| Huang Hu,Ding Pingxing,Lü Xiuhong. 2000. Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms. Acta Oceanologica Sinica, (3):23－31 |
| Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms |
| Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms |
| Received:July 14, 1999 Revised:January 15, 2000 |
| DOI： |
| Key words:Mild-slope equation wave-current-uneven bottom interactions Hamiltonian formulation for irrotational motions Bragg reflection |
| 中文关键词: Mild-slope equation wave-current-uneven bottom interactions Hamiltonian formulation for irrotational motions Bragg reflection |
| 基金项目:This project was supported by the National Outstanding Youth Science Foundation of China under contract No. 49825161. |
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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 compon}ts: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. |
| 中文摘要: |
| 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 compon}ts: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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