Parametric Study of the Accuracy of an Approximate Solution for the Mild-Slope Equation

In this paper, we call and study a classical equation modeling the refraction and diffraction phenomena of water waves in harbors. This equation is called the mild-slope equation. By using a family of bottom profiles, we construct analytically an approximate solution of this linear equation and perform, with various norm comparisons, a parametric study of this approximate solution. We evaluate ∇· u for the resulting irrotational flow using various parameters, such as the mean slope, the averaged water depth...