.x
  265. Kline, S. J., Reynolds, W. C., Schraub F. A. and Runstadler P. W. (1967). The structure of turbulent boundary layers . J. Fluid Mech. 30(4):741-773
  266. Kline, S. J. and Runstadler, W. (1959) J. Appl. Mech. Trans. ASME, 26 (Ser. E), no. 2, 167
  267. Kolmogorov, A. N. (1941) Dokl. Akad. Nauk. SSSR. 30, 3201. (English translation,
  268. Kolmogorov, A. N. (1991). The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Proc. R. Soc. Lond. 434:9-13)
  269. Kolmogorov, A.N. (1942) Equations of turbulent motion in an incompressible fluid. Izv. Akad Nauk. SSSR ser. Fiz. 6, 56-58
  270. Komar, P.D. and Li, Z. (1986): Pivoting analyses of the selective entrainment of sediments by shape and size with application to the gravel threshold, Sedimentology 33, 425-36
  271. Kovacs, A., and G. Parker, (1994) A new vectorial bedload formulation and its application to the time evolution of straight river channels, J. Fluid Mech., 267, 153- 183
  272. Lague, D., N. Hovius, and P. Davy (2005), Discharge, discharge variability, and the bedrock channel profile, J. Geophys. Res., 110, F04006 DOI: 10.1029/2004JF000259
  273. Lajeunesse, E., Malverti, L., and Charru, F. (2010). Bed load transport in turbulent flow at the grain scale : Experiments and modeling. Journal of Geophysical Research, 115(F04001), 1-16 DOI: 10.1029/2009JF001628
  274. Lamb, M. P. (2008) Formation of Amphitheater-Headed Canyons A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Earth Planetary Science, University of California at Berkeley
  275. Lamb, M. P., W. E. Dietrich, and L. S. Sklar (2008), A model for fluvial bedrock incision by impacting suspended and bedload sediment, J. Geophys. Res., 113, F03025 DOI: 10.1029/2007JF000915
  276. Lamb, M. P., Finnegan, N. J., Scheingross, J. S., and Sklar, L. S. (2015). New insights into the mechanics of fluvial bedrock erosion through flume experiments and theory. Geomorphology, 244(33-55) DOI: 10.1016/j.geomorph.2015.03.003
  277. Landau, L. D. (1944). On the problem of turbulence. In Dokl. Akad. Nauk SSSR (Vol. 44, No 8, pp. 339-349)
  278. Lanzoni, S. (1995). Experiments on free and forced bar formation in a straight flume. Vol. I: Uniform sediment. Delft Hydraulics Res. Report Q1774
  279. Lanzoni, S., (2000a). Experiments on bar formation in a straight flume: 1. Uniform sediment, Water Resour. Res., 36, 3337-3349
  280. Lanzoni, S., (2000b). Experiments on bar formation in a straight flume: 1. Graded sediment, Water Resour. Res., 36, 3351-3363
  281. Lanzoni, S. and G. Seminara (2002). Long-term evolution and morphodynamic equilibrium of tidal channels, Journal of Geophysical Research, 107(C1), 3001, 10.1029/2000JC000468 DOI: 10.1029/2000JC000469
  282. Lanzoni, S., and M. Tubino (1999), Grain sorting and bar instability, J. Fluid Mech., 393, 149-174
  283. Lanzoni, S., Tubino, M. and Bruno, S. (1994) Formazione di barre alternate in alvei incoerenti a granulometria non uniforme. XXIII Convegno di Idraulica e Costruzioni Idrauliche, Napoli, II, T4/pp. 171-181 (in Italian)
  284. Lanzoni, S., Bolla Pittaluga, M. and Luchi R. (2014). Modeling the morphodynamic equilibrium of an intermediate reach of the Po River (Italy). Adv. Water. Resour DOI: 10.1016/j.advwatres.2014.11.004
  285. Launder, E. and Spalding, B. (1974) The numerical computation of turbulent flow. Comp. Meth Appl. Mech. & Engng 3, 269-289
  286. Leclair, S. F. (1999). Preservation of cross-strata due to migration of subaqueous dunes. PhD thesis, Binghamton University, New York
  287. Leighly, J. B. (1932). Toward a theory of the morphologic significance of turbulence in the flow of water in streams. Univ. Calif. Publ. Geogr., 6(1), 1-22
  288. Leopold, L. B. (1994), A View of the River, 298 pp., Harvard Univ. Press, Cambridge, Mass
  289. Leopold, L. B. and Maddock, T. Jr. (1953) The hydraulic geometry of stream channels and some physiographic implications. Prof. Paper 252, U. S. Geol. Survey, 57
  290. Leopold L. and Wolman M. (1957). River channel patterns: braided, meandering and straight Geological Survey professional paper 282-B. US Government Printing Office, Washington, D.C.
  291. Leopold, L. B., and M. G. Wolman (1960), River Meanders, Geol. Soc. Am. Bull., 71(6), 769-793
  292. Lesieur, M. (1997), Turbulence in Fluids, Kluver Academic Publishers, Dordrecht, The Netherlands
  293. Lesieur M. and O. Metais (1996) New Trends in Large-Eddy Simulations of Turbulence, Annu. Rev Fluid Mech. 28, 45-82 DOI: 10.1146/annurev.fl.28.010196.000401
  294. Lesser, G. R., Roelvink, J. A., Kester, J. A. T. M. Van, and Stelling, G. S. (2004). Development and validation of a three-dimensional morphological model, Coastal Engineering, 51, 883-915 DOI: 10.1016/j.coastaleng.2004.07.014
  295. Lewin, J. (1976), Initiation of bedforms and meanders in coarse grained sediment, Bull. Geol Soc. Am., 87(2), 281-285
  296. Lisle, T. (1982), Effects of Aggradation and Degradation on Riffle-Pool Morphology in Natural Gravel Channels, Northwestern California, Water Resour. Res., 18(6), 1643-1651
  297. Lisle, T. E., H. Ikeda, and F. Iseya, (1991) Formation of stationary alternate bars in a steep channel with mixed-size sediment: A flume experiment, Earth Surf. Processes Landforms, 16, 463-469
  298. Lisle, T.E., Iseya, F. and Ikeda, H. (1993) Response of a channel with alternate bars to a decrease in supply of mixed-size bed load: a flume experiment. Water Resour. Res., 29(11), 3623-3629
  299. Liu, H. K. (1957) Mechanics of sediment-ripple formation. J. Hydraul. Div. 83(2):1-23
  300. Luchi, R., J. M. Hooke, G. Zolezzi, and W. Bertoldi (2010), Width variations and midchannel bar inception in meanders: River Bollin (UK), Geomorphology, 119(1-2), 1-8, DOI: 10.1016/j.geomorph.2010.01.010
  301. Luchi, R., M. Bolla Pittaluga, and G. Seminara (2012), Spatial width oscillations in meandering rivers at equilibrium, Water Resour. Res., 48, W05551 DOI: 10.1029/2011WR011117
  302. Lumley, J.L. (1978) Computational modeling of turbulence flows. Adv. Appl. Mech. 18, 123-177
  303. Lumley, J.L. (1970) Toward a turbulent constitutive equation. J. Fluid Mech. 41, 413-434
  304. Lundgren, T. S. (1972) Slow flow through stationary random beds and suspensions of spheres. J Fluid Mech. 51, 273-299
  305. Luque, F. R. and Van Beek, R. (1976) Erosion and transport of bed sediment J. Hydraul. Res., 14(2): 127-144
  306. Luu, L. X., Egashira, S., & Takebayashi, H. (2004). Investigation of Tan Chau reach in lower Mekong using field data and numerical simulation, Annual Journal of Hydraulic Engineering, JSCE, 48, 1057-1062
  307. Lysne, D. K. (1969). Movement of sand in tunnels. J. Hydraul. Div. Am. Soc. Civil Eng., 95(HY6),1835-46 Magnaudet, J. and I. Eames 2000. The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32:659-708
  308. Mantz, P.A. (1980) Low Sediment Transport Rates over Flat Beds Journal of the Hydraulic Division, Proc. ASCE, 106(HY7): 1173-1190
  309. Marble FE. (1970). Dynamics of dusty gases. Annu. Rev. Fluid Mech. 2:397-446
  310. Maxey, M. R. (1987). The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174: 441-465
  311. Maxey, M. R. and J. J. Riley (1983). Equation of motion for a small rigid sphere in a nonuniform flow, Phys. Fluids 26, 883
  312. Mazzuoli, M., Kidanemariam, A. G., Blondeaux, P., Vittori, G. and Uhlmann, M. (2016) On the formation of sediment chains in an oscillatory boundary layer. J. Fluid Mech. 789, 461–480
  313. Mazzuoli, M., Kidanemariam, A., and Uhlmann, M. (2019). Direct numerical simulations of ripples in an oscillatory flow. Journal of Fluid Mechanics 863, 572-600
  314. Mazzuoli, M., Blondeaux, P., Vittori, G., Uhlmann, M., Simeonov, J. and J. Calantoni (2020) Interface-resolved direct numerical simulations of sediment transport in a turbulent oscillatory boundary layer, J. Fluid Mech., vol. 885, A28
  315. McTigue, D. F. (1981). Mixture theory for suspended sediment transport. J. Hydr. Div. ASCE, 107, 659-673
  316. Metais, E. (2002). Large-eddy simulations of turbulence. In: New Trends in Turbulence, Edited by Lesier, M., Yaglom, A., David, F., Springer, Berlin
  317. Meyer-Peter, E. and Müller, R. (1948) Formulas for bedload transport, 2nd IAHR Congress, Int Assoc. for Hydraul. Res., Stockholm
  318. Michaelides, E. E. (2006). Particles, Bubbles and Drops. Their Motion, Heat and Mass transfer World Scientific Publishers, New Jersey
  319. Milhous, R. T., (1973), Sedimant transport in a gravel-bottomed stream, Ph.D. thesis, Dept. of Civil Engineering, Oregon State University, U.S.A., 232 p.
  320. Mishra, J., and T., Inoue (2020) State of the Art Study of Influence of Bed Roughness and Alluvial Cover on Bedrock Channels and Comparisons of Existing Models with Laboratory Scale Experiments, Earth Surf. Dynam. Discussions DOI: 10.5194/esurf-2019-78
  321. Moin, P. and Kim, J. (1982). Numerical investigation of turbulent channel flow. Journal of Fluid Mechanics 118, 341-377 DOI: 10.1017/S0022112082001116
  322. Moin, P., Mahesh, K. (1998), Direct Numerical Simulation: A Tool in Turbulence Research Annu. Rev. Fluid Mech. 30:539-78
  323. Monin, A.S. and Yaglom, A.M. (1971) Statistical fluid mechanics, vol.1, MIT Press
  324. Morse, P. M. and Feshback, H. (1953). Methods of Theoretical Physics, McGraw-Hill, New York
  325. Mosley, M. P. (1976) An experimental study of channel confluences. J. Geol. 4, 535-562
  326. Muramoto, Y. and Fujita, Y. (1978) The classification of meso-scale river bed configuration and the criterion of its formation. Proc. 22nd Japanese Conf. on Hydraulics, 275-282. JSCE
  327. Nakagawa, H. and Tsujimoto, T. (1980) Sand bed instability due to bed load motion. J. Hydraul Div., ASCE, 106, 12
  328. Nayfeh A. H. (2000). Perturbation methods. John Wiley & Sons
  329. Nayfeh, A. H. (2011) Introduction to Perturbation Techniques John Wiley & Sons
  330. Nelson, P. A., and G. Seminara (2011), Modeling the evolution of bedrock channel shape with erosion from saltating bed load, Geophys. Res. Lett., 38, L17406 DOI: 10.1029/2011GL048628
  331. Nelson, P. A., and G. Seminara (2012), A theoretical framework for the morphodynamics of bedrock channels, Geophys. Res. Lett., 39, L06408, DOI: 10.1029/2011GL050806
  332. Nelson, J. M., and J. D. Smith, (1989). Flow in meandering channels with natural topography, in River Meandering, Water Resour. Monogr., vol. 12, edited by S. Ikeda and G. Parker, pp 69-102, AGU, Washington, D. C.
  333. Nelson, J.M., Shreve, R.L., McLean, S.R. & Drake, T.G. (1995) Role of near-bed turbulence structure in bed load transport and bed form mechanics. Water Resources Research, 31(8): 2071-2086
  334. Nelson, P. A., J. G. Venditti, W. E. Dietrich, J. W. Kirchner, H. Ikeda, F. Iseya, and L. S. Sklar (2009), Response of bed surface patchiness to reductions in sediment supply, J. Geophys Res., 114, F02005 DOI: 10.1029/2008JF001144
  335. Nezu, I. and Nakagawa, H. (1993). Turbulence in open-channel flows. Balkema, Rotterdam NL
  336. Nikuradse J. (1933). Strömungsgesetze in Rauhen Rohren, VDI-Forsch. 361 (Engl. transl. 1950 Laws of flow in rough pipes. NACA TM 1292 )
  337. Niño, Y. (1995) Particle motion in the near bed region of a turbulent open channel flow: implications for bedload transport by saltation and sediment entrainment in suspension Thesis submitted in partial fulfillment of the requirements of the degree of Philosophy Doctor Graduate School of Civil Engineering. University of Illinois at Urbana-Champaign
  338. Niño, Y. and Garcia, M. H. (1994) Gravel saltation Modelling Water Resources Research, 30(6): 1915-1924
  339. Niño, Y. and Garcia, M. H. (1996) Experiments on particle turbulent interactions in the near wall region of an open channel flow: implications for sediment transport. J. Fluid Mech., 326: 285-319
  340. Niño, Y., Lopez F. and Garcia, M. (2003) Threshold for particle entrainment into suspension Sedimentology 50: 247-263
  341. Nittrouer, J. A. (2010) Sediment Transport Dynamics in the lower Mississippi river: non-uniform flow and its effects on river channel morphology. Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
  342. Nittrouer, J. A., D. Mohrig, M. A. Allison and A-P. B. Peyret (2011) Sedimentology 58, 1914-1934, DOI: 10.1111/j.1365-3091.2011.01245.
  343. Olesen, K. W. (1984), Alternate bars in and meandering of alluvial rivers, in River Meandering, Proceedings of the Conference Rivers 1983, edited by C. M. Elliott, pp. 873-884, American Society of Civil Engineers, New York
  344. Owen, P.R. (1964) Saltation of uniform grains in air. J. Fluid Mech., 20: 225-242
  345. Panton, R. L. (2001) Overview of the self-sustaining mechanisms of wall turbulence. Progress in Aerospace Sciences 37, 341-383
  346. Parker G. (1975) Sediment inertia as cause of river antidunes J. Hydraul. Div., ASCE 101, 211–221
  347. Parker G. (1976) On the cause and characteristic scales of meandering and braiding in rivers. J Fluid Mech. 76, 457
  348. Parker, G. (1978a). Self-formed straight rivers with equilibrium banks and mobile bed. Part 1 The sand-silt river. J. Fluid Mech, 89:109-125
