A Note on Applications of the Mild-slope Equation for Random Waves

Abstract

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.