1. Key Laboratory of Engineering Sediment, Tianjin Research Institute for Water Transport Engineering, Ministry of Transport, Tianjin 300456, China 2. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300350, China 3. CCCC First Harbor Consultants Limited Company, Tianjin 300222, China
A three-dimensional coupled wave-current model was established based on a new three-dimensional radiation stress formulation including the beach slope effects in order to reasonably simulate the nearshore waves and circulations. Two kinds of surface roller models were implemented, and the wave-induced horizontal turbulent mixing effects were included in the coupled model. A number of experimental cases were used to validate the established model. The validation results show that the model can accurately simulate the nearshore wave propagation and various wave-induced circulation phenomena, including the wave setup, longshore current, undertow and rip current. The present wave-current coupling system can comprehensively describe the nearshore wave-current interaction, and the new three-dimensional radiation stress formulation used in the model can provide better performances than the other formulations for vertical flow structure simulations. The different surface roller models were used to obtain more accurate simulation results for different nearshore circulation cases, indicating that a more generally appropriate surface roller model requires further investigation. The wave-induced horizontal turbulent mixing can make the flow field smoother and avoid a too sharp velocity distribution.
Chao JI,Qing-he ZHANG,Dian-guang MA,Yue-feng WU,Qi JIANG. Nearshore coupled wave-current model based on new three-dimensional radiation stress formulation. Journal of ZheJiang University (Engineering Science), 2022, 56(1): 128-136.
Fig.1Information exchange between model components
Fig.2Validation of wave height, wave setup and setdown, and longshore current for experiment with oblique wave incidence
Fig.3Validation of wave height, wave setup and setdown, and undertow for experiment with normal wave incidence
Fig.4Validation of wave height for DUCK94 experiment
Fig.5Validation of vertical profiles of wave-induced nearshore circulation for DUCK94 experiment
Fig.6Wave and flow fields from model simulations for rip current case
Fig.7Validation of normalized cross-shore velocities in different cross-shore transects for rip current case
Fig.8Simulated wave fields by only wave model and coupled model for test T of rip experiment
Fig.9Comparison of simulated wave height distributions in cross-shore transect located at y = 8.5 m by only wave model and coupled model with measured data for test T of rip experiment
Fig.10Comparison of undertow from model simulations using different radiation stress formulations with measured data
Fig.11Comparison of normalized cross-shore velocities from model simulations using different radiation stress formulations with measured data for rip current case
Fig.12Comparison of wave setup and setdown, and longshore current from model simulations using different surface roller models with measured data
Fig.13Comparison of undertow from model simulations using different surface roller models with measured data
Fig.14Effects of wave-induced horizontal turbulent mixing on longshore current distributions
Fig.15Effects of wave-induced horizontal turbulent mixing on rip current distributions
[1]
XIA M, MAO M, NIU Q Implementation and comparison of the recent three-dimensional radiation stress theory and vortex-force formalism in an unstructured-grid coastal circulation model[J]. Estuarine, Coastal and Shelf Science, 2020, 240: 106771
doi: 10.1016/j.ecss.2020.106771
[2]
MELLOR G On surf zone fluid dynamics[J]. Journal of Physical Oceanography, 2021, 51 (1): 37- 46
doi: 10.1175/JPO-D-19-0318.1
MELLOR G The depth-dependent current and wave interaction equations: a revision[J]. Journal of Physical Oceanography, 2008, 38 (11): 2587- 2596
doi: 10.1175/2008JPO3971.1
[5]
MELLOR G A combined derivation of the integrated and vertically resolved, coupled wave-current equations[J]. Journal of Physical Oceanography, 2015, 45 (6): 1453- 1463
doi: 10.1175/JPO-D-14-0112.1
[6]
ZHANG D. Numerical simulation of large-scale waves and currents [D]. Singapore: National University of Singapore, 2004.
[7]
WARNER J C, SHERWOOD C R, SIGNELL R P, et al Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model[J]. Computers and Geosciences, 2008, 34 (10): 1284- 1306
doi: 10.1016/j.cageo.2008.02.012
[8]
张敬. 海岸、河口区三维近岸环流与物质输运数值研究[D]. 青岛: 中国海洋大学, 2010. ZHANG Jing. Numerical study of nearshore circulation and substance transport in coastal and estuary areas [D]. Qingdao: Ocean University of China, 2010.
[9]
BOLAÑOS R, OSUNA P, WOLF J, et al Development of the POLCOMS-WAM current-wave model[J]. Ocean Modelling, 2011, 36 (1/2): 102- 115
[10]
王平. 非结构波流耦合模型及近岸物质输运应用研究[D]. 大连: 大连理工大学, 2014. WANG Ping. An unstructured wave-current coupled model and its application in the nearshore mass transport [D]. Dalian: Dalian University of Technology, 2014.
[11]
MARSOOLI R, ORTON P M, MELLOR G, et al A coupled circulation-wave model for numerical simulation of storm tides and waves[J]. Journal of Atmospheric and Oceanic Technology, 2017, 34 (7): 1449- 1467
doi: 10.1175/JTECH-D-17-0005.1
[12]
ARDHUIN F, JENKINS A D, BELIBASSAKIS K A Comments on "The three-dimensional current and surface wave equations"[J]. Journal of Physical Oceanography, 2008, 38 (6): 1340- 1350
doi: 10.1175/2007JPO3670.1
[13]
ARDHUIN F, SUZUKI N, MCWILLIAMS J C, et al Comments on "A combined derivation of the integrated and vertically resolved, coupled wave-current equations"[J]. Journal of Physical Oceanography, 2017, 47 (9): 2377- 2385
doi: 10.1175/JPO-D-17-0065.1
[14]
BENNIS A C, ARDHUIN F, DUMAS F On the coupling of wave and three-dimensional circulation models: choice of theoretical framework, practical implementation and adiabatic tests[J]. Ocean Modelling, 2011, 40 (3/4): 260- 272
[15]
UCHIYAMA Y, MCWILLIAMS J C, SHCHEPETKIN A F Wave-current interaction in an oceanic circulation model with a vortex-force formalism: application to the surf zone[J]. Ocean Modelling, 2010, 34 (1/2): 16- 35
[16]
KUMAR N, VOULGARIS G, WARNER J C, et al Implementation of the vortex force formalism in the coupled ocean-atmosphere-wave-sediment transport (COAWST) modeling system for inner shelf and surf zone applications[J]. Ocean Modelling, 2012, 47: 65- 95
doi: 10.1016/j.ocemod.2012.01.003
[17]
ZHENG P, LI M, VAN DER A D A, et al A 3D unstructured grid nearshore hydrodynamic model based on the vortex force formalism[J]. Ocean Modelling, 2017, 116: 48- 69
doi: 10.1016/j.ocemod.2017.06.003
[18]
NGUYEN D T, JACOBSEN N G, ROELVINK D Development and validation of quasi-Eulerian mean three-dimensional equations of motion using the generalized Lagrangian mean method[J]. Journal of Marine Science and Engineering, 2021, 9 (1): 76
doi: 10.3390/jmse9010076
[19]
JI C, ZHANG Q, WU Y Derivation of three-dimensional radiation stress based on Lagrangian solutions of progressive waves[J]. Journal of Physical Oceanography, 2017, 47 (11): 2829- 2842
doi: 10.1175/JPO-D-16-0277.1
[20]
CHEN C, LIU H, BEARDSLEY R C An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: application to coastal ocean and estuaries[J]. Journal of Atmospheric and Oceanic Technology, 2003, 20 (1): 159- 186
doi: 10.1175/1520-0426(2003)020<0159:AUGFVT>2.0.CO;2
[21]
CHEN C, HUANG H, BEARDSLEY R C, et al A finite volume numerical approach for coastal ocean circulation studies: comparisons with finite difference models[J]. Journal of Geophysical Research: Oceans, 2007, 112: C03018
[22]
MELLOR G, YAMADA T Development of a turbulence closure model for geophysical fluid problems[J]. Reviews of Geophysics, 1982, 20 (4): 851- 875
doi: 10.1029/RG020i004p00851
[23]
解鸣晓, 张玮 近岸波生流运动三维数值模拟及验证[J]. 水科学进展, 2011, 22 (3): 391- 399 XIE Ming-xiao, ZHANG Wei 3D numerical modeling of nearshore wave-induced currents[J]. Advances in Water Science, 2011, 22 (3): 391- 399
[24]
SVENDSEN I A Wave heights and set-up in a surf zone[J]. Coastal Engineering, 1984, 8 (4): 303- 329
doi: 10.1016/0378-3839(84)90028-0
[25]
RENIERS A J H M, ROELVINK J A, THORNTON E B Morphodynamic modeling of an embayed beach under wave group forcing[J]. Journal of Geophysical Research: Oceans, 2004, 109: C01030
[26]
LARSON M, KRAUS N C Numerical model of longshore current for bar and trough beaches[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 1991, 117 (4): 326- 347
doi: 10.1061/(ASCE)0733-950X(1991)117:4(326)
[27]
SMAGORINSKY J General circulation experiments with the primitive equations, I. the basic experiment[J]. Monthly Weather Review, 1963, 91 (3): 99- 164
doi: 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
[28]
BOOIJ N, RIS R C, HOLTHUIJSEN L H A third-generation wave model for coastal regions, 1. model description and validation[J]. Journal of Geophysical Research: Oceans, 1999, 104 (C4): 7649- 7666
doi: 10.1029/98JC02622
[29]
DIETRICH J C, ZIJLEMA M, ALLIER P E, et al Limiters for spectral propagation velocities in SWAN[J]. Ocean Modelling, 2013, 70: 85- 102
doi: 10.1016/j.ocemod.2012.11.005
[30]
CHEN T, ZHANG Q, WU Y, et al Development of a wave-current model through coupling of FVCOM and SWAN[J]. Ocean Engineering, 2018, 164: 443- 454
doi: 10.1016/j.oceaneng.2018.06.062
[31]
KIRBY J T, CHEN T M Surface waves on vertically sheared flows: approximate dispersion relations[J]. Journal of Geophysical Research: Oceans, 1989, 94 (C1): 1013- 1027
doi: 10.1029/JC094iC01p01013
[32]
张振伟. 波生流垂向分布规律和模拟[D]. 大连: 大连理工大学, 2013. ZHANG Zhen-wei. Feature of the vertical distribution of wave induced currents with experimental and numerical simulations [D]. Dalian: Dalian University of Technology, 2013.
[33]
TING F C K Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone[J]. Coastal Engineering, 2001, 43 (3/4): 183- 208
[34]
GARCEZ FARIA A F, THORNTON E B, STANTON T P, et al Vertical profiles of longshore currents and related bed shear stress and bottom roughness[J]. Journal of Geophysical Research: Oceans, 1998, 103 (C2): 3217- 3232
doi: 10.1029/97JC02265
[35]
GARCEZ FARIA A F, THORNTON E B, LIPPMANN T C, et al Undertow over a barred beach[J]. Journal of Geophysical Research: Oceans, 2000, 105 (C7): 16999- 17010
doi: 10.1029/2000JC900084
[36]
HAAS K A, SVENDSEN I A Laboratory measurements of the vertical structure of rip currents[J]. Journal of Geophysical Research: Oceans, 2002, 107 (C5): 3047
doi: 10.1029/2001JC000911
[37]
HALLER M C, DALRYMPLE R A, SVENDSEN I A Experimental study of nearshore dynamics on a barred beach with rip channels[J]. Journal of Geophysical Research: Oceans, 2002, 107 (C6): 3061
doi: 10.1029/2001JC000955