Numerical models for evolution of extreme wave groups

Abstract

The paper considers the application of two numerical models to simulate the evolution of steep breaking waves. The first one is a Lagrangian wave model based on equations of motion of an inviscid fluid in Lagrangian coordinates. A method for treating spilling breaking is introduced and includes dissipative suppression of the breaker and correction of crest shape to improve the post breaking behaviour. The model is used to create a Lagrangian numerical wave tank, to reproduce experimental results of wave group evolution. