A Generalized Multiple Discrete Interaction Approximation for resonant four-wave interactions in wind wave models

Ocean Modelling

Volumn 70, Issue , 2013, Pages 11-24

  Tolman, Hendrik L ^a  

^a NOAA EARTH SYSTEM RESEARCH LABORATORY   (United States)

Author keywords

Discrete interaction approximation; Numerical modeling; Quadruplets; Resonant nonlinear interactions; Wind waves

Indexed keywords

BACKWARD COMPATIBLE; DISCRETE INTERACTION; FOUR-WAVE INTERACTIONS; MULTIPLE REPRESENTATIVES; NONLINEAR INTERACTIONS; QUADRUPLETS; WIND WAVE; WIND-WAVE MODELS;

ERRORS; FOUR WAVE MIXING; HURRICANES; NUMERICAL MODELS; OPTIMIZATION;

WAVES;

DEEP WATER; HURRICANE; NUMERICAL MODEL; SHALLOW WATER; WATER DEPTH; WAVE MODELING; WIND WAVE; WIND-WAVE INTERACTION;

EID: 84882873876     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2013.02.005     Document Type: Article

References (57)

1. Bretherthon F.P., Garrett C.J.R. Wave trains in inhomogeneous moving media. Proc. Roy. Soc. Lond. A 1968, 302:529-554.
2. Gelci R., Cazalé H., Vassal J. Ulitization des diagrammes de propagation à la prévision énergétique de la houle. Bulletin d'Information du Commité Central d'Océanographie et d'Études des CÔtes 1956, 8:169-197.
3. Gelci R., Cazalé H., Vassal J. Prévision de la haule. La méthode des densités spectroangulaires. Bulletin d'Information du Commité Central d'Océanographie et d'Études des CÔtes 1957, 9:416-435.
4. Hargreaves J.C., Annan J.D. Comments on "Improvement of the short fetch behavior in the ocean wave model (WAM)". J. Atmos. Oceanic Technol. 2001, 18:711-715.
5. Hashimoto N., Kawaguchi K. Extension and modification of discrete interaction approximation (DIA) for computing nonlinear energy transfer of gravity wave spectrum. Fourth International Symposium on Ocean Wave Measurement and Analysis 2001, 530-539. ASCE.
6. Hashimoto, N., Haagsma, I.G., Holthuijsen, L.H., 2002. Four-wave interactions in SWAN. In: Proc. 28th Int. Conf. Coastal Eng., ASCE, Cardiff, pp. 392-404.
7. Hasselmann K. Grundgleichungen der seegangsvoraussage. Schiffstechnik 1960, 7:191-195.
8. Hasselmann K. On the non-linear energy transfer in a gravity wave spectrum. Part 1: General theory. J. Fluid Mech. 1962, 12:481-500.
9. Hasselmann K. On the non-linear transfer in a gravity wave spectrum. Part 2: Conservation theory, wave-particle correspondence, irreversibility. J. Fluid Mech. 1963, 15:273-281.
10. Hasselmann K. On the non-linear transfer in a gravity wave spectrum. Part 3: Evaluation of energy flux and sea-swell interactions for a Neuman spectrum. J. Fluid Mech. 1963, 15:385-398.
11. Hasselmann K. Feynman diagrams and interaction rules of wave-scattering processes. Rev. Geophys. Space Phys. 1966, 4:1-32.
12. Hasselmann S., Hasselmann K. Computations and parameterizations of the nonlinear energy transfer in a gravity-wave spectrum. Part I: A new method for efficient computations of the exact nonlinear transfer integral. J. Phys. Oceanogr. 1985, 15:1369-1377.
13. Hasselmann K., Barnett T.P., Bouws E., Carlson H., Cartwright D.E., Enke K., Ewing J.A., Gienapp H., Hasselmann D.E., Kruseman P., Meerburg A., Müller P., Olbers D.J., Richter K., Sell W., Walden H. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Ergänzungsh. Deutschen Hydrogr. Z., Reihe A 1973, 8(12). 95 pp.
14. Hasselmann S., Hasselmann K., Allender J.H., Barnett T.P. Computations and parameterizations of the nonlinear energy transfer in a gravity-wave spectrum. Part II: Parameterizations of the nonlinear energy transfer for application in wave models. J. Phys. Oceanogr. 1985, 15:1378-1391.
