A theoretical hierarchy of the mild-slope equations for wave-current interactions in coastal waters

Abstract

Based on total investigation, analysis and judgment of one main class of coastal wave models, the mild-slope equations， an operator representing the wide wave-current interactions in coastal waters is introduced to develop a time-dependent theoretical hierarchy of the mild-slope equations for wave-current interactions by means of the universal Hamiltonian variational principle for water waves, which reaches a comparatively high degree of harmony and unity of form and content.