  349. Parker, G. (1978b), Self-formed straight rivers with equilibrium banks and mobile bed. Part 2 The gravel river, Journal of Fluid Mechanics, 89:127-146
  350. Parker, G. (1979), Hydraulic geometry of active gravel rivers, Journal of the Hydraulic Division (ASCE), 105(9), 1185-1201
  351. Parker G. (1984). Lateral bed load transport on side slopes. J. Hydraul. Eng. ASCE 110(HY2):197-99
  352. Parker, G. (1990): Surface-based bedload transport relation for gravel rivers, Journal of Hydraulic Research, 28, 417-36
  353. Parker, G. (1992), Some random notes on grain sorting, Proceedings, International Seminar on Grain Sorting, Ascona, Switzerland, 19-76
  354. Parker G. (2008). Transport of Gravel and Sediment Mixtures, Ch. 3 in Sedimentation Engineering (Manual 110) Processes, Measurements, Modeling, and Practice, M. Garcia Ed., 1132 pp.
  355. Parker, G., and E. D. Andrews, (1985) Sorting of bed load sediment by flow in meander bends, Water Resources Reserach, 21(9), 1361-1373
  356. Parker, G., and N. Izumi (2000). Purely erosional cyclic and solitary steps created by flow over a cohesive bed, J. Fluid Mech., 419, 203-238
  357. Parker, G. and Klingeman, P.C. (1982). On why gravel bed streams are paved, Water Resources Research, 18, 1409-23
  358. Parker, G., and Toro-Escobar, C. M. (2002). Equal mobility of gravel in streams: The remains of the day, Water Resour. Res., 38(11), 1264, DOI: 10.1029/2001WR000669
  359. Parker, G., Dhamotharan, S. and Stefan, H. (1982a): Model experiments on mobile, paved gravel-bed streams. Water Resources Research 18, 1395-408
  360. Parker, G., Klingeman, P.C. and McLean, D.C. (1982b): Bedload and size distribution in paved, gravel-bed streams. Proceedings of the American Society of Civil Engineers, Journal of the Hydraulics Division 108, 544-71
  361. Parker, G., C. Paola, and S. F. Leclair (2000), Probabilistic Exner sediment continuity equation for mixtures with no active layer, J. Hydraul. Eng., 126(11), 818-826
  362. Parker, G., G. Seminara, and L. Solari, (2003) Bed load at low Shields stress on arbitrarily sloping beds: Alternative entrainment formulation,Water Resour. Res., 39(7), 1183 DOI: 10.1029/2001WR001253.
  363. Parker, G., P. R. Wilcock, C. Paola, W. E. Dietrich, and J. Pitlick (2007), Physical basis for quasi-universal relations describing bankfull hydraulic geometry of single-thread gravel bed rivers, J. Geophys. Res., 112, F04005 DOI: 10.1029/2006JF000549
  364. Passman, S. L., Nunziato, J. W., and Walsh, E. K. (1984) A theory for multiphase mixtures. In Rational Thermodynamics, ed. C. Truesdell (second editor). Springer, NY. 286-325
  365. Perry, A.E., Lim, T.T. and Teh, E.W. (1981), A visual study of turbulent spots, Journal of Fluid Mechanics, 104, 387–405
  366. Peskin C., (2002), The immersed boundary method, Acta Numerica 11, 1–39
  367. Perry, A.E., Lim, T.T. and Teh, E.W. (1981), A visual study of turbulent spots, Journal of Fluid Mechanics, 104, 387–405
  368. Picano, F., W. Breugem, and L. Brandt (2005), Turbulent channel flow of dense suspensions of neutrally buoyant spheres. Journal of Fluid Mechanics, 764, 463-487 DOI: 10.1017/jfm.2014.704
  369. Pintor, L. (1991) Servabo (memoria di fine secolo) Bollati Boringhieri ed., 95 p. (in Italian)
  370. Piomelli, U., and Balaras, E. (2002). Wall-layer models for large-eddy simulations, Annual Review of Fluid Mechanics, 34, 349–75
  371. Pope, S. B. (2000) Turbulent Flows. Cambridge University Press
  372. Posada-García, L. (1995). Transport of sands in deep rivers. Ph.D. Dissertation, Department of Civil Engineering, Colorado State University, Fort Collins, Colorado
  373. Powell, D. M. (1998). Patterns and processes of sediment sorting in gravel-bed rivers, Progress in Physical Geography, 22(1), 1-32
  374. Powell, D. M., Reid, I. and Laronne, J. B. (2001), Evolution of bedload grain-size distribution with increasing flow strength and the effect of flow duration on the caliber of bedload sediment yield in ephemeral gravel-bed rivers, Water Resources Research, 37(5), 1463-1474
  375. Prandtl, L. (1925). Ãœber die ausgebildete turbulenz. ZAMM 5, p. 136
  376. Prandtl, L. (1927), Turbulent Flow, NACA-TM-435, Washington, USA
  377. Prandtl, L. (1945) Über ein neues formelsystem für die ausgebildete turbulenz. Nachr. Akad Wiss., Göttingen, Math.-Phys. Klasse, p. 7
  378. Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing (3rd ed.): Section 18.1 New York: Cambridge University Press. ISBN 978-0-521-88068-8
  379. Prosperetti, A. and Jones, A. V. (1984) Pressure forces in disperse two-phase flows. Int. J Multiphase Flow 10, 425-440
  380. Ramette, M. and Heuzel, M, (1962), A study of pebble movements in the Rhone by means of tracers, La Houille Blanche, Spécial A, 389-398 (in French)
  381. Rattray, M. and Mitsuda, E. (1974) Theoretical Analysis of Conditions in a Salt Wedge, Estuarine and Coastal Marine Science 2, 375-394
  382. Raudkivi, A. J. (1990). Loose Boundary Hydraulics, 3rd ed., Pergamon Press, New York
  383. Recking, A., Liebault, F., Peteuil, C., and Jolimet, T. (2012). Testing bedload transport equations with consideration of time scales. Earth Surface Processes and Landforms, 37, 774-789. DOI: 10.1002/esp.3213
  384. Repetto, R. (2000). Unit processes in braided rivers, Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Hydrodynamics and Environmental Modeling. Univ. of Padua
  385. Repetto, R., and M. Tubino, (1999a) Topographic expressions of bars in channels with variable width. XXIV EGS General Assembly, The Hague, The Netherlands
  386. Repetto, R., and M. Tubino, (1999b) Transition from migrating alternate bars to steady central bars in channels with variable width, Proc. of first IAHR-RCEM Symposium, Int. Assoc for Hydraul. Res., Genoa, Italy, 6-10 Sept
  387. Repetto, R., M. Tubino, and C. Paola (2002), Planimetric instability of channels with variable width, J. Fluid Mech., 457, 79-109
  388. Reynolds, O. (1895) On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. Soc., pp. 123-164
  389. Ribberink, J. S. (1987). Mathematical modelling of one-dimensional morphological changes in rivers with non-uniform sediment, Ph.D. thesis, Delft Univ. of Technol., Delft, Netherlands
  390. Richards, K. (1976), Channel width and the riffle-pool sequence, Geol. Soc. Am. Bull., 87, 883-890
  391. Richardson, L.F. (1922), Weather prediction by numerical process, Cambridge University Press, OCLC 3494280
