Abstract
In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refraction and diffraction of shallow-water waves.
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References
Berkhoff, J. C. W., Computation of combined refraction-diffraction, Proc. 13th Int. Cof. Coastal Eng., Vancouver, 1972.
Hedges, T. S., An empirical modification to linear wave theory, Proc. Inst. Civ. Eng., 1976, 61: 575.
Booij, N., Gravity waves on water with non-uniform depth and current, Rept. 1981, No. 81-1, Dept. of Civ. Eng., Delft University of Technology.
Kirby, J. T., Dalrymple, R. A., Verification of a parabolic equation for propagation of weakly-nonlinear waves, Coastal Engineering, 1984, 8: 219–232.
Kirby, J. T., Dalrymple, R. A., An approximate model for nonlinear dispersion in monochromatic wave propagation models, Coastal Engineering, 1986, 9: 545.
Li Ruijie, Wang Houjie, Nonlinear effect of wave propagation in shallow water, China Ocean Engineering, 1999a, 13(1): 109.
Li Ruijie, Wang Houjie, A modified form of mild-slope equation with weakly nonlinear effect, China Ocean Engineering, 1999b, 13(3): 327.
Whitman, G. B., Non-linear dispersion of water waves, J. Fluid Mech., 1967, 27: 399.
Yoo, D., O’Connor, B. A., Diffraction of waves in caustics, Journal of Waterway, Port, Coastal and Ocean Engineering, 1989, 114(6): 715.
Xu Shikai, Wang Hongchuan, Hong Guangwen, Refraction and diffraction mathematical model for waves and its numerical simulation by use of wave energy balance equation, The Ocean Engineering (in Chinese), 1996, 14(4): 38.
Berkhoff, J.C.W., Booij, N. and Radder, A.C., Verification of numerical wave propagation models for simple harmonic linear water waves, Coastal Engineering, 1982, 6: 255.
Ebsole, B. A., Rafraction-diffraction model for linear water waves, Journal of Waterway, Port, Coastal and Ocean Engineering, 1985, 111(6): 939.
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Wang, H., Zuosheng, Y., Ruijie, L. et al. A nonlinear RDF model for waves propagating in shallow water. Sc. China Ser. B-Chem. 44 (Suppl 1), 158–164 (2001). https://doi.org/10.1007/BF02884822
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DOI: https://doi.org/10.1007/BF02884822