A review of the state of research on bridge pier scour under combined action of waves and current

Kumar, Lalit; Afzal, Mohammad Saud

doi:10.1007/s11600-022-01001-4

Artykuł - szczegóły

Tytuł artykułu

A review of the state of research on bridge pier scour under combined action of waves and current

Autorzy

Kumar Lalit , Afzal Mohammad Saud

Wybrane pełne teksty z tego czasopisma

https://www.springer.com/journal/11600

Identyfikatory

DOI

10.1007/s11600-022-01001-4

Warianty tytułu

Języki publikacji

Abstrakty

This article presents a review of the state of research on bridge pier scour under combined wave–current flow. The hydrodynamics and scour around the bridge pier under combined wave–current flow have been explained in detail based on the information available in the literature. The impact of relative flow velocity (U_cw), Keulegan–Carpenter number (KC), absolute Reynolds number (R_ea), and sediment characteristics on bridge pier scour under combined wave–current flow is presented. This study includes physical modelling of scour with various formulations to predict scour depth and calculation procedures related to scour under combined wave–current flow in the coastal environment. In addition, this study also provides the development of numerical models to investigate bridge pier scour in detail. In the end, future prospects of hydrodynamics and scour around the bridge pier under combined wave–current flow are delineated.

Słowa kluczowe

bridge pier scour hydrodynamics horseshoe vortex lee-wake vortex combined wave–current flow

Wydawca

Instytut Geofizyki PAN
Springer

Czasopismo

Acta Geophysica

Rocznik

2023

Tom

Vol. 71, no. 5

Strony

2359--2379

Opis fizyczny

Bibliogr. 149 poz., rys.