  392. Richardson, K., and Carling, P.A. (2005), A typology of sculpted forms in open bedrock channels: Geological Society of America, Special Paper 392, 108 p. DOI: 10.1130/2005.2392
  393. Rodi, W. and N. N. Mansour (1993). Low Reynolds number K − ϵ modelling with the aid of direct numerical simulation data. J. Fluid Mech. 250, 509-529
  394. Rodriguez-Iturbe, I. and Rinaldo, A., (2010). Fractal River Basins. Chance and Selforganization, Cambridge University Press, 564 pp
  395. Roelvink, J.A. (2006), Coastal morphodynamic evolution techniques, Coastal Engineering, 53, 2, 277 - 287
  396. Rosenbloom, A., and R. S. Anderson, (1994) Evolution of the marine terraced landscape Santa Cruz, California, J. Geophys. Res., 99, 14,013-14,030
  397. Rouse, H., (1937). Modern conceptions of the mechanics of fluid turbulence. Trans. A.S.C.E., 102, 463-543
  398. Rouse, H. (1939). An analysis of sediment transportation in light of fluid turbulence. Rep. No SCS-TP-25, Sediment Division, U.S. Dept. of Agr., Soil Conservation Service, Washington, D.C.
  399. Saffman P.G. (1970). A model for inhomogeneous turbulent flow. Proc. Roy. Soc. Lond. A. 317, 417-433 Saffman, P. (1971) On the boundary condition at the surface of a porous medium. Studies in Appl. Math., 93
  400. Saffman, P. G. and Wilcox, D. C. (1974). Turbulence-model predictions for turbulent boundary layers. AIAA J. 12: 541-46
  401. Sani, R. L., Gresho, P. M. (1994), Reśumé and remarks on the Open Boundary Condition Minisymposium, International Journal for Numerical Methods in Fluids, 18, 983-1008
  402. Scheingross, J. S. (2016) Mechanics of sediment transport and bedrock erosion in steep landscapes, Dissertation In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology, Pasadena, California
  403. Scheingross, J. S. and Lamb, M. P. (2017). A mechanistic model of waterfall plunge pool erosion into bedrock. Journal of Geophysical Research: Earth Surface, 122, 2079-2104 DOI: 10.1002/2017JF004195
  404. Scheingross, J. S., Brun, F., Lo, D. Y., Omerdin, K., & Lamb, M. P. (2014). Experimental evidence for fluvial bedrock incision by suspended and bedload sediment. Geology, 42(6), 523-526 DOI: 10.1130/G35432.1
  405. Scheingross, J. S., Lamb, M. P. and Fuller, B. M. (2019). Self-formed bedrock waterfalls. Nature, 567(7747), 229-233 DOI: 10.1038/s41586-019-0991-z
  406. Scheingross, J. S., Limaye, A. B., McCoy, S. W. and Whittaker, A. C. (2020). The shaping of erosional landscapes by internal dynamics. Nature Reviews Earth ann Environment, 1(12), 661-676 DOI: 10.1038/s43017-020-0096-0
  407. Scherer, M., Kidanemariam A. G. and Uhlmann, M. (2020) On the scaling of the instability of a flat sediment bed with respect to ripple-like patterns. J. Fluid Mech. 900, A1
  408. Scherer, M., Uhlmann, M., Kidanemariam A. G., and M. Krayer (2022) On the role of turbulent large-scale streaks in generating sediment ridges, J. Fluid Mech., vol. 930, A11 DOI: 10.1017/jfm.2021.891
  409. Schielen, R. M. J., (1995) Nonlinear Stability Analysis and Pattern Formation in Morphological Models, Phd Thesis
  410. Schielen R, Doelman A, de Swart HE. (1993). On the nonlinear dynamics of free bars in straight channels. J. Fluid Mech. 252:325-56
  411. Schiller, L. and A. Neumann (1933). Uber die grundlegenden Berechungen bei der Schwerkraftaufbereitung Ver. Deutt. Ing. 77:318
  412. Schmeeckle, M. W. (2014). Numerical simulation of turbulence and sediment transport of medium sand, Journal of Geophysical Research: Earth Surface, 119, 1240-1262 DOI: 10.1002/2013JF002911.1
  413. Schumm, S. A., (1960) The shape of alluvial channels in relation to sediment type, Geological survey professional paper, n. 352-B, 17-30
  414. Sekine, M., and H. Kikkawa (1992) Mechanics of saltating grains, J. Hydraul. Eng., 118(4), 536-558
  415. Sekine, M., and G. Parker (1992), Bed-load transport on transverse slope. I, Journal of Engineering - ASCE, 118 (4), 513-535
  416. Seminara, G. (1995), Effect of grain sorting on the formation of bedforms, Applied Mechanics Reviews, 48: 549-563
  417. Seminara, G. (2010) Fluvial Sedimentary Patterns,Annu. Rev. Fluid Mech. 42:43-66
  418. Seminara G. and Tubino M. (1989). Alternate bars and meandering: free, forced and mixed interactions. In River Meandering (ed. S. Ikeda & G. Parker). AGU Water Resour Monograph, 12, pp. 267–320
  419. Seminara G. and Tubino M. (1992) Weakly nonlinear theory of regular meanders. J. Fluid Mech 244:257-88
  420. Seminara, G., Colombini, M. and Parker, G. (1996). Nearly pure sorting waves and formation of bedload sheets, J. Fluid Mech., 312, 253-278
  421. Seminara, G., Solari, L., Parker G. (2000) Trasporto solido a bassi Shields e non validita’ dell’ipotesi di Bagnold, XXVII Convegno di Idraulica e Costruzioni Idrauliche, 349-356
  422. Seminara, G., Zolezzi, G., Tubino, M. and Zardi, D. (2001a) Downstream and upstream influence in river meandering. Part 2. Planimetric development. J. Fluid Mech., 438, 213-230
  423. Seminara, G., L. Solari, and G. Parker, (2001b) Bed-load transport on arbitrarily sloping beds at low Shields stress and validity of Bagnold’s hypothesis. 2nd IAHR Symposium on River, Coastal and Estuarine Morphodynamics, RCEM 2001, 10-14 September 2001, Obihiro Japan
  424. Seminara, G., L. Solari, and G. Parker, (2002) Bed load at low Shields stress on arbitrarily sloping beds: Failure of the Bagnold hypothesis, Water Resour. Res., 38(11), 1249 DOI: 10.1029/2001WR000681
  425. Seminara, G., Bolla Pittaluga, M., and Luchi, R. (2011). Valutazione dell'efficacia di interventi di dragaggio del tratto terminale del Fiume Magra ai fini della riduzione delle condizioni di rischio idraulico. Technical Report, Department of Civil, Chemical and Environmental Engineering, University of Genova, Italy
  426. Seminara, G., Bolla Pittaluga, M., and Luchi, R. (2012). Attività di studio della morfodinamica del Fiume Magra e degli affluenti principali in relazione all'evento alluvionale del 25/10/2011 e definizione delle azioni e degli interventi di messa in sicurezza. Technical Report, Department of Civil, Chemical and Environmental Engineering, University of Genova, Italy
  427. Seminara G. and S. Lanzoni and N. Tambroni (2023) Theoretical Morphodynamics: River Meandering, Firenze University Press
  428. Serlet, A. (2018) Biomorphodynamics of river bars in channelized, hydropower-regulated rivers Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Erasmus Mundus Joint Doctorate School in Science for Management of Rivers and their Tidal System. University of Trent, Queen Mary University of London
