Huang Hu, Ding Pingxing, Lü Xiuhong. Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms[J]. Acta Oceanologica Sinica, 2000, (3): 23-31.
Citation: Huang Hu, Ding Pingxing, Lü Xiuhong. Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms[J]. Acta Oceanologica Sinica, 2000, (3): 23-31.

Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms

  • Received Date: 1999-07-14
  • Rev Recd Date: 2000-01-15
  • 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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