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Many analytical solutions to the extended mild slope equation were presented by adopting Hunt’s approximated solution of linear dispersion in order to investigate how to be affected water wave when wave propagating on a shallow water depth suddenly encounter a much deeper water depth. In this study, an analytical solution to the extended mild slope equation is derived for waves propagating over an axi-symmetric pit in which the water depth varies in proportion to a power of radial distance from the center of it. First, the governing equation is transformed into ordinary differential equation by using the method of separation of variables, and the coefficients expressed in terms of phase velocity and group velocity are transformed into explicit forms by using Hunt’s (1979) approximate solution for wave dispersion. The functions related to higher order terms such as bottom curvature and bottom slope-squared are expressed as power series. Finally, by using the Frobenius series, the analytical solution to the extended mild slope equation is derived. The validity of the analytical solution is demonstrated by comparison with the numerical solution computed by the finite element method. The present solution shows more accurate result than the solution of the mild slope equation while less accurate in intermediate depth region due to the feature of Hunt’s solution.
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참고문헌 (11)
참고문헌 신청
Berkhoff, J. C. W. / 1972 / Computation of combined refraction-diffractioni / Proceedings of the 13th International Conference on Coastal Engineering :471~490
Chamberlain, P. G. / 1995 / The modified mild-slope equation / Journal of Fluid Mechanics 291:393~407
Chandrasekera, C. N. / 1997 / Extended linear refraction-diffraction model / Journal of Waterway, Port, Coastal and Ocean Engineering 123:280~296
Homma, S. / 1950 / On the behavior of seismic sea waves around circular island / Geophysics Management 21:199~208
Jonsson, I. G. / 1976 / Diffraction and refraction calculations for waves incident on an island / Journal of Marine Research 34:469~496
Chamberlain, P. G. / 1995 / The modified mild-slope equation / Journal of Fluid Mechanics 291:393~407
Chandrasekera, C. N. / 1997 / Extended linear refraction-diffraction model / Journal of Waterway, Port, Coastal and Ocean Engineering 123:280~296
Homma, S. / 1950 / On the behavior of seismic sea waves around circular island / Geophysics Management 21:199~208
Jonsson, I. G. / 1976 / Diffraction and refraction calculations for waves incident on an island / Journal of Marine Research 34:469~496
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