15. Herterich K., Hasselmann K. A similarity relation for the nonlinear energy transfer in a finite-depth gravity-wave spectrum. J. Fluid Mech. 1980, 97:215-224.
16. Janssen P.A.E.M., Onorato M. The intermediate depth limit of the Zakharov equations and consequences for wave prediction. J. Phys. Oceanogr. 2007, 37:2389-2400.
17. Komatsu, K., 1996. Development of a new generation wave forecast model based on a new schema of nonlinear energy transfer among wind waves (in Japanese). Ph.D. Thesis, Kyoto University, 155 pp.
18. Komatsu K., Masuda A. A new scheme of nonlinear energy transfer among wind waves: RIAM method - algorithm and performance. J. Oceanogr. 1996, 52:509-537.
19. Komen G.J., Cavaleri L., Donelan M., Hasselmann K., Hasselmann S., Janssen P.A.E.M. Dynamics and Modelling of Ocean Waves 1994, Cambridge University Press, 532 pp.
20. Masuda A. Nonlinear energy transfer between wind waves. J. Phys. Oceanogr. 1980, 10:2082-2093.
21. Phillips O.M. On the dynamics of unsteady gravity waves of finite amplitude. J. Fluid Mech. 1960, 9:193-217.
22. Phillips O.M. Wave interaction: the evolution of an idea. J. Fluid Mech. 1981, 106:215-227.
23. Rasmussen, J.H., 1998. Deterministic and stochastic modelling of surface gravity waves in finite depth. Ph.D. Thesis, Institute of Hydrodynamics and Water Resources (ISVA), Techn. Univ. Denmark.
24. Resio D.T., Perrie W. A numerical study of nonlinear energy fluxes due to wave-wave interactions. Part 1: Methodology and basic results. J. Fluid Mech. 1991, 223:603-629.
25. Rice S.O. Mathematical analysis of random noise. Bell Syst. Tech. J. 1944, 23:282-332.
26. Snyder R.L., Long R.B., Neu W.L. A fully nonlinear regional wave model for the Bight of Abaco 1. Nonlinear-transfer computation. J. Geophys. Res. 1998, 103:3119-3141.
27. Sverdrup, H.U., Munk, W.H., 1947. Wind, sea and swell: theory and relations for forecasting. Tech. Rep. H.O. Pub. No. 601, United States Navy Department, Hydrographic Office.
28. SWAMP Group Ocean Wave Modelling 1985, Plenum Press, 256 pp.
29. Tamura H., Waseda T., Miyazawa Y., Komatsu K. Current-induced modulation of the ocean wave spectrum and the role of nonlinear energy transfer. J. Phys. Oceanogr. 2008, 38:2662-2684.
30. Tolman H.L. Effects of numerics on the physics in a third-generation wind-wave model. J. Phys. Oceanogr. 1992, 22:1095-1111.
31. Tolman, H.L., 2003. Optimum discrete interaction approximations for wind waves. Part 1: Mapping using inverse modeling. Tech. Note 227, NOAA/NWS/NCEP/MMAB, 57 pp + Appendices.
32. Tolman H.L. Inverse modeling of discrete interaction approximations for nonlinear interactions in wind waves. Ocean Modell. 2004, 6:405-422.
33. Tolman, H.L., 2005. Optimum discrete interaction approximations for wind waves. Part 2: Convergence of model integration. Tech. Note 247, NOAA/NWS/NCEP/MMAB, 74 pp + Appendices.
34. Tolman H.L. A mosaic approach to wind wave modeling. Ocean Modell. 2008, 25:35-47.
35. Tolman, H.L., 2008b. Optimum discrete interaction approximations for wind waves. Part 3: Generalized multiple DIAs. Tech. Note 269, NOAA/NWS/NCEP/MMAB, 117 pp.
36. Tolman, H.L., 2009a. Practical nonlinear interaction algorithms. In: 11th International Workshop on Wave Hindcasting and Forecasting & Coastal Hazards Symposium, JCOMM Tech. Rep. 52, WMO/TD-No. 1533, Paper J2.