Twórcy

autor

Kumar Lalit

lkumar@iitkgp.ac.in

Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India

https://orcid.org/0000-0001-8792-4078

autor

Afzal Mohammad Saud

saud@civil.iitkgp.ac.in

Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India

Bibliografia

1. Abbasnia AH, Ghiassi R (2011) Improvements on bed-shear stress formulation for pier scour computation. Int J Numer Methods Fluids 67:383–402
2. Afzal MS, Kumar L (2021) Propagation of waves over a rugged topography. J Ocean Eng Sci 7(1):14–28. https://doi.org/10.1016/j.joes.2021.04.004
3. Afzal MS, Holmedal LE, Myrhaug D (2015) Three-dimensional streaming in the seabed boundary layer beneath propagating waves with an angle of attack on the current. J Geophys Res Ocean. https://doi.org/10.1002/2015JC010793
4. Afzal MS, Bihs H, Kumar L (2020) Computational fluid dynamics modeling of abutment scour under steady current using the level set method. Int J Sediment Res 35:355–364. https://doi.org/10.1016/j.ijsrc.2020.03.003
5. Afzal MS, Holmedal LE, Myrhaug D (2021) Sediment transport in combined wave–current seabed boundary layers due to streaming. J Hydraul Eng 147:4021007. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001862
6. Afzal MA, Bihs H, Arntsen ØA (2014) 3D Numerical Modelling of Contraction Scour under Steady Current Using the Level Set Method. In: ICHE 2014. Proceedings of the 11th International Conference on Hydroscience and Engineering. pp 525–530.
7. Agrawal KA, Khan MA, Yi Z (2005) Handbook of Scour Countermeasures Designs (No FHWA-NJ-2005–027). New Jersey Department of Transportation.
8. Agui JH, Andreopoulos J (1992) Experimental investigation of a three-dimensional boundary layer flow in the vicinity of an upright wall mounted cylinder. J Fluids Eng 114(4):566–576. https://doi.org/10.1115/1.2910069
9. Ali KHM, Karim O (2002) Simulation of flow around piers. J Hydraul Res 40:161–174
10. Apsilidisl N, Diplas P, Dancey CL, et al (2010) Local scour at bridge piers: the role of reynolds number on horseshoe vortex dynamics. In: Proceedings 5th international conference on scour and Erosion (ICSE-5), 2010, San Francisco, USA. pp 86–94
11. Arneson LA, Zevenbergen LW, Lagasse PF, Clopper PE (2012) Hydraulic Engineering Circular No 18: evaluating scour at bridges. US Dep Transp
12. Azamathulla HM, Ghani AA, Zakaria NA, Guven A (2010) Genetic programming to predict bridge pier scour. J Hydraul Eng 136:165
13. Baker VR (1979) Erosional processes in channelized water flows on Mars. J Geophys Res Solid Earth 84:7985–7993
14. Belibassakis KA, Athanassoulis GA, Gerostathis TP (2001) A coupled-mode model for the refraction–diffraction of linear waves over steep three-dimensional bathymetry. Appl Ocean Res 23:319–336
15. Bouratsis P, Diplas P, Dancey CL, Apsilidis N (2017) Quantitative spatio-temporal characterization of scour at the base of a cylinder. Water 9:227
16. Breusers HNC, Nicollet G, Shen HW (1977) Local scour around cylindrical piers. J Hydraul Res 15:211–252
17. Breusers HNC, Raudkivi AJ (1991) Scouring AA Balkema
18. Chabert J, Engeldinger P (1956) Study of scour around bridge piers. Rep Prep Lab Natl d’Hydraulique
19. Chen B, Li S (2018) Experimental Study of Local Scour around a vertical cylinder under wave-only and combined wave-current conditions in a large-scale flume. J Hydraul Eng 144:4018058
20. Chiew Y-M (1992) Scour protection at bridge piers. J Hydraul Eng 118:1260–1269
21. Chiew YM, Melville BW (1989) Local scour at bridge piers with non-uniform sediments. Proc Inst Civ Eng 87:215–224
22. Chiew YM (1984) Local scour at bridge piers. ResearchSpace@ Auckland
23. Craswell T, Akib S (2020) Reducing bridge pier scour using gabion mattresses filled with recycled and alternative materials. Eng 1(2):188–210
24. Dargahi B (1989) The turbulent flow field around a circular cylinder. Exp Fluids 8:1–12
25. Dargahi B (2003) Three-dimensional modelling of ship-induced flow and erosion. Proc Instit Civ EngWater Marit Eng 152(2):193–204
26. Debnath K, Chaudhuri S (2010) Bridge pier scour in clay-sand mixed sediments at near-threshold velocity for sand. J Hydraul Eng 136(9):597–609
27. Dey S (2001) Experimental studies on incipient motion of sediment particles on generalized sloping fluvial beds. J Sediment Res 16(3):391–398
28. Dey S (2014) Fluvial hydrodynamics. Springer
29. Dey S, Bose SK, Sastry GLN (1995) Clear water scour at circular piers: a model. J Hydraul Eng 121(12):869–876