  429. Serlet A. J., Gurnell A. M., Zolezzi G., Wharton G., Belleudy P., Jourdain C. (2018). Biomorphodynamics of alternate bars in a channelized, regulated river: an integrated historical and modelling analysis. Earth Surface Processes and Landforms 43: 1739-1756 DOI: 10.1002/esp.4349
  430. Shields, A. (1936) Application of similarity principles and turbulence research to bed-load movement. Mitteilungen der Preussichen Versuchssanstalt fur Wasserbau und Shiffbau, Berlin. In: Ott, W.P. & van Uchelen, J.C. (traslators), California Inst. Tech., W.M. Keck Lab. of Hydraulics and Water Resources, Rept. No. 167
  431. Shimizu, Y., and T. Itakura, (1989) Calculation of bed variation in alluvial channels, J. Hydraul Div. Am. Soc. Civ. Eng., 115(HY3), 367-384
  432. Simons, D. B. and Richardson, E. V. (1961) Forms of bed roghness in alluvial channels, Journal of the Hydraulics Division, ASCE, 87 (3), 87-105 Simons, D. B. and Richardson, E. V. (1966) Resistance to Flow in Alluvial Channels, U.S. Geol Survey Prof. Paper 422J, 70 p
  433. Sinha S. K. and G. Parker (1996) Causes of concavity in longitudinal profiles of rivers, Water Resources Rresearch, 32(5): 1417-1428
  434. Siviglia A., Stecca G., Vanzo D., Zolezzi G., E.F. Toro and M. Tubino (2013) Numerical modelling of two-dimensional morphodynamics with applications to river bars and bifurcations Advances in Water Resources, 52: 243-260 DOI: 10.1016/j.advwatres.2012.11.010
  435. Sklar, L. S., and W. E. Dietrich (2001), Sediment and rock strength controls on river incision into bedrock, Geology, 29, 1087-1090
  436. Sklar, L. S., and W. E. Dietrich (2002), Thresholds of alluviation in an experimental bedrock channel and controls on river incision into bedrock, Eos Trans. AGU, 83(47), Fall Meet Suppl., Abstract H12F-09
  437. Sklar, L. S., and W. E. Dietrich (2004), A mechanistic model for river incision into bedrock by saltating bed load, Water Resour. Res., 40, W06301, DOI: 10.1029/2003WR002496
  438. Sklar, L. S., and W. E. Dietrich (2006), The role of sediment in controlling bedrock channel slope: Implications of the saltation-abrasion incision model, Geomorphology, 82, 58-83 DOI: 10.1016/j.geomorph.2005.08.019
  439. Sklar, L. S., and W. E. Dietrich (2008) Implications of the Saltation-Abrasion Bedrock Incision Model for Steady-State River Longitudinal Profile Relief and Concavity. Earth Surf. Process Landforms 33, 1129-1151 DOI: 10.1002/9S164
  440. Smith, J. D., and McLean S. R. (1977). Spatially averaged flow over a wavy surface. Journal of Geophysical Research, 83, 1735-1746
  441. Sotiropoulos, F. (2019) Hydraulic Engineering in the Era of Big Data and Extreme Computing: Can Computers Simulate River Turbulence?, J. Hydraul. Eng., 145(6): 02519002 DOI: 10.1061/(ASCE)HY.1943-7900.0001594
  442. Spalart, P. R. (2009), Detached eddy-simulation, Annu. Rev. Fluid Mech., 41, 181–202
  443. Speziale, C.G. (1985) Modeling the pressure gradient-velocity correlation of turbulence. Phys Fluids 28, pp. 69-71
  444. Speziale, C.G., (1987) On nonlinear K − l and K − ϵ models of turbulence. J. Fluid Mech. 178, pp. 459-4675
  445. Speziale, C.G. (1991) Analytical methods for the development of Reynolds-stress closures in turbulence. Ann. Rev. Fluid Mech. 23, pp. 107-157
  446. Springer, G.S., and E.E. Wohl, (2002), Empirical and theoretical investigations of sculpted forms in Buckeye Creek, west Virginia. Journal of Geology, 110, 469-481
  447. Stark, C. P. (2006), A self-regulating model of bedrock river channel geometry, Geophys. Res Lett., 33, L04402 DOI: 10.1029/2005GL023193
  448. Stecca, G. (2012) Numerical modelling of gravel-bed river morphodynamics. Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Hydrodynamics and Environmental Modeling. University of Trent
  449. Stecca, G., A. Siviglia and A. Blom, (2014). Mathematical analysis of the Saint-Venant-Hirano model for mixed-sediment morphodynamics,Water Resour. Res., 50 DOI: 10.1002/2014WR015251
  450. Stecca, G., A. Siviglia and A. Blom, (2016). An accurate numerical solution to the Saint-Venant- Hirano model for mixed-sediment morphodynamics in rivers, Advances in Water Resources, 93, 39-61 DOI: 10.1016/j.advwatres.2015.05.022
  451. Stefan, S. J. (1871) Sber. Akad. Wise. Wien. 63: 63
  452. Stock J. D. and W. E. Dietrich (2003). Valley incision by debris flows: evidence of a topographic signature. Water Resources Research, 39, 1089, DOI: 10.1029/2001wr001057
  453. Stoesser, T. (2014) Large-eddy simulation in hydraulics: Quo Vadis?, Journal of Hydraulic Research, 52:4, 441-452
  454. Struiksma, N. and A. Crosato, (1989) Analysis of a 2-D bed topography model for rivers, in River Meandering Water Resour. Monogr.,vol. 12, edited by S. Ikeda and G. Parker, pp. 153-180, AGU, Washington, D.C.
  455. Struiksma, N., K. W. Olesen, C. Flokstra, and H. J. de Vriend, Bed deformation in a curved alluvial channel, J. Hydraul. Res., 23(1), 57- 79
  456. Stuart, J. T. (1958). On the non-linear mechanics of hydrodynamic stability. Journal of Fluid Mechanics, 4(1), 1-21
  457. Sukegawa, M., (1971) Study on meandering of streams in straight channels. Rep. Bureau of Resources, Dept. Science and Technology, Japan, 335-363
  458. Surian, N. and Rinaldi, M. (2003). Morphological response to river engineering and management in alluvial channels in italy. Geomorphology, 50(4):307-326
  459. Sutherland, A.J. (1967) Proposed mechanism for sediment entrainment by turbulent flows. J geophys. Res., 72, 6183-6194
  460. Taki, K. and Parker, G. (2005). Transportational cyclic steps created by flow over an erodible bed. Part 1. Experiments, Journal of Hydraulic Research, 43, 488-501
  461. Talmon, A. M. (1992). Bed topography of river bends with suspended sediment transport, Communications on Hydraulics and geotechnical Engineering, Delft University of technology, n. 92-5
  462. Talmon, A. M., M. C. L. M. Mierlo, and N. Van Struiskma (1995), Laboratory measurements of the direction of sediment transport on transverse alluvial-bed slopes., J. Hydraul. Res., 33, 495-517
  463. Tambroni, N., Seminara, G. and C. Paola (2019), On the incipient formation of bars and channels on alluvial fans. Earth Surf. Process. Landforms, 44, 2479-2493
  464. Tambroni, N., Seminara, G. and C. Paola (2019), On the incipient formation of bars and channels on alluvial fans. Earth Surf. Process. Landforms, 44, 2479-2493 Taylor, B.D. (1971) Temperature Effects in Alluvial Streams. Report No. KH-R-27, W.M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California