37. Tolman, H.L., 2009b. User manual and system documentation of WAVEWATCH III ™version 3.14. Tech. Note 276, NOAA/NWS/NCEP/MMAB, 194 pp + Appendices.
38. Tolman, H.L., 2010. Optimum discrete interaction approximations for wind waves. Part 4: Parameter optimization. Tech. Note 288, NOAA/NWS/NCEP/MMAB, 175 pp.
39. Tolman H.L. A conservative nonlinear filter for the high-frequency range of wind wave spectra. Ocean Modell. 2011, 39:291-300.
40. Tolman H.L., Alves J.H.G.M. Numerical modeling of wind waves generated by tropical cyclones using moving grids. Ocean Modell. 2005, 9:305-323.
41. Tolman, H.L., Grumbine, R.W., 2013. Holistic genetic optimization of a Generalized Multiple Discrete Interaction Approximation for wind waves. Ocean Modell. 70, 25-37.
42. Tolman, H.L., Krasnopolsky, V.M., 2004. Nonlinear interactions in practical wind wave models. In: Eighth International Workshop on Wave Hindcasting and Forecasting, JCOMM Tech. Rep. 29, WMO/TD-No. 1319, Paper E1.
43. Tracy, B., Resio, D.T., 1982. Theory and calculation of the nonlinear energy transfer between sea waves in deep water. WES Report 11, US Army Corps of Engineers.
44. Ueno K., Ishizaka M. On an efficient calculation method of the nonlinear energy transfer in wind waves. Sottukojiho JMA 1997, 64:75-80. (in Japanese).
45. Van Vledder, G.P., 2000. Improved method for obtaining the integration space for the computation of nonlinear quadruplet wave-wave interaction. In: Proceedings of the Sixth International Workshop on Wave Forecasting and Hindcasting, pp. 418-431.
46. Van Vledder G.P. Extension of the discrete interaction approximation for computing nonlinear quadruplet wave-wave interactions in operational wave prediction models. Fourth International Symposium on Ocean Wave Measurement and Analysis 2001, 540-549. ASCE.
47. Van Vledder, G.P., 2002a. A subroutine version of the Webb/Resio/Tracy method for the computation of nonlinear quadruplet interactions in a wind-wave spectrum. Report 151b, Alkyon, The Netherlands.
48. Van Vledder, G.P., 2002b. Improved parameterizations of nonlinear four wave interactions for application in operational wave prediction models. Report 151a, Alkyon, The Netherlands.
49. Van Vledder G.P. The triplet method for the computation of nonlinear four-wave interactions in discrete spectral wave models. Fifth International Symposium on Ocean Wave Measurement and Analysis 2005, ASCE, (Paper 48). B.L. Edge, J.M. Hemsley (Eds.).
50. Van Vledder G.P. The WRT method for the computation of non-linear four wave interactions in discrete spectral wave models. Coastal Eng. 2006, 53:223-242.
51. Van Vledder G.P., Bottema M. Improved modelling of nonlinear four-wave interactions in shallow water. Proc. 28th Int. Conf. Coastal Eng. 2002, 459-471. ASCE, Cardiff, Wales.
52. Van Vledder G.P., Herbers T.H.C., Jenssen R.E., Resio D.T., Tracy B. Modelling of non-linear quadruplet wave-wave interactions in operational wave models. Proc. 27th Int. Conf. Coastal Eng. 2000, 797-811. ASCE, Sydney, Australia.
53. WAMDIG The WAM model - a third generation ocean wave prediction model. J. Phys. Oceanogr. 1988, 18:1775-1810.
54. Webb D.J. Non-linear transfers between sea waves. Deep Sea Res. 1978, 25:279-298.
55. WISE Group Wave modelling - the state of the art. Prog. Oceanogr. 2007, 75:603-674.
56. Young I.R., Van Vledder G.P. A review of the central role of nonlinear interactions in wind-wave evolution. Trans. Roy. Soc. Lond. 1993, 342:505-524.
57. Zakharov V.E. Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 1968, 2:190-194.