30. Dey S, Sumer BM, Fredsøe J (2006) Control of scour at vertical circular piles under waves and current. J Hydraul Eng 132(3):270–279
31. Dey S, Bose S, Sastry GLN (1992a) Clear water scour at circular piers, part I: Flow model. In Proceedings of the 8th Conference IAHR Asian and Pacific Division. pp. 69–80.
32. Dey S, Bose S, Sastry GLN (1992b) Clear water scour at circular piers, part II: Flow model. In Proceedings of the 8th Conference IAHR Asian and pacific division. pp. 81–92
33. Drake DE, Cacchione DA, Grant WD (1992) Shear stress and bed roughness estimates for combined wave and current flows over a rippled bed. J Geophys Res Ocean 97(C2):2319–2326
34. Dyrseth S (2015) Time scales for scour below pipelines and around vertical piles in nonlinear random waves and current. NTNU.
35. Eadie RW IV, Herbich JB (1987) Scour about a single, cylindrical pile due to combined random waves and a current. Coast Eng 206:1858–1870
36. Ebersole BBA (1985) Refraction-diffraction model for linear water waves. J Waterw Port, Coast, Ocean Eng 111(6):939–953
37. Engelund F, Fredsøe J (1976) A sediment transport model for straight alluvial channels. Hydrol Res 7(5):293–306
38. Engelund F, Fredsøe J (1982) Hydraulic theory of alluvial rivers. Adv Hydrosci Elsev 13:187–215
39. Escauriaza C, Sotiropoulos F (2011) Initial stages of erosion and bed form development in a turbulent flow around a cylindrical pier. J Geophys Res Earth Surf 116(3):109
40. Ettema R, Constantinescu G, Melville BW (2017) Flow-field complexity and design estimation of pier-scour depth: sixty years since Laursen and Toch. J Hydraul Eng 143(9):3117006
41. Ettema R (1980) Scour at bridge piers
42. Fotherby LM (1993) Alternatives to riprap for protection against local scour at bridge piers. Tran Res Rec 1420:1–12
43. Fredsoe J, Sumer BM, Arnskov MM, others (1991) Time scale for wave/current scour below pipelines. In: the first international offshore and polar engineering conference.
44. Fredsoe J, Sumer BM (2006) Hydrodynamics around cylindrical structures (revised edition). World Scientific, Singapore
45. Gautam S, Dutta D, Bihs H, Afzal MS (2021) Three-dimensional computational fluid dynamics modelling of scour around a single pile due to combined action of the waves and current using level-set method. Coast Eng 170:104002. https://doi.org/10.1016/j.coastaleng.2021.104002
46. Gazi AH, Afzal MS, Dey S (2019) Scour around piers underwaves: current status of research and its future prospect. Water 11(11):1–14
47. Ge L, Sotiropoulos F (2005) 3D unsteady RANS modeling of complex hydraulic engineering flows I: numerical model. J Hydraul Eng 131(9):800–808
48. Ge L, Sotiropoulos F (2007) A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries. J Comput Phys 225(2):1782–1809. https://doi.org/10.1016/j.jcp.2007.02.017
49. Ghorbani B, Kells JA (2008) Effect of submerged vanes on the scour occurring at a cylindrical pier. J Hydraul Res 46(5):610–619
50. Graf WH, Istiarto I (2002) Flow pattern in the scour hole around a cylinder. J Hydraul Res 40(1):13–20
51. Hartvig PA, Thomsen JM, Frigaard P, Andersen TL (2010) Experimental study of the development of scour and backfilling. Coast Eng J 52(02):157–194. https://doi.org/10.1142/S0578563410002154
52. Heidarpour M (2002) Control and reduction of local scour at bridge piers by using slot. In: Proceeding International Conference on Fluvial Hydraulics. pp 3–6
53. Hjorth P (1975) Studies on the nature of local scour. Inst. för Teknisk Vattenresurslära, Lunds Tekniska Högskola, Lunds Univ
54. Hudspeth RT (2006) Waves and wave forces on coastal and ocean structures. World scientific, Singapure, p 109
55. Hussein HJ, Martinuzzi RJ (1996) Energy balance for turbulent flow around a surface mounted cube placed in a channel. Phys Fluids 8(5):764–780
56. Jia YY, Wang X, Wang SS (2002) Numerical simulation of local scouring around a cylindrical pier. First Int Conf Scour Foundat 17:1181–1187
57. Jing L, Ridd PV (1996) Wave-current bottom shear stresses and sediment resuspension in Cleveland Bay. Australia Coast Eng 29(1):169–186
58. Jonsson IG (1990) Wave-current interactions. In: LeMehaute B, Hanes DM (eds) the sea, ocean engineering science Journal. Wile, New Sersey, pp 65–120
59. Kawata Y, Tsuchiya Y (1989) Local scour around cylindrical piles due to waves and currents combined. Coast Eng 1988:1310–1322
