Three-dimensional simulation of wave-induced circulation: Comparison of three radiation stress formulations

Journal of Geophysical Research: Oceans

Volumn 116, Issue 5, 2011, Pages

  Sheng, Y Peter ^a   Liu, Tianyi ^a  

^a University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; FLOODS; INDUCED CURRENTS; MECHANICS; REEFS; STORMS; THREE DIMENSIONAL COMPUTER GRAPHICS; WAVE TRANSMISSION;

ANALYTICAL SOLUTIONS; CHESAPEAKE BAY; HURRICANE ISABEL; INTEGRATED EQUATIONS; LINEAR WAVE THEORY; MODELING SYSTEMS; NEARSHORES; OBSERVED DATA; RADIATION STRESS; SIMULATING WAVES; STEADY-STATE WAVES; STORM SURGES; SURF ZONES; THREE DIMENSIONAL SIMULATIONS; THREE-DIMENSIONAL EQUATIONS OF MOTION; WAVE SETUP; WAVE-INDUCED CURRENTS;

THREE DIMENSIONAL;

COMPARATIVE STUDY; FRINGING REEF; GYRE; HURRICANE ISABEL 2003; LINEARITY; STORM SURGE; THREE-DIMENSIONAL MODELING; TURBULENCE; WAVE-CURRENT INTERACTION;

CHESAPEAKE BAY; NORTH CAROLINA; OUTER BANKS; UNITED STATES;

EID: 79958021196     PISSN: None     EISSN: 21699291     Source Type: Journal    
DOI: 10.1029/2010JC006765     Document Type: Article

References (60)

1. Andrews, D. G., and M. E. McIntyre (1978), An exact theory of nonlinear waves on a Lagrangian-mean flow, J. Fluid Mech., 89, 609-646, doi:10.1017/S0022112078002773. (Pubitemid 9413277)
2. Ardhuin, F., N. Rascle, and K. A. Belibassakis (2008a), Explicit wave-averaged primitive equations using a generalized lagrangian mean, Ocean Modell., 20, 35-60, doi:10.1016/j.ocemod.2007.07.001. (Pubitemid 350121186)
3. Ardhuin, F., A. D. Jenkins, and K. A. Belibassakis (2008b), Comments on "The three-dimensional current and surface wave equations," J. Phys. Oceanogr., 38, 1340-1350, doi:10.1175/2007JPO3670.1.
4. Bagnold, R. A. (1940), Beach formation by waves: Some model experiments in a wave tank, J. Inst. Civ. Eng., 15,27-52, doi:10.1680/ijoti.1940.14279.
5. Battjes, J. A. (1972), Radiation stresses in short-crested waves, J. Mar. Res., 30, 56-64.
6. Battjes, J. A. (1975), A note on modeling of turbulence in the surf-zone, in Symposium on Modeling Techniques, pp. 1050-1061, Am. Soc. of Civ. Eng., Reston, Va.
7. Booij, N., R. C. Ris, and L. H. Holthuijsen (1999), A third-generation wave model for coastal regions: 1. Model description and validation, J. Geophys. Res., 104, 7649-7666, doi:10.1029/98JC02622. (Pubitemid 29410061)
8. Christensen, E. A. (2006), Large eddy simulation of spilling and plunging breakers, Coastal Eng., 53, 463-485, doi:10.1016/j.coastaleng.2005. 11.001.
9. Craik, A. D. D., and S. Leibovich(1976), A rational model for Langmuir circulation, J. FluidMech., 73,401-426, doi:10.1017/S0022112076001420.
10. Demirbilek, Z., O. G. Nwogu, and D. L. Ward (2007), Laboratory study of wind effect on runup over fringing reefs, report 1: Data report, Coastal Hydraul. Lab. Tech. Rep. ERDC/CHL-TR-07-4, U.S. Army Eng. Res. and Dev. Cent., Vicksburg, Miss.
11. De Vriend, D., and M. J. F. Stive (1987), Quasi-3D modeling of near-shore currents, Coastal Eng., 11, 565-601, doi:10.1016/0378-3839(87)90027-5.
12. Dongeren, A. R., F. E. Sancho, I. A. Svendsen, and U. Putrevu (1994), SHORECIRC: A quasi 3-D nearshore model, in Proceedings of the Twenty-Fourth International Conference, edited by B. L. Edge, pp. 2741-2754, Am. Soc. of Civ. Eng., New York.
13. Feddersen, F. (2004), Effect of wave directional spread on the radiation stress: Comparing theory and observations, Coastal Eng., 51, 473-481, doi:10.1016/j.coastaleng.2004.05.008. (Pubitemid 40106384)
14. Gemmrich, J. (2010), Strong turbulence in the wave crest region, J. Phys. Oceanogr., 40, 583-595, doi:10.1175/2009JPO4179.1.
15. Grant, W. D., and O. S. Madsen (1979), Combined wave and current interaction with a rough bottom, J. Geophys. Res., 84, 1797-1808, doi:10.1029/JC084iC04p01797.
16. Groeneweg, J. (1999), Wave-current interactions in a generalized Lagrang-ian mean formulation, Ph.D. thesis, Delft Univ. of Technology, Delft, Netherlands.
17. Haas, K. A., and I. A. Svendsen (2000), Three-dimensional modeling of rip current system, Res. Rep. CACR-00-06, 250 pp., Cent. for Appl. Coastal Res., Univ. of Del., Newark, Del.
18. Haas, K. A., and J. C. Warner (2009), Comparing a quasi-3D to a full 3D nearshore circulation model: SHORECIRC and ROMS, Ocean Modell., 26, 91-103, doi:10.1016/j.ocemod.2008.09.003.
19. Haas, K. A., I. A. Svendsen, M. C. Haller, and Q. Zhao (2003), Quasi-three-dimensional modeling of rip current systems, J. Geophys. Res., 108(C7), 3217, doi:10.1029/2002JC001355.
20. Hansen, J. B., and I. A. Svendsen (1984), A theoretical and experimental study of undertow, in Nineteenth Coastal Engineering Conference: Proceedings of the International Conference, edited by B. L. Edge, pp. 2246-2262, Am. Soc. of Civ. Eng., New York.
21. Interagency Performance Evaluation Task Force (2006), Performance evaluation of the New Orleans and southeast Louisiana hurricane protection system, technical report, U.S. Army Corps of Eng., Vicksburg, Miss.
22. Leonard, B. P. (1979), A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng., 19, 59-98, doi:10.1016/0045-7825(79)90034-3. (Pubitemid 9468362)
