Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications

Coastal Engineering

Volumn 58, Issue 12, 2011, Pages 1097-1117

  Kumar, N ^a   Voulgaris, G ^a   Warner, J C ^b  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

^b U S GEOLOGICAL SURVEY   (United States)

Author keywords

Nearshore circulation; Radiation stress; Rip currents; ROMS; SWAN; Wave current interaction

Indexed keywords

NEARSHORE CIRCULATION; RADIATION STRESS; RIP CURRENTS; SWAN; WAVE CURRENT INTERACTION;

ANOXIC SEDIMENTS; BEACHES; COASTAL ENGINEERING; MORPHOLOGY; OCEANOGRAPHY; SEDIMENT TRANSPORT; WAVE PROPAGATION;

THREE DIMENSIONAL;

BATHYMETRY; MORPHOLOGY; NEARSHORE DYNAMICS; NUMERICAL MODEL; RIP CURRENT; SHALLOW-WATER EQUATION; SURF ZONE; THREE-DIMENSIONAL MODELING; TROUGH; VERTICAL DISTRIBUTION; WAVE BREAKING; WAVE FORCE; WAVE PROPAGATION;

EID: 79961167299     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.coastaleng.2011.06.009     Document Type: Article

References (82)

1. Aagaard T., Greenwood B., Nielsen J. Mean currents and sediment transport in a rip channel. Mar. Geol. 1997, 140:25-45.
2. Ardhuin F., Jenkins A.D., Belibassakis K.A. Comments on "The three-dimensional current and surface wave equations". J. Phys. Oceanogr. 2008, 38:1340-1350.
3. Arthur R.S. A note on the dynamics of rip currents. J. Geophys. Res. 1962, 67(7):2777-2779.
4. Battjes J.A., Janssen J.P.F.M. Energy loss and set-up due to breaking of random waves. Proc. 16th Int. Conf. Coastal Engineering, ASCE 1978, 569-587.
5. Bennis, A., Ardhuin, F., in press. Comments on The Depth-Dependent Current and Wave Interaction Equations: A Revision. J. Phys. Oceanogr. doi:. http://doi:10.1175/JPO-D-11-055.1.
6. Booij N., Ris R.C., Holthuijsen L.H. A third-generation wave model for coastal regions 1. Model description and validation. J. Geophys. Res. 1999, 104(C4):7649-7666.
7. Bowen A.J. Rip currents 1. Theoretical investigations. J. Geophys. Res. 1969, 74(23):5467-5478.
8. Bowen A.J., Inman D.L. Rip currents 2. Laboratory and field observations. J. Geophys. Res. 1969, 74(23):5479-5490.
9. Brander R.W., Short A.D. Flow kinematics of low-energy rip current systems. J. Coastal Res. 2001, 17(2):468-481.
10. Brocchini M., Kennedy A.B., Soldini L., Mancinelli A. Topographically controlled, breaking-wave-induced macrovortices. Part 1. Widely separated breakwaters. J. Fluid Mech. 2004, 507:289-307.
11. Chapman D.C. Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model. J. Phys. Oceanogr. 1985, 15:1060-1075.
12. Chen Q., Dalrymple R.A., Kirby J.T., Kennedy A.B., Haller M.C. Boussinesq modeling of a rip current system. J. Geophys. Res. 1999, 104(C9):20,617-20,637.
13. Church J.C., Thornton E.B. Effects of breaking wave induced turbulence within a longshore current model. Coastal Eng. 1993, 20:1-28.
14. Dalrymple R.A. A mechanism for rip current generation on an open coast. J. Geophys. Res. 1975, 80(24):3485-3487.
15. Dingemans M.W., Radder A.C., Vriend H.J.D. Computation of the driving forces of wave-induced currents. Coastal Eng. 1987, 11:539-563.
16. Drønen N., Karunarathna H., Fredsoe J., Sumer M., Deigaard R. An experimental study of rip channel flow. Coastal Eng. 2002, 45:223-238.
17. Eldeberky Y., Battjes J.A. Spectral modeling of wave breaking: application to Boussinesq equations. J. Geophys. Res. 1996, 101:1253-1264.
18. Elgar S., Guza R.T., Raubenheimer B., Herbers T.H.C., Gallagher E.L. Spectral evolution of shoaling and breaking waves on a barred beach. J. Geophys. Res. 1998, 103:15797-15805.