  465. Tennekes, H. and J. L. Lumley (1972). A first course in turbulence. MIT Press
  466. Theodorsen, T. (1952), Mechanism of turbulence, Proceedings of the Second Midwestern Conference on Fluid Mechanics, Ohio State University, 1-18
  467. Thorne, P.D., Williams, J.J. and Heathershaw, A.D. (1989) In situ acoustic measurements of marine gravel threshold and transport. Sedimentology 36, 61-74
  468. Tjerry, S., and J. Fredsøe (2005), Calculation of dune morphology, J. Geophys. Res., 110, F04013 DOI: 10.1029/2004JF000171
  469. Toffolon, M., and G. Vignoli (2007), Suspended sediment concentration profiles in nonuniform flows: Is the classical perturbative approach suitable for depth-averaged closures?, Water Resour. Res., 43, W04432 DOI: 10.1029/2006WR005183
  470. Toro-Escobar, C. M., Parker G. and Paola, C. (1996). Transfer function for the deposition of poorly sorted gravel in response to streambed aggradation. Journal of Hydraulic Research, 34(1), 35-53
  471. Townsend, A.A. (1976) The structure of turbulent shear flow. (2nd ed.), Cambridge University Press
  472. Truesdell, C. (1957) Atti Accad. naz. Lincei Re. Ser. 8 22 33, 158. (Also translation by the author in Continuum Mechanics H. The Rational Mechanics of Materials p. 295 (Ed. C Truesdell) Gordon and Breach, New York, 1965.)
  473. Tubino, M. (1991). Growth of alternate bars in unsteady flow, Water Resources Research, 27, 37-52
  474. Tubino, M. (1992) Il campo di moto e la forma di equilibrio della sezione in correnti a fondo mobile e curvatura costante, Proceedings of 23rd Convegno di Idraulica e Costruzioni Idrauliche (in Italian), D447-D458
  475. Tubino, M. and M. Colombini (1992) Correnti uniformi a superficie libera e sezione lentamente variabile, Proceedings of 23rd Convegno di Idraulica e Costruzioni Idrauliche (in Italian), D375-D386
  476. Tubino, M. and G. Seminara (1987) Unsteady alternate bars. Seminario su Leggi morfologiche e loro verifica di campo - Cosenza 25/26 giugno 1987 Editoriale Bios. ISBN 8877400730 (In Italian)
  477. Tubino, M., R. Repetto, and G. Zolezzi (1999), Free bars in rivers, J. Hydraul. Res., 37:759-775
  478. Turowski, J. M. and Bloem, J.-P. (2015) The influence of sediment thickness on energy delivery to the bed by bedload impacts, Geodin. Acta, 28, 1-10 DOI: 10.1080/09853111.2015.1047195
  479. Turowski, J. M. and Hodge, R. (2017) A probabilistic framework for the cover effect in bedrock erosion, Earth Surf. Dynam., 5, 311-330
  480. Turowski, J. M., D. Lague, and N. Hovius (2007), Cover effect in bedrock abrasion: A new derivation and its implications for the modeling of bedrock channel morphology, J. Geophys Res., 112, F04006 DOI: 10.1029/2006JF000697
  481. Turowski, J. M., D. Lague, and N. Hovius (2009), Response of bedrock channel width to tectonic forcing: Insights from a numerical model, theoretical considerations, and comparison with field data, J. Geophys. Res., 114, F03016 DOI: 10.1029/2008JF001133
  482. Uhlmann, M. (2005) An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys., 209(2):448-476
  483. Urushihara T, Meinhart C D and Adrian R J (1993) Investigation of the logarithmic layer in pipe flow using particle image velocimetry,Near-WallTurbulent Flows ed. R So et al. (New York Elsevier) 433-46
  484. Van Driest, E. R. (1956). On turbulent flow near a wall, Journal of the Aeronautical Sciences, 23, 1007
  485. Vanoni, V. A. ed., (1975) Sedimentation Engineering, ASCE Manual n. 54 van Rijn, L.C. (1984a) Sediment transport, I, Bed load transport, J. Hydraul. Eng. Am. Soc Civ. Eng., 110(10): 1431-1456
  486. van Rijn, L. C. (1984b). Sediment transport, Part II: Suspended load transport. J. Hydr. Engrg., 110(11), 1613-1641
  487. van Rijn, L. C. (1984c). Sediment transport, part III: Bed forms and alluvial roughness. Journal of Hydraulic Engineering, ASCE, 110(12), 1733-1754
  488. van Rijn, L. C. (1993). Principles of sediment transport in rivers, estuaries, and coastal areas Aqua Publications, Amsterdam, The Netherlands
  489. van Rijn, L. C. (1996). Combining laboratory, field, and mathematical modeling research for bed forms, hydraulic roughness, and sediment transport during floods. Issues and Directions in Hydraulics , T. Nakato and R. Ettema, eds., Balkema, Rotterdam, 55-73
  490. Venditti, J. G., P. A. Nelson, J. T. Minear, J. Wooster, and W. E. Dietrich (2012). Alternate bar response to sediment supply termination, J. Geophys. Res., 117, F02039 DOI: 10.1029/2011JF002254
  491. Vetsch D., Siviglia A., Caponi F., Ehrbar D., Gerke E., Kammerer S., Koch A., Peter S., Vanzo D., Vonwiller L., Facchini M., Gerber M., Volz C., Farshi D., Mueller R., Rousselot P., Veprek R., Faeh R. (2018). System Manuals of BASEMENT, Version 2.8. Laboratory of Hydraulics, Glaciology and Hydrology (VAW). ETH Zurich. Available from http://www.basement.ethz.ch
  492. Villaret, C., Hervouet, J.-M., Kopmann, R., Merkel, U., and Davies, A. G. (2013). Morphodynamic modeling using the Telemac finite-element system. Computers and Geosciences, 53, 105-113 DOI: 10.1016/j.cageo.2011.10.004
  493. Voltaire (1765) Preface to the Varberg edition of Dictionnaire philosophique portatif, London, 1765
  494. Vreugdenhil, C. B. (1994). Numerical Methods for Shallow-Water flow, Kluver Academic Publishers, Dordrecht, The Netherlands
  495. Wallace J.M. (1985). The vortical structure of bounded turbulent shear flow. In: Meier G.E.A., Obermeier F. (eds) Flow of Real Fluids. Lecture Notes in Physics, vol 235. Springer, Berlin, Heidelberg
  496. Wang, Z. B. (1989). Mathematical modelling of morphological processes in estuaries, Ph.D thesis, Communications on Hydraulic and Geotechnical Engineering, Report n. 89-1, Delft University of Technology, Netherlands, ISSN 0169-6548
  497. Wang, Z. B. (1992). Theoretical analysis on depth-integrated modelling of suspended sediment transport, J. Hydraul. Res., 30(3):403-421
  498. Warner, J. C., Sherwood, C. R., Arango, H. G., and Signell, R. P. (2005). Performance of four turbulence closure models implemented using a generic length scale method, Ocean Modellin, 8, 81-113 DOI: 10.1016/j.ocemod.2003.12.003
  499. Welford, M. R. (1994), A field test of Tubino’s (1991) model of alternate bar formation, Earth Surf. Processes Landforms, 19(4), 287-297 DOI: 10.1002/esp.3290190402
  500. Well, M.R. and Stock, D. E. (1983) The effects of crossing trajectories on the dispersion of particles in a turbulent flow, J. Fluid Mech. 136: 31-62
  501. Whipple, K. X. (2004). Bedrock rivers and the geomorphology of active orogens, Ann. Rev Earth Pl. Sci., 32, 151-185
