A Note on Applications of the Mild-slope Equation for Random Waves
Keywords:Green’s identity method, modified mild-slope equation, finite element solutions, wave dispersion relation, Bragg resonance scattering
Based on the formal derivation of the mild-slope equation (Smith & Sprinks, 1975), the neglected 'forcing terms' are rederived. It is shown that the slope terms are of order ϵ2, which are negligible according to the mild-slope assumption, where ϵ = |∇h|/kh represents the classical definition of small parameter for mild-slope. It is found that the curvature terms depend not only on ϵ but also on the wave frequency and the terms have considerable effect on wave phase in the lower range of wave frequencies. Therefore, in the broad wave spectrum case, the curvature terms discarded by Smith & Sprinks (1975) are necessary to accurately predict waves over a bottom with severe curvatures.