19. Feddersen F., Trowbridge J.H. The effect of wave breaking on surfzone turbulence and alongshore currents: a modeling study. J. Phys. Oceanogr. 2005, 35:2187-2203.
20. Feddersen F., Guza R.T., Elgar S., Herbers T.H.C. Alongshore momentum balances in the nearshore. J. Geophys. Res. 1998, 103:15,667-15,676.
21. Gallagher E.L., Boyd W., Elgar S., Guza R.T., Woodward B. Performance of a sonar altimeter in the nearshore. Mar. Geol. 1996, 133:241-248.
22. Gallagher E.L., Elgar S., Guza R.T. Observations of sand bar evolution on a natural beach. J. Geophys. Res. 1998, 103:3203-3215.
23. Garcez-Faria A.F., Thornton E.B., Stanton T.P., Soares C.V., Lippmann T.C. Vertical profiles of longshore currents and related bed stress and bottom roughness. J. Geophys. Res. 1998, 103:15667-15676.
24. Garcez-Faria A.F., Thornton E.B., Lippmann T.C., Stanton T.P. Undertow over a barred beach. J. Geophys. Res. 2000, 105. 16,999-17,010.
25. Groeneweg J., Klopman G. Changes in the mean velocity profiles in the combined wave-current motion described in GLM formulation. J. Fluid Mech. 1998, 370:271-296.
26. Haas K.A., Svendsen I.A. Laboratory measurements of the vertical structure of rip currents. J. Geophys. Res. 2002, 107(C5):3047. 10.1029/2001JC000911.
27. Haas K.A., Warner J.C. Comparing a quasi-3D to a full 3D nearshore circulation model: SHORECIRC and ROMS. Ocean Model. 2009, 26:91-103.
28. Haas K.A., Svendsen I.A., Zhao Q. 3D modeling of rip currents. Proceedings 27th Coastal Engineering Conference, American Society Civil Engineers, Sydney, Australia 2000, 2:1113-1126.
29. Haas K.A., Svendsen I.A., Haller M.C., Zhao Q. Quasi-three-dimensional modeling of rip current systems. J. Geophys. Res. 2003, 108(C7):3217. 10.1029/2002JC001355.
30. Haidvogel D.B., Beckmann A. Numerical Ocean Circulation Modeling: Series on Environmental Science and Management 1999, vol. 2. Imperial College Press, 319pp.
31. Haidvogel D.B., Arango H.G., Hedstrom K., Beckmann A., Malanotte-Rizzoli P., Shchepetkin A.F. Model evaluation experiments in the North Atlantic basin: simulations in nonlinear terrain-following coordinates. Dyn. Atmos. Oceans 2000, 17(32):239-281.
32. Haidvogel D.B., Arango H.G., Budgell W.P., Cornuelle B.D., Curchitser E., Di Lorenzo E., Fennel K., Geyer W.R., Hermann A.J., Lanerolle L., Levin J., McWilliams J.C., Miller A.J., Moore A.M., Powell T.M., Shchepetkin A.F., Sherwood C.R., Signell R.P., Warner J.C., Wilkin J. Regional ocean forecasting in terrain-following coordinates: model formulation and skill assessment. J. Comput. Phys. 2008, 227:3595-3624.
33. Haller M.C., Dalrymple R.A. Rip current instabilities. J. Fluid Mech. 2001, 433:161-192.
34. Haller M.C., Dalrymple R.A., Svendsen I.A. Experimental study of nearshore dynamics on a barred beach with rip channels. J. Geophys. Res. 2002, 107(C6):3061. 10.1029/2001JC000955.
35. Hayes O.M. Lognormal distribution of inner continental shelf widths and slopes. Deep Sea Res. Oceanogr. Abstr. 1964, 11(1):53-78. 10.1016/0011-7471(64)91082-4.
36. Hughes S.A. Physical Models and Laboratory Techniques in Coastal Engineering 1993, World Scientific, Singapore.
37. Huntley D.A., Short A.D. On the spacing between observed rip currents. Coastal Eng. 1992, 17:211-225.
38. Kennedy A.B., Brocchini M., Soldini L., Gutierrez E. Topographically controlled, breaking-wave-induced macrovortices. Part 2. Changing geometries. J. Fluid Mech. 2006, 559:57-80.
39. LeBlond P.H., Tang C.L. On energy coupling between waves and rip currents. J. Geophys. Res. 1974, 79(6):811-816.
40. Lesser G.R., Roelvink J.A., van Kester J.A.T.M., Stelling G.S. Development and validation of a three-dimensional morphological model. Coastal Eng. 2004, 51:883-915.
41. Long C.E. Index and bulk parameters for frequency-direction spectra measured at CERC Field Research Facility, June 1994 to August 1995 1996, US Army Corps of Engineers Waterway Experiment Station, Vicksburg, MI, USA.
42. Long J.W., Özkan-Haller H.T. Low-frequency characteristics of wave group-forced vortices. J. Geophys. Res. 2009, 114:C08004. 10.1029/2008JC004894.
43. Longuet-Higgins M.S. Mass transport in water waves. Philos. Trans. R. Soc. Lond. A 1953, 245:535-581. 10.1098/rsta.1953.0006.
44. Longuet-Higgins M.S. Longshore currents generated by obliquely incident sea waves. a, b. J. Geophys. Res. 1970, 75(33):6778-6801.
45. Longuet-Higgins M.S., Stewart R.W. Radiation stresses in water waves: a physical discussion, with applications. Deep Sea Res. 1964, 11:529-562.
46. MacMahan J.H., Thornton E.B., Stanton T.P., Reniers A.J.H.M. RIPEX: Observations of a rip current system. Mar. Geol. 2005, 218(1-4):113-134. 10.1016/j.margeo.2005.03.019.
47. Madsen O.S., Poon Y.K., Graber H.C. Spectral wave attenuation by bottom friction: theory. Proc. 21th Int. Conf. Coastal Engineering, ASC 1988, 492-504.
48. McWilliams J.C., Restrepo J.M., Lane E.M. An asymptotic theory for the interaction of waves and currents in coastal waters. J. Fluid Mech. 2004, 511:135-178.
49. Mellor G.L. The three-dimensional current and surface wave equations. J. Phys. Oceanogr. 2003, 33:1978-1989.
50. Mellor G.L. Some consequences of the three-dimensional currents and surface wave equations. J. Phys. Oceanogr. 2005, 35:2291-2298.
51. Mellor G.L. The depth-dependent current and wave interaction equations: a revision. J. Phys. Oceanogr. 2008, 38:2587-2596.
52. Mellor G.L. Wave radiation stress. Ocean Dyn. 2011, 61(5):563-568. 10.1007/s10236-010-0359-2.
53. Mellor, G.L., in press-a. Reply to Comments by A-C Bennis and F. Ardhuin. doi:. http://doi:10.1175/JPO-D-11-071.1.
54. Mellor, G.L., in press-b. CORRIGENDA: The three-dimensional current and wave equations. J. Phys. Oceanogr.
55. Nairn R.B., Roelvink J.A., Southgate H.N. Transition zone width and implications for modeling surf zone hydrodynamics. Proceedings of the 22nd International Conference on Coastal Engineering Delft 1990, 68-81. American Society of Civil Engineers, New York.
56. Newberger P.A., Allen J.S. Forcing a three-dimensional, hydrostatic, primitive-equation model for application in the surf zone: 1. Formulation. J. Geophys. Res. 2007, 112:C08018. 10.1029/2006JC003472.
57. Newberger P.A., Allen J.S. Forcing a three-dimensional, hydrostatic, primitive-equation model for application in the surf zone: 2. Application to DUCK94. J. Geophys. Res. 2007, 112:C08019. 10.1029/2006JC003474.
58. Noda E.K. Wave-induced nearshore circulation. J. Geophys. Res. 1974, 79(27):4097-4106.
59. Patankar S.V. Numerical heat transfer and fluid flow 1980, Hemisphere Publishing Corporation, Washington, DC.
60. Phillips, O.M., 1977. The Dynamics of the Upper Ocean, 2nd ed., Cambridge Monogr. Mech. Appl. Math., vol. 1, 336 pp., Cambridge Univ. Press, New York.
61. Reniers A.J.H.M., Van Dongeren A.R., Battjes J.A., Thornton E.B. Linear modeling of infragravity waves during Delilah. J. Geophys. Res. 2002, 107(C10):3137. 10.1029/2001JC001083.
62. Reniers A.J.H.M., Roelvink J.A., Thornton E.B. Morphodynamic modeling of an embayed beach under wave group forcing. J. Geophys. Res. 2004, 109:C01030. 10.1029/2002JC001586.
