A Lagrangian Model for Irregular Waves and Wave Kinematics

Abstract

It has proven difficult to describe the kinematics in irregular waves satisfactorily, in particular for the surface zone in broad-banded waves. A Lagrangian approach offers distinct advantages in this respect, eliminating the need for extrapolation of solutions or “stretching” of coordinates. This paper presents a model of irregular waves based on superposition of linear Lagrangian wave components, using an iterative method to obtain the Eulerian solution. This approach yields theoretically consistent results everywhere in the waves, and comparisons with wave flume measurements show good agreement. Also, the linear Lagrangian model includes wave interactions that would be nonlinear in an Eulerian formulation.