23. Leonard, B. P. (1991), The ultimate conservative difference scheme applied to unsteady one-dimensional advection, Comput. Methods Appl. Mech. Eng., 88, 17-74, doi:10.1016/0045-7825(91)90232-U. (Pubitemid 21699098)
24. Liu, H., and L. Xie (2009), A numerical study on the effects of wave-current-surge interactions on the height and propagation of sea surface waves in Charleston Harbor during Hurricane Hugo 1989, Cont. Shelf Res., 29, 1454-1463, doi:10.1016/j.csr.2009.03.013.
25. Longuet-Higgins, M. S. (1970a), Longshore currents generated by obliquely incident waves, 1, J. Geophys. Res., 75, 6778-6789, doi:10.1029/ JC075i033p06778.
26. Longuet-Higgins, M. S. (1970b), Longshore currents generated by obliquely incident waves, 2, J. Geophys. Res., 75, 6790-6801, doi:10.1029/ JC075i033p06790.
27. Longuet-Higgins, M. S., and R. W. Stewart (1962), Radiation stress and mass transport in gravity waves with application to "surf beats," J. Fluid Mech., 13, 481-504, doi:10.1017/S0022112062000877.
28. Longuet-Higgins, M. S., and R. W. Stewart (1964), Radiation stresses in water waves; a physical discussion with applications, Deep Sea Res., 11, 529-562.
29. Luettich, R., J. J. Westerink, and N. W. Scheffner (1992), ADCIRC: An advanced three-dimensional circulation model for shelves coasts and estuaries, report 1: Theory and methodology of ADCIRC-2DDI and ADCIRC-3DL, Dredging Res. Program Tech. Rep. DRP-92-6, U.S. Army Corps of Eng., Washington, D. C.
30. Lynett, P., and P. L.-F. Liu (2004), A two-layer approach to water wave modeling, Proc. R. Soc. London A, 460, 2637-2669, doi:10.1098/rspa.2004.1305. (Pubitemid 40522389)
31. McWilliams, J. C, J. M. Restrepo, and E. M. Lane (2004), An asymptotic theory for the interaction of waves and currents in coastal waters, J. Fluid Mech., 511, 135-178, doi:10.1017/S0022112004009358. (Pubitemid 39039729)
32. Mellor, G. L. (1996), Users Guide for a Three Dimensional, Primitive Equation Numerical Ocean Model, 39 pp., Princeton Univ. Press, Princeton, N. J.
33. Mellor, G. L. (2003), The three-dimensional current and surface wave equations, J. Phys. Oceanogr., 33, 1978-1989, doi:10.1175/1520-0485 (2003)033<1978:TTCASW>2.0.CO;2. (Pubitemid 37240750)
34. Mellor, G. L. (2008), The depth-dependent current and wave interaction equations; a revision, J. Phys. Oceanogr., 38, 2587-2596, doi:10.1175/ 2008JPO3971.1.
35. Mocke, G. P. (2001), Structure and modeling of surf zone turbulence due to wave breaking, J. Geophys. Res., 106, 17,039-17,057, doi:10.1029/ 2000JC900163.
36. Mukai, A. Y., J. J. Westerink, and R. A. Luettich (2002), Guidelines for using the Eastcoast 2001 database of tidal constituents within the western North Atlantic Ocean, Gulf of Mexico and Caribbean Sea, Coastal Hydraul. Eng. Tech. Note ERDC/CHL CHETN-IV-40, U.S. Army Corps of Eng., Washington, D. C.
37. Newberger, P. A., and J. S. Allen (2007), Forcing a three-dimensional, hydrostatic, primitive-equation model for application in the surf zone: 1. Formulation, J. Geophys. Res., 112, C08018, doi:10.1029/2006JC003472. (Pubitemid 47610300)
38. Okayasu, A., T. Shibayama, and K. Horikawa (1988), Vertical variation of undertow in the surf zone, paper presented at 21st International Conference on Coastal Engineering, Am. Soc. of Civ. Eng., Torremolinos, Spain.
39. Putrevu, U., and I. A. Svendsen (1993), Vertical structure of the undertow outside the surf zone, J. Geophys. Res., 98, 22,707-22,716, doi:10.1029/93JC02399.
40. Rodi, W. (1980), Turbulence Models and Their Application in Hydraulics - A State of the Art Review, 104 pp., Assoc. for Hydraul. Res, Delft, Netherlands.
41. Roland, A., A. Cucco, C. Ferrarin, T. Hsu, J. Liau, S. Ou, G. Umgiesser, and U. Zanke (2009), On the development and verification of a 2-D coupled wave-current model on unstructured meshes, J. Mar. Syst., 78, S244-S254, doi:10.1016/j.jmarsys.2009.01.026.