  502. Whipple, K. X. and Tucker, G. E. (1999). Dynamics of the stream-power river incision model: implications for height limits of mountain ranges, landscape response timescales, and research needs, J. Geophys. Res., 104, 17661-17674
  503. Whipple, K.X., Hancock, G.S., and Anderson, R.S., (2000). River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion and cavitation. Geological Society of America Bulletin, 112, 490-503 DOI: 10.1130/0016-7606(2000)1122.3.CO;2
  504. Whiting, P. J., Dietrich W. E., Leopold L. B., Drake T. G. and Shreve R. L. (1988). Bedload sheets in heterogeneous sediment, Geology, 16, 105-109
  505. Wiberg, P. L. and Smith J. D. (1985) A theoretical model for saltating grains in water, Journal of Geophysical Research Atmospheres 90(NC4):7341-7354 DOI: 10.1029/JC090iC04p07341
  506. Wiberg, P.L. and Smith, J.D. (1987). Calculations of the critical shear stress for motion of uniform and heterogeneous sediments, Water Resources Research, 23, 1471-80
  507. Wiggins, S. (2003). Introduction to applied nonlinear dynamical systems and chaos (Vol. 2) Berlin, Heidelberg: Springer Science & Business Media
  508. Wilcock, P. R. (1993), Critical shear stress of natural sediments, Journal of Hydraulic Engineering, 119, 491-505
  509. Wilcock, P. R., and J. C. Crowe (2003), A surface-based transport model for sand and gravel, Journal of Hydraulic Engineering, 29, 120- 128
  510. Wilcox, D.C. (1993), Turbulence modelling for CFD, DCW Industries Inc., La Canãda, California
  511. Wilcox, D. C. (1994). Simulation of transition with a two-equation turbulence model. AIAA J., 42(2), 247-255
  512. Wilcox, D. C. (2006) Turbulence modeling for CFD. DCW Industries, Inc. La CaËœnada, California
  513. Wilcox, D. C. (2008). Formulation of the K − ω Turbulence Model Revisited. AIAA JOURNAL, 46(11):2823-2839
  514. Wilkerson, G.V. and G. Parker (2011) Physical Basis for Quasi-Universal Relationships Describing Bankfull Hydraulic Geometry of Sand-Bed Rivers, Journal of Hydraulic Engineering, 137(7)
  515. Wilkinson, C., Harbor, D.J., Helgans, E., and Kuehner, J.P., (2018). Plucking phenomena in nonuniform flow, Geosphere, 14 (5), 2157-2170
  516. Williams, P.G. (1970) Flume Width and Water Dept Effects in Sediment Transport Experiments, U.S. Geological Survey, Professional Paper 562-H
  517. Williams, G. P. (1978). Bank-full discharge of rivers. Water Resources Research, 14(6):1141-1154
  518. Whitham, G.B. (1974) Linear and Non-Linear Waves, John Wiley, New York, 636 pp.
  519. Wohl, E., and G. C. L. David (2008). Consistency of scaling relations among bedrock and alluvial channels, J. Geophys. Res., 113, F04013 DOI: 10.1029/2008JF000989
  520. Wolman, M. G. and Miller, J. P. (1960). Magnitude and frequency of forces in geomorphic processes. The Journal of Geology, 68(1):54-74
  521. Wong, M. and Parker, G. (2006) Reanalysis and Correction of Bed-Load Relation of Meyer-Peter and Müller Using Their Own Database. Journal of Hydraulic Engineering, ASCE 132(11): 1159-1168
  522. Wright, S.A., (2003), Density stratification, suspended-sediment transport, and downstream fining in large, low-slope, sand-bed rivers. Ph.D. Thesis, University of Minnesota
  523. Wright, S., and Parker, P. (2004a). Density stratification effects in sand-bed rivers. Journal of Hydraulic Engineering, 130(8), 783-795
  524. Wright, S., and Parker, P. (2004b). Flow Resistance and Suspended Load in Sand-Bed Rivers: Simplified Stratification Model Density. Journal of Hydraulic Engineering, 130(8), 796-805
  525. Wobus, C. W., G. E. Tucker, and R. S. Anderson (2006). Self-formed bedrock channels, Geophys Res. Lett., 33, L18408, DOI: 10.1029/2006GL027182
  526. Wobus, C. W., J. W. Kean, G. E. Tucker, and R. S. Anderson (2008). Modeling the evolution of channel shape: Balancing computational efficiency with hydraulic fidelity, J. Geophys. Res., 113 , F02004 DOI: 10.1029/2007JF000914
  527. Wu, F.-C., Yeh, T.-H. (2005). Forced bars induced by variations of channel width: Implications for incipient bifurcation, Journal of Geophysical Research: Earth Surface, 110(2), F02009
  528. Wu, W., and Wang, S. S. Y. (2008). One-dimensional explicit finite-volume model for sediment transport with transient flows over movable beds, Journal of Hydraulic Research, 46(1), 87-98
  529. Wu, F. -C., Y.-C. Shao, and Y.-C. Chen (2011), Quantifying the forcing effect of channel width variations on free bars: Morphodynamic modeling based on characteristic dissipative Galerkin scheme, J. Geophys. Res., 116, F03023 DOI: 10.1029/2010JF001941
  530. Yalin, M. S. (1964) Geometrical properties of sand waves, Journal of the Hydraulics Division, ASCE, 90, HY5
  531. Yalin, M. S. (1972) Mechanics of Sediment Transport, Pergamon Press, London, England
  532. Yamamoto, Y., Potthoff M, Tanaka T, Kajishima T and Y. Tsuji. (2001). Large eddy simulation of turbulent gas-particle flow in a vertical channel: effect of considering interparticle collisions J. Fluid Mech. 442:303-34
  533. Yamasaka, M., and S. Ikeda (1988), Lateral sediment transport of heterogeneous bed materials, in Proceedings, IAHR, 6th Congress Asian and Pacific Regional Division, Kyoto, Japan
  534. Yang, S. Q., S. K. Tan, and X. K. Wang (2012), Mechanism of secondary currents in open channel flows, J. Geophys. Res., 117, F04014 DOI: 10.1029/2012JF002510
  535. Zhang, Z. and Prosperetti, A. (2003) A method for particle simulation, J. Appl. Mech., 70, 64–74
  536. Zhang, Z. and Prosperetti, A. (2005) A second-order method for three-dimensional particle simulation, Journal of Computational Physics, 210, 292–324
  537. Zhang, L., Parker, G., Stark, C. P., Inoue, T., Viparelli, E. , Fu, X., and Izumi, N. (2015) Macro-roughness model of bedrock-alluvial river morphodynamics, Earth Surf. Dynam., 3, 113-138 DOI: 10.5194/esurf-3-113-2015
  538. Zhong, D., Wang, G., and Sun, Q. (2011). Transport Equation for Suspended Sediment Based on Two-Fluid Model of Solid/Liquid Two-Phase Flows. J. Hydraul. Eng., 137(5), 530-542 DOI: 10.1061/(ASCE)HY.1943-7900.0000331
  539. Zolezzi, G., and G. Seminara (2001), Downstream and upstream influence in river meandering Part 1. General theory and application to overdeepening, J. Fluid Mech., 438, 183-211
  540. Zolezzi G, Guala M, Seminara G, Termini D. (2005). Experimental observations of upstream overdeepening. J. Fluid Mech. 531:191-219
PDF
  • Publication Year: 2023
  • Pages: 378
  • eISBN: 979-12-215-0213-8
  • Content License: CC BY 4.0
  • © 2023 Author(s)

