Load of the Small-Scale Vertical Cylinder in a Wave–Current Field

Abstract

Studies of wave–current interactions are vital for the safe design of structures. Regular waves in the presence of uniform, linear shear, and quadratic shear currents are explored by the High-Level Green–Naghdi model in this paper. The five-point central difference method is used for spatial discretization, and the fourth-order Adams predictor–corrector scheme is employed for marching in time. The domain-decomposition method is applied for the wave–current generation and absorption. The effects of currents on the wave profile and velocity field are examined under two conditions: the same velocity of currents at the still-water level and the constant flow volume of currents. Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity. Then, loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated. The maximum load intensity and load fluctuation amplitude in uniform, linear shear, and quadratic shear currents increase sequentially. The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents. The stretched superposition method obtains a poor approximation for strong nonlinear waves, particularly in the case of the opposing quadratic shear current.

Keywords

Wave-current interaction / Cylinder load / HLGN model / Morison equation / Regular waves

References

[1] AbbasniaA, Guedes SoaresC. Fully nonlinear propagation of waves in a uniform current using NURBS numerical wave tank. Ocean Engineering, 2018, 163: 115-125

[2] BaddourRE, SongSW. The rotational flow of finite amplitude periodic water waves on shear currents. Applied Ocean Research, 1998, 20: 163-171

[3] BanihashemiS, KirbyJT, DongZ. Approximation of wave action flux velocity in strongly sheared mean flows. Ocean Modelling, 2017, 116: 33-47

[4] ChenHF, ZouQP. Effects of following and opposing vertical current shear on nonlinear wave interactions. Applied Ocean Research, 2019, 89: 23-35

[5] ChenL, BasuB. Numerical continuation method for large-amplitude steady water waves on depth-varying currents in flows with fixed mean water depth. Applied Ocean Research, 2021, 111: 102631

[6] ChenLF, NingDZ, TengB, ZhaoM. Numerical and experimental investigation of nonlinear wave-current propagation over a submerged breakwater. Journal of Engineering Mechanics, 2017, 143(9): 04017061

[7] ChoiW. Nonlinear surface waves interacting with a linear shear current. Mathematics and Computers in Simulation, 2009, 80(1): 29-36

[8] ConstantinA, EscherJ. Symmetry of steady periodic surface water waves with vorticity. Journal of Fluid Mechanics, 2004, 498: 171-181

[9] ConstantinA, KalimerisK, ScherzerO. Approximations of steady periodic water waves in flows with constant vorticity. Nonlinear Analysis-Real World Applications, 2015, 25: 276-306

[10] DalrympleRA. A finite amplitude wave on a linear shear current. Journal of Geophysical Research, 1974, 79(30): 4498-4504

[11] DalrympleRA, CoxJC. Symmetric finite-amplitude rotational water waves. Journal of Physical Oceanography, 1976, 6(6): 847-852

[12] DNVDNVGL-RP-C205: Environmental conditions and environmental loads, 2021, Oslo, Det Norske Veritas

[13] DuanWY, ZhengK, ZhaoBB, DemirbilekZ, ErtekinRC, WebsterWC. On wave-current interaction by the Green-Naghdi equations in shallow water. Natural Hazards, 2016, 84: S567-S583

[14] HsuHC, ChenYY, HsuJRC, TsengWJ. Nonlinear water waves on uniform current in Lagrangian coordinates. Journal of Nonlinear Mathematical Physics, 2009, 16(1): 47-61

[15] KirbyJT, ChenTM. Surface waves on vertically sheared flows: approximate dispersion relations. Journal of Geophysical Research: Oceans, 1989, 94: 1013-1027

[16] KoJ, StraussW. Effect of vorticity on steady water waves. Journal of Fluid Mechanics, 2008, 608: 197-215

[17] KumarA, HayatdavoodiM. On wave-current interaction in deep and finite water depths. Journal of Ocean Engineering and Marine Energy, 2023, 9: 455-475

[18] KumarA, HayatdavoodiM. Effect of currents on nonlinear waves in shallow water. Coastal Engineering, 2023, 181: 104278

[19] LiY, EllingsenS. A framework for modeling linear surface waves on shear currents in slowly varying waters. Journal of Geophysical Research-Oceans, 2019, 124(4): 2527-2545

[20] NwoguOG. Interaction of finite-amplitude waves with vertically sheared current fields. Journal of Fluid Mechanics, 2009, 627: 179-213

[21] SonS, LynettPJ. Interaction of dispersive water waves with weakly sheared currents of arbitrary profile. Coastal Engineering, 2014, 90: 64-84

[22] SteerJN, BorthwickAGL, StagonasD, BuldakovE, van den BremerTS. Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents. Journal of Fluid Mechanics, 2020, 884: A40

[23] SwanC. An experimental study of waves on a strongly sheared current profile. Proceeding of 22nd Coastal Engineering, 1990489-502

[24] SwanC, CumminsIP, JamesRL. An experimental study of two-dimensional surface water waves propagating on depth-varying current. Part 1. Regular waves. Journal of Fluid Mechanics, 2001, 428: 273-304

[25] SwanC, JamesRL. A simple analytical model for surface water waves on a depth-varying current. Applied Ocean Research, 2000, 22: 331-347

[26] ThomasGP. Wave-current interactions: an experimental and numerical stud. Part 1. Linear waves. Journal of Fluid Mechanics, 1981, 110: 457-474

[27] ThomasGP. Wave-current interactions: an experimental and numerical study. Part 2. Nonlinear waves. Journal of Fluid Mechanics, 1990, 216: 505-536

[28] TouboulJ, CharlandJ, ReyV, BelibassakisK. Extended mildslope equation for surface waves interacting with a vertically sheared current. Coastal Engineering, 2016, 116: 77-88

[29] UmeyamaM. Coupled PIV and PTV measurements of particle velocities and trajectories for surface waves following a steady current. Journal of Waterway Port Coastal and Ocean Engineering, 2011, 137(2): 85-94

[30] UmeyamaM. Dynamic-pressure distributions under Stokes waves with and without a current. Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2017, 376(2111): 20170103

[31] YangZT, LiuPLF. Depth-integrated wave-current model. Part 1. Two-dimensional formulation and applications. Journal of Fluid Mechanics, 2020, 883: A4

[32] YangZT, LiuPLF. Depth-integrated wave-current model. Part 2. Current with an arbitrary profile. Journal of Fluid Mechanics, 2022, 936: A31

[33] ZhangJS, ZhangY, JengDS, LiuPLF, ZhangC. Numerical simulation of wave-current interaction using a RANS solver. Ocean Engineering, 2014, 75: 157-164

[34] ZhaoBB, DuanWY, ErtekinRC. Application of higher-level GN theory to some wave transformation problems. Coastal Engineering, 2014, 83: 177-189

[35] ZhaoBB, LiMJ, DuanWY, ErtekinRC, HayatdavoodiM. An effective method for nonlinear wave-current generation and absorption. Coastal Engineering, 2023, 185: 104359

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