Steady periodic waves over a planar seabed: a global characterization

Abstract

The problem of propagation of steady periodic waves over a planar seabed is faced through the definition of a suitable semi-analytical iterative scheme. The latter is capable of describing highly nonlinear waves in deep, intermediate and shallow water conditions. Comparisons with the existing fifth-order theories show that the proposed model is accurate in all the regimes of motion and that it does not present any of the limitations affecting the Stokes and cnoidal wave solutions. Further, it also provides a reliable approximation of the dynamics of maximum-amplitude waves. The definition of the iterative scheme is preceded by a detailed study of the geometrical wave parameters. This latter part is aimed at the definition of a global scaling for water waves valid in all the regimes of motion.