Proceedings of the 32nd International Conference


nonlinear wave-wave interaction
wave-action balance equation
directional wave spectrum

How to Cite

RAPID CALCULATION OF NONLINEAR WAVE-WAVE INTERACTIONS. (2011). Coastal Engineering Proceedings, 1(32), waves.36. https://doi.org/10.9753/icce.v32.waves.36


This paper presents an efficient numerical algorithm for the nonlinear wave-wave interactions that can be important in the evolution of coastal waves. Indeed, ocean waves truly interact with each others. However, because ocean waves can also interact with the atmosphere such as under variable wind and pressure fields, and waves will deform from deep to shallow water, it is generally difficult to differentiate the actual amount of the nonlinear energy transfer among spectral waves mixed with the atmospheric input and wave breaking. The classical derivation of the nonlinear wave energy transfer has involved tedious numerical calculation that appears impractical to the engineering application. The present study proposed a theoretically based formulation to efficiently calculate nonlinear wave-wave interactions in the spectral wave transformation equation. It is approved to perform well in both idealized and real application examples. This rapid calculation algorithm indicates the nonlinear energy transfer is more significant in the intermediate depth than in deep and shallow water conditions.


Demirbilek, Z., L. Lin, and W.C. Seabergh. 2009. Laboratory and numerical studies of hydrodynamics near jetties. Coastal Engineering Journal 51(2):143-175 JSCE. http://dx.doi.org/10.1142/S0578563409001989

Hasselmann, K. 1962. On the nonlinear energy transfer in a gravity-wave spectrum. Part 1: General theory, Journal of Fluid Mech, 12, 481-500. http://dx.doi.org/10.1017/S0022112062000373

Hasselmann, K., T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerbrug, P. Muller, D. J. Olbers, K. Richter, W. Sell, and H. Walden. 1973. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutsche Hydrographische Zeitschrift A80(12), 95 P.

Hasselmann, S., K. Hasselmann, J. H. Allender, and T.P. Barnett. 1985. 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. Journal of Physical Oceanography 15:1378-1391. http://dx.doi.org/10.1175/1520-0485(1985)015<1378:CAPOTN>2.0.CO;2

Holthuijsen, L. H., A. Herman, and N. Booij. 2004. Phase-decoupled refraction-diffraction for spectral wave models. Coastal Engineering, 49, 291-305. http://dx.doi.org/10.1016/S0378-3839(03)00065-6

Jenkins, A. D., and O. M. Phillips. 2001. A simple formula for nonlinear wave-wave interaction. International Journal of Offshore and Polar Engineering 11(2):81-86.

Lin, L. Z. Demirbilek, H. Mase, J. Zheng, and F. Yamada. 2008. CMS-Wave: a nearshore spectral wave processes model for coastal inlets and navigation projects. Coastal Inlets Research Program, Coastal and Hydraulics Laboratory Technical Report ERDC/CHL TR-08-13. Vicksburg, MS: U.S. Army Engineer Research and Development Center.

Lin, L., and Z. Demirbilek. 2010. CMS: A Coastal Modeling System for inlets and navigation projects. Proceedings of the 5th International Ocean-Atmosphere Conference.

Mase, H., 2001. Multidirectional random wave transformation model based on energy balance equation. Coastal Engineering Journal 43(4):317-337 JSCE. http://dx.doi.org/10.1142/S0578563401000396

Mase, H., H. Amamori, and T. Takayama. 2005a. Wave prediction model in wave-current coexisting field. Proceedings of the 12th Canadian Coastal Conference (CD-ROM).

Mase, H., K. Oki, T. S. Hedges, and H. J. Li. 2005b. Extended energy-balance-equation wave model for multidirectional random wave transformation. Ocean Engineering 32(8-9):961-985. http://dx.doi.org/10.1016/j.oceaneng.2004.10.015

Osborne, P.D., and M. H. Davies. 2004. South jetty sediment processes study, Grays Harbor, Washington: Processes along Half Moon Bay, PIE Technical Report. Edmonds, WA: Pacific International Engineering.

Resio, D., and B. Tracy. 1982. Theory and calculation of the nonlinear energy transfer between sea waves in deep water, Hydraulics Laboratory WIS Report 11. Vicksburg, MS: U.S. Army Engineer Waterways Experiment Station.

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