XML
  • Publication Year: 2023
  • eISBN: 979-12-215-0214-5
  • Content License: CC BY 4.0
  • © 2023 Author(s)

PRINT
  • Publication Year: 2023
  • Pages: 378
  • ISBN: 979-12-215-0212-1
  • Content License: CC BY 4.0
  • © 2023 Author(s)

Bibliographic Information

Book Title

Theoretical Morphodynamics: Straight Channels

Authors

Giovanni Seminara, Stefano Lanzoni, Nicoletta Tambroni

Peer Reviewed

Number of Pages

378

Publication Year

2023

Copyright Information

© 2023 Author(s)

Content License

CC BY 4.0

Metadata License

CC0 1.0

Publisher Name

Firenze University Press

DOI

10.36253/979-12-215-0213-8

ISBN Print

979-12-215-0212-1

eISBN (pdf)

979-12-215-0213-8

eISBN (xml)

979-12-215-0214-5

Series Title

Studies in Sciences and Technology

95

Fulltext
downloads

274

Views

Search in This Book
Export Citation
Suggested Books

1,303

Open Access Books

in the Catalogue

1,746

Book Chapters

3,161,365

Fulltext
downloads

3,987

Authors

from 820 Research Institutions

of 63 Nations

63

scientific boards

from 339 Research Institutions

of 43 Nations

1,148

Referees

from 346 Research Institutions

of 37 Nations