Boundary Integral Equation Method for Limit Surface Gravity Waves

Abstract

A numerical solution to periodic nonlinear irrotational surface gravity waves on a horizontal sea floor is developed using an iterative Boundary Integral Equation Method (BIEM). This solution technique is subsequently applied to determine the characteristics of limit waves for which the wave crest theoretically ceases to be rounded and become angled with an included angle of 120°. The analysis includes waves with and without mean currents and can also be used to estimate the wave set‐down. Solutions with zero mean current are parameterized as functions of relative water depth and presented in graphs. In the cases with current, the results are given in terms of the relative water depth and a dimensionless current speed.