WKB APPROXIMATION TO THE MODIFIED MILD-SLOPE EQUATION

Seung-Nam Seo

Abstract


WKB approximation for water wave scattering by rapidly varying topography is obtained from a modified mild-slope equation of the general form by Porter (2003). The present WKB solution is reduced to the previous study where shallow water conditions are present. WKB models from the transformed mild-slope equation, without the described bottom curvature modification, show better performance than those by the original developed mild-slope equation. The underlying significance of the present equation is discussed in the context of linear wave scattering. The selected figures representing our results further characterize main feature of this study.

Keywords


modified mild-slope equation; WKB approximation; transformed mild-slope equations

References


Athanassoulis, G.A., and K.A. Belibassakis. 1999. A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions. J. Fluid Mech., 389, 275-301.http://dx.doi.org/10.1017/S0022112099004978

Berkhoff, J.C.W. 1972. Computation of combined refraction-diffraction. Proc. 13th Coastal Eng. Conf., 1, 471-490.

Chamberlain, P.G., and D. Porter. 1995. The modified mild-slope equation. J. Fluid Mech., 291, 393-407.http://dx.doi.org/10.1017/S0022112095002758

Chamberlain, P.G., and D. Porter. 2006. Multi-mode approximations to wave scattering by an uneven bed. J. Fluid Mech., 556, 421-441.http://dx.doi.org/10.1017/S0022112006009797

Davies, A.G., and A.D. Heathershaw. 1984. Surface-wave propagation over sinusoidally varying topography. J. Fluid Mech., 144, 419-443.http://dx.doi.org/10.1017/S0022112084001671

Guazzelli, E., Rey, V. and Belzons, M. (1992). Higher-order Bragg reflection of gravity surface waves by periodic beds. J. Fluid Mech., 245, 301-317.http://dx.doi.org/10.1017/S0022112092000478

Kajiura, K. 1961. On the partial reflection of water waves passing over a bottom of variable depth. Proc. Tsunami Meetings 10th Pacific Science Congress, IUGG Monograph 24, 206-234.

Kirby, J.T. 1986. A general wave equation for waves over rippled beds. J. Fluid Mech., 162, 171-186.http://dx.doi.org/10.1017/S0022112086001994

Massel, S.R. 1993. Extended refraction-diffraction equation for surface waves. Coastal Eng., 19, 97-126.http://dx.doi.org/10.1016/0378-3839(93)90020-9

Mei, C.C. 1985. Resonant reflection of surface water waves by periodic sandbars. J. Fluid Mech., 152, 315-335.http://dx.doi.org/10.1017/S0022112085000714

Mei, C.C. 1989. The Applied Dynamics of Ocean Surface Waves. World Scientific, Singapore.

Mei, C.C., M. Stiassnie, and D.K.-P. Yue. 2005. Theory and applications of Ocean Surface Waves. World Scientific, Singapore.

Porter, D. 2003. The mild-slope equations. J. Fluid Mech., 494, 51-63.http://dx.doi.org/10.1017/S0022112003005846

Porter, R., and D. Porter. 2003. Scattered and free waves over periodic beds. J. Fluid Mech., 483, 129-163.http://dx.doi.org/10.1017/S0022112003004208

Porter, D., and D.J. Staziker. 1985. Extension of the mild-slope equation. J. Fluid Mech., 300, 367-382.http://dx.doi.org/10.1017/S0022112095003727


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