63. Ruessink B.G., Miles J.R., Feddersen F., Guza R.T., Elgar S. Modeling the alongshore current on barred beaches. J. Geophys. Res. 2001, 106(C10):22,451-22,463.
64. Shchepetkin A.F., McWilliams J.C. The Regional Oceanic Modeling System: A split-explicit, free-surface, topography-following coordinate oceanic model. Ocean Model. 2005, 9:347-404. 10.1016/j.ocemod.2004.08.002.
65. Shchepetkin A.F., McWilliams J.C. Correction and commentary for "Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system" by Haidvogel et al., J. Comp. Phys. 227, pp. 3595-3624. J. Comput. Phys. 2009, 228:8985-9000.
66. Sheng P., Liu T. Three-dimensional simulation of wave-induced circulation: comparison of three radiation stress formulations. J. Geophys. Res. 2011, 116:C05021. 10.1029/2010JC006765.
67. Sonu C.J. Field observation of nearshore circulation and meandering currents. J. Geophys. Res. 1972, 77(18):3232-3247.
68. Stive M.J.F., De Vriend H.J. Shear stresses and mean flow in shoaling and breaking waves. Proc. of the 24th Coastal Engineering International Conference 1994, Kobe, Japan 1994, 594-608. American Society of Civil Engineers, New York.
69. Svendsen I.A. Wave heights and set-up in a surf zone. Coastal Eng. 1984, 8:303-329.
70. Svendsen I.A., Haas K.A., Zhao Q. Analysis of rip current systems. Proceedings 27th Coastal Engineering Conference, ASCE, Sydney 2000, 1127-1140.
71. Svendsen I.A., Haas K.A., Zhao Q. Quasi-3D nearshore circulation model SHORECIRC, User's Manual, Draft Report, Center for Applied Coastal Research, Department of Civil Engineering, University of Delaware, Newark 2002.
72. Tam C.K.W. Dynamics of rip currents. J. Geophys. Res. 1973, 78(12):1937-1943.
73. Terrile E., Brocchini M. A dissipative point-vortex model for nearshore circulation. J. Fluid Mech. 2007, 589:455-478.
74. Ting F.C.K., Kirby J.T. Observations of undertow and turbulence in a laboratory surf zone. Coastal Eng. 1994, 24:177-204.
75. 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. Ocean Model. 2010, 10.1016/j.ocemod.2010.04.002.
76. van Dongeren A.R., Sancho F.E., Svendsen I.A., Putrevu U. Application of the Q3d SHORECIRC model to surfbeat. Proc. Coastal Dynamics, Gdynia, Poland, ASCE, New York 1995, 233-244.
77. Voulgaris G., Kumar N., Warner J.C. A Methodology for the Prediction of Rip Currents using a 3-D Numerical, Coupled, Wave-Current Model. Rip Currents: Beach Safety, Physical Oceanography, and Wave Modeling 2011, CRC Press, ISBN, 9781439838969. S. Leatherman, J. Fletemeyer (Eds.).
78. Walstra D.J.R., Roelvink J.A., Groeneweg J. Calculation of wave-driven currents in a 3D mean flow model. Proc. of the 27th Coastal Engineering International Conference 2000, Sydney, Australia 2000, 1050-1063. American Society of Civil Engineers, New York.
79. Wang J., Shen Y. Modeling oil spills transportation in seas based on unstructured grid, finite volume, wave-ocean model. Ocean Model. 2010, 35(4):332-344.
80. Warner J.C., Sherwood C.R., Arango H.G., Signell R.P., Butman B. Performance of four turbulence closure models implemented using a generic length scale method. Ocean Model. 2005, 8:81-113.
81. Warner J.C., Sherwood C.R., Signell R.P., Harris C., Arango H.G. Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model. Comput. Geosci. 2008, 34:1284-1306.
82. Yu J., Slinn D.N. Effects of wave-current interaction on rip currents. J. Geophys. Res. 2003, 108(C3):3088. 10.1029/2001JC001105.