Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms |
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Authors: | Huang Hu Ding Pingxing and L Xiuhong |
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Institution: | State Key Laboratory of Estuarine & Coastal Research, East China Normal University, Shanghai 200062, China |
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Abstract: | A time-dependent mild-slope equation for the extension of the classic mild-slope equation of Berkhoff is developed for the interactions of large ambient currents and waves propagating over an uneven bottom, using a Hamiltonian formulation for irrotational motions. The bottom topography consists of two components the slowly varying component which satisfies the mild-slope approximation, and the fast varying component with wavelengths on the order of the surface wavelength but amplitudes which scale as a small parameter describing the mild-slope condition. The theory is more widely applicable and contains as special cases the following famous mild-slope type equations: the classical mild-Slope equation, Kirby's extended mild-slope equation with current, and Dingemans's mild-slope equation for rippled bed. Finally, good agreement between the classic experimental data concerning Bragg reflection and the present numerical results is observed. |
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Keywords: | Mild-slope equation wave-current-uneven bottom interactions Hamiltonian formulation for irrotational motions Bragg reflection |
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