42. Sheng, Y. P. (1986), A three-dimensional numerical model of coastal and estuarine circulation and transport in generalized curvilinear grids, Tech. Rep. 587, 255 pp., Aeronaut. Res. Assoc. of Princeton, Princeton, N. J.
43. Sheng, Y. P. (1987), On modeling three-dimensional estuarine and marine hydrodynamics, in Three-Dimensional Models of Marine and Estuarine Dynamics, Elsevier Oceanogr. Ser., vol. 45, edited by J. C. J. Nihoul and B. M. Jamart, pp. 35-54, doi:10.1016/S0422-9894(08)70441-0, Elsevier, Amsterdam.
44. Sheng, Y. P., and V. Alymov (2002), Coastal flooding analysis of Pinellas County using ALSM data: A comparison between UFs 2-D method and results vs. FEMA's method and results, report, Dep. of Civ. and Coastal Eng., Univ. of Fla., Gainesville, Fla.
45. Sheng, Y. P., and C. Villaret (1989), Modeling the effect of suspended sediment stratification on bottom exchange process, J. Geophys. Res., 94, 14,429-14,444, doi:10.1029/JC094iC10p14429.
46. Sheng, Y. P., V. Alymov, and V. A. Paramygin (2010a), Simulation of storm surge, wave, currents, and inundation in the Outer Banks and Chesapeake Bay during Hurricane Isabel in 2003: The importance of waves, J. Geophys. Res., 115, C04008, doi:10.1029/2009JC005402.
47. Sheng, Y. P., Y. Zhang, and V. A. Paramygin (2010b), Simulation of storm surge, wave, and inundation in the northeastern Gulf of Mexico during Hurricane Ivan in 2004, Ocean Modell, 35, 314-331, doi:10.1016/j. ocemod.2010.09.004.
48. Song, Y. T., and D. Haidvogel (1994), A semi-implicit ocean circulation model using a generalized topography following coordinate system, J. Comput. Phys., 115, 228-244, doi:10.1006/jcph.1994.1189. (Pubitemid 124012851)
49. Stive, M. J. F., and H. G. Wind (1986), Cross-shore mean flow in the surf zone, Coastal Eng., 10, 325-340, doi:10.1016/0378-3839(86)90019-0.
50. Svendsen, I. A. (1984a), Wave heights and set-up in a surf zone, Coastal Eng., 8, 303-329, doi:10.1016/0378-3839(84)90028-0.
51. Svendsen, I. A. (1984b), Mass flux and undertow in a surf zone, Coastal Eng., 8, 347-365, doi:10.1016/0378-3839(84)90030-9.
52. Svendsen, I. A., W. Qin, and B. A. Ebersole (2003), Modeling waves and currents at the LSTF and other laboratory facilities, Coastal Eng., 50, 19-45, doi:10.1016/S0378-3839(03)00077-2. (Pubitemid 37436368)
53. Ting, F. C. K., and J. T. Kirby (1994), Observation of undertow and turbulence in a laboratory surf zone, Coastal Eng., 24, 51-80, doi:10.1016/0378-3839(94)90026-4. (Pubitemid 289188)
54. Tolman, H. L. (1999), User manual and system documentation of WAVEATCH-III 1000 version 1.18, OMB Tech. Note 167, Natl. Cent. for Environ. Predict., Washington, D. C.
55. Uchiyama, Y., J. C. McWilliams, and A. F. Shchepetkin (2010), Wave-current interaction in an oceanic circulation model with a vortex-force formalism: Application to the surf zone, Ocean Modell., 34, 16-35, doi:10.1016/j.ocemod.2010.04.002.
56. Wang, B., A. J. Chadwick, and A. K. Otta (2008), Derivation and application of new equations for s radiation stress and volume flux, Coastal Eng., 55, 302-318, doi:10.1016/j.coastaleng.2007.11.008.
57. Xia, H., Z. Xia, and L. Zhu (2004), Vertical variation in radiation stress and wave-induced current, Coastal Eng., 51, 309-321, doi:10.1016/j. coastaleng.2004.03.003. (Pubitemid 38791037)
58. Xie, L., K. Wu, L. Pietrafesa, and C. Zhang (2001), A numerical study of wave-current interaction through surface and bottom stresses: Wind-driven circulation in the South Atlantic Bight under uniform winds, J. Geophys. Res., 106, 16,841-16,855, doi:10.1029/2000JC000292.
59. Xie, L., H. Liu, and M. Peng (2008), The effect of wave-current interactions on the storm surge and inundation in Charleston Harbor during Hurricane Hugo 1989, Ocean Modell., 20, 252-269, doi:10.1016/j. ocemod.2007.10.001.
60. Zhang, M. Y., and Y. S. Li (1996), The synchronous coupling of a third-generation wave model and a two-dimensional storm surge model, Ocean Eng., 23, 533-543, doi:10.1016/0029-8018(95)00067-4.