60. Keulegan GH, Carpenter LH et al (1958) Forces on cylinders and plates in an oscillating fluid. J Res Natl Bur Stand 60(5):423–440
61. Keutner C (1932) Stromungsvorgange an strompfeilern von verschiedenen grundrissformen und ihre einwirkung auf die flussohle. Die Bautechnik 10:161–170
62. Kharif C, Pelinovsky E (2003) Physical mechanisms of the rogue wave phenomenon. Eur J Mech B/fluids 22(6):603–634
63. Khosronejad A, Kang S, Borazjani I, Sotiropoulos F (2011) Curvilinear immersed boundary method for simulating coupled flow and bed morphodynamic interactions due to sediment transport phenomena. Adv Water Resour 34(7):829–843
64. Khosronejad A, Kang S, Sotiropoulos F (2012) Experimental and computational investigation of local scour around bridge piers. Adv Water Resour 37:73–85
65. Kim UY, Kim Jon-S, Ahn SJ, Hahm C-H (2005) Scour countermeasure using additional facility in front of bridge pier. Proc 31st IAHR Congr Seoul 1289–1290.
66. Kirkil G, Constantinescu SG, Ettema R (2008) Coherent structures in the flow field around a circular cylinder with scour hole. J Hydraul Eng 134(5):572–587
67. Kirkil G, Constantinescu G, Ettema R (2009) Detached eddy simulation investigation of turbulence at a circular pier with scour hole. J Hydraul Eng 135(11):888
68. Kirkil G, Constantinescu SG, Ettema R (2005) The horseshoe vortex system around a circular bridge pier on a flat bed. In: XXXIst International association hydraulic research congress, Seoul, Korea.
69. Kothyari UC, Kumar A (2010) Temporal variation of scour around circular bridge piers. ISH J Hydraul Eng 169(sup1):35–48
70. Kumar V, Raju KGR, Vittal N (1999) Reduction of local scour around bridge piers using slots and collars. J Hydraul Eng 125(12):1302–1305
71. Larsen BE, Fuhrman DR, Sumer BM (2016) Simulation of wave-plus-current scour beneath submarine pipelines. J Waterw Port Coast Ocean Eng 142(5):4016003
72. Laursen EM, Toch A (1956) Scour around bridge piers and abutments. Iowa highway research board Ames, IA.
73. Li J, Zhang B, Shen C, Fu X, Li W (2021) Experimental study on local scour depth around Monopile foundation in combined waves and current. Sustainability 13(24):13614
74. Link O, Castillo C, Pizarro A, Rojas A, Ettmer B, Escauriaza C, Manfreda S (2017) A model of bridge pier scour during flood waves. J Hydraul Res 55(3):310–323
75. Liu W, Wang B, Guo Y, Zhang J, Chen Y (2020) Experimental investigation on the effects of bed slope and tailwater on dam-break flows. J Hydrol 590:125256. https://doi.org/10.1016/j.jhydrol.2020.125256
76. Mallory JK (2015) Abnormal Waves on the South East Coast of South Africa. Int Hydrogr Rev 51:105
77. Melville BW, Coleman SE (2000) Bridge scour. Water Resources Publication.
78. Melville BW, Chiew Y-M (1999) Time scale for local scour at bridge piers. J Hydraul Eng 125(1):59–65
79. Melville BW, Raudkivi AJ (1977) Flow characteristics in local scour at bridge piers. J Hydraul Res 15(4):373–380
80. Melville BW, Raudkivi AJ (1996) Effects of foundation geometry on bridge pier scour. J Hydraul Eng 122(4):203–209
81. Melville BW (1975) Local scour at bridge sites. Researchspace @ auckland
82. Mostafa YE, Agamy AF (2011) Scour around single pile and pile groups subjected to waves and currents. Int J Eng Sci Technol IJEST 3(11):8160–8178
83. Nagata N, Hosoda T, Nakato T, Muramoto Y (2005) Three-dimensional numerical model for flow and bed deformation around river hydraulic structures. J Hydraul Eng 131(12):1074–1087
84. Nielsen P (1992) Coastal bottom boundary layers and sediment transport. World scientific.
85. Nurtjahyo PY (2002) Numerical simulation of pier scour and contraction scour. Dept of Civ Eng, Ocean Eng Prog 15:15
86. Oliveto G, Hager WH (2002) Temporal evolution of clear-water pier and abutment scour. J Hydraul Eng 128(9):811–820
87. Olsen NRB, Kjellesvig HM (1998) Three-dimensional numerical flow modelling for estimation of maximum local scour depth. IAHR J Hydraul Res 36(4):579–590
88. Olsen NRB, Melaaen MC (1993) Three-dimensional calculation of scour around cylinders. J Hydraul Eng 119(9):1048–1054
89. Paik J, Sotiropoulos F, Porté-Agel F (2009) Detached eddy simulation of flow around two wall-mounted cubes in tandem. Int J Heat Fluid Flow 30(2):286–305. https://doi.org/10.1016/j.ijheatfluidflow.2009.01.006
90. Park JH, Kim KH (2010) The local scour around a slender pile in combined waves and current. J Korean Soc Coast Ocean Eng 22(6):405–414
91. Park C-W, Il PH, Cho Y-K (2017) Evaluation of the applicability of pier local scour formulae using laboratory and field data. Mar Georesources Geotechnol 35(1):1–7
92. Parker G, Toro-Escobar C, Voigt Jr RL (1998) Countermeasures to protect bridge piers from scour.
93. Peregrine DH (1976) Interaction of water waves and currents. Advances in applied mechanics. Elsevier, New Jersey, pp 9–117
94. Petersen TU, Sumer BM, Fredsøe J (2012) Time scale of scour around a pile in combined waves and current. In: International Conference on Coastal Engineering. pp 30:08
95. Porter K, Simons R, Harris J, Ferradosa TF (2012) Scour development in complex sediment beds. Coast Eng 2:33
96. Qi W-G, Gao F-P (2014a) Physical modeling of local scour development around a large-diameter monopile in combined waves and current. Coast Eng 83:72–81
97. Qi W, Gao F (2014b) Equilibrium scour depth at offshore monopile foundation in combined waves and current. Sci China Technol Sci 57:1030–1039
98. Qi M, Li J, Chen Q (2016) Comparison of existing equations for local scour at bridge piers: parameter influence and validation. Nat Hazards 82(3):2089–2105
99. Qi W, Gao F, Han X, et al (2012) Local scour and pore-water pressure around a monopile foundation under combined waves and currents. In: The Twenty-second International Offshore and Polar Engineering Conference.
100. Quezada M, Tamburrino A, Niño Y (2019) Numerical study of the hydrodynamics of waves and currents and their effects in pier scouring. Water 11(11):2256
101. Raaijmakers T, Rudolph D (2008) Time-dependent scour development under combined current and Waves conditions-laboratory experiments with online monitoring technique. In: proceedings 4th international conference on scour and erosion (ICSE-4). 5: 7, 2008, Tokyo, Japan. 152–161.
102. Reeve D, Chadwick A, Fleming C (2018) Coastal engineering: processes, theory and design practice. CRC Press
103. Richardson E V, Davis SR, others (2001) Evaluating scour at bridges.
104. Richardson JE, Panchang VG (1998) Three-dimensional simulation of scour-inducing flow at bridge piers. J Hydraul Eng 124(5):530–540
105. Roelvink D (2011) A guide to modeling coastal morphology. Singapure, World scientific, pp 3–33
106. Rooney DM, Machemehl JL (1977) Using suction to minimize sand-bed scour. J Hydraul Div 103(4):443–449
107. Roper AT, Schneider VR, Shen HW (1967) Analytical approach to local scour, pre-congress. Proc Pap 3:10–19
108. Roulund A, Sumer BM, Fredsøe J, Michelsen J (2005) Numerical and experimental investigation of flow and scour around a circular pier. J Fluid Mech 534:351–401
109. Roulund A, Sutherland J, Todd D, Sterner J (2016) Parametric equations for Shields parameter and wave orbital velocity in combined current and irregular waves. 8 th international conference of scour and erosion. Taylor & Francis Group, Oxford, UK, pp 313–318
110. Salaheldin TM, Imran J, Chaudhry MH (2004) Numerical modeling of three-dimensional flow field around circular piers. J Hydraul Eng 130(2):91–100
111. Schendel A, Welzel M, Schlurmann T, Hsu T-W (2020) Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coast Eng 161:103751
112. Shatanawi KM, Aziz NM, Khan AA (2008) Frequency of discharge causing abutment scour in South Carolina. J Hydraul Eng 134(10):1507–1512
113. Sheppard DM, Melville B, Demir H (2014) Evaluation of existing equations for local scour at bridge piers. J Hydraul Eng 140(1):14–23
114. Simarro G, Civeira S, Cardoso AH (2012) Influence of riprap apron shape on spill-through abutments. J Hydraul Res 50(1):138–141
115. Simons DB, Chen Y-H, Swenson LJ (1984) Hydraulic test to develop design criteria for the use of Reno mattresses. Rep Maccaferri 3:12
116. Soltani-Gerdefaramarzi S, Afzalimehr H, Chiew Y-M, Gallichand J (2014) Reduction of pier scour using bed suction and jet injection. In: proceedings of the institution of civil engineers-water management. 105–114.
117. Soulsby R (1997) Dynamics of marine sands: a manual for practical applications. Oceanog Literat Rev 9(44):947
118. Soulsby R (1997) Dynamics of marine sands. Oceanogr Literat Rev 9(44):947–1997
119. Soulsby RL, Clarke S (2005) Bed shear-stress under combined waves and currents on smooth and rough beds (TR 137).
120. Sumer BM, Fredsøe J (1997) Scour at the head of a vertical-wall breakwater. Coast Eng 29(3–4):201–230
121. Sumer BM, Fredsøe J (2001) Scour around pile in combined waves and current. J Hydraul Eng 127(5):403–411
122. Sumer B, Fredsøe J, Christiansen N (1992a) Scour around vertical pile in waves. J Waterw Port, Coastal, Ocean Eng 118(1):15–31. https://doi.org/10.1061/(ASCE)0733-950X(1992)118:1(15)
123. Sumer B, Christiansen N, Fredsøe J (1993) Influence of cross section on wave scour around piles. J Waterw Port, Coastal, Ocean Eng 119(5):477–495. https://doi.org/10.1061/(ASCE)0733-950X(1993)119:5(477)
124. Sumer BM, Christiansen N, Fredsøe J (1997) The horseshoe vortex and vortex shedding around a vertical wall-mounted cylinder exposed to waves. J Fluid Mech 332:41–70
125. Sumer BM, Whitehouse RJS, Tørum A (2001) Scour around coastal structures: a summary of recent research. Coast Eng 44(2):153–190
126. Sumer BM, Hatipoglu F, Fredsøe J (2007) Wave scour around a pile in sand, medium dense, and dense silt. J Waterw Port, Coastal, Ocean Eng 133(1):14–27
127. Sumer BM, Petersen TU, Locatelli L et al (2013) Backfilling of a scour hole around a pile in waves and current. J Waterw Port, Coastal, Ocean Eng 139(1):9–23
128. Sumer BM, Fredsøe J, others (2002) Time scale of scour around a large vertical cylinder in waves. In: the twelfth international offshore and polar engineering conference.
129. Sumer BM, Christiansen N, Fredsoe J, others (1992b) Time scale of scour around a vertical pile. In: the second international offshore and polar engineering conference.
130. Tafarojnoruz A, Gaudio R, Dey S (2010) Flow-altering countermeasures against scour at bridge piers: a review. J Hydraul Res 48(4):441–452
131. Tanaka S, Yano M (1967) Local scour around a circular cylinder.
132. Tang Z, Melville B, Singhal N et al (2022) Countermeasures for local scour at offshore wind turbine monopile foundations: a review. Water Sci Eng 33:e101572
133. Thomas GP, Klopman G (1997) Wave-current interactions in the near shore region. Int Ser Adv Fluid Mech 10:255–319
134. Tison LJ (1940) Erosion autour des piles de ponts en riviere. In: Annales des Travaux publics de Belgique. pp 813–817
135. Tseng M-H, Yen C-L, Song CCS (2000) Computation of three-dimensional flow around square and circular piers. Int J Numer Methods Fluids 34(3):207–227
136. Umeda S (2011) Scour regime and scour depth around a pile in waves. J Coast Res 845–849
137. Unger J, Hager WH (2007) Down-flow and horseshoe vortex characteristics of sediment embedded bridge piers. Exp Fluids 42(1):1–19
138. van Rijn LC (1984) Sediment transport, part II: suspended load transport. J Hydraul Eng 110:1613–1641
139. van Rijn LC (1984) Sediment Transport, Part I: Bed Load Transport. J Hydraul Eng 110(10):1431–1457
140. Wang J, Geng L, Ding L et al (2020) The state-of-the-art review on energy harvesting from flow-induced vibrations. Appl Energy 267:114902
141. Wang RK, Herbich JB (1983) Combined current and wave-produced scour around a single pile. Texas Engineering Experiment Station
142. Wilcox DC (1994) Turbulence Modeling for {CFD}. DCW Industries Inc, La Canada, California
143. Wu W, Wang SS (2002) Prediction of local scour of non-cohesive sediment around bridge piers using FVM-based CCHE2D Model. In: first international conference on scour of foundations. November 17–20, 2002, College Station, USA. pp 1176–1180.
144. Yang Y, Melville BW, Macky GH, Shamseldin AY (2019) Local scour at complex bridge piers in close proximity under clear-water and live-bed flow regime. Water 11(8):1530
145. Yang P, Li R, Pan L (2022) Effects of bed roughness on a horseshoe vortex in overland water flowing past a cylinder. J Hydrol 606:127385
146. Yin Z, Wang Y, Jia Q (2019) Hydrodynamic Characteristics of a Pneumatic Breakwater with Combined Wave-Current Actions: A Numerical Investigation. J Coast Res 36(1):196–203. https://doi.org/10.2112/JCOASTRES-D-18-00140.1
147. Younis MY, Zhang H, Hu B et al (2014) Investigation of different aspects of laminar horseshoe vortex system using PIV. J Mech Sci Technol 28(2):527–537
148. Zeng J, Constantinescu G., Weber L (2005) A fully 3d non- hydrostatic model for prediction of flow, sediment transport and bed morphology in open channels. In: n proceedings of the 31st IAHR Congress, pp 1327–1338.
149. Zhang W, Zapata MU, Bai X et al (2020) Three-dimensional simulation of horseshoe vortex and local scour around a vertical cylinder using an unstructured finite-volume technique. Int J Sediment Res 35(3):295–306

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Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).

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