Water waves over a strongly undulating bottom

Abstract

Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the variational method for arbitrary seabed shape parameterized by an analytical function. As applications of this theory, band structure of linear waves over periodic bottoms is calculated and evolution of a strong solitary wave running from a deep region to a shallow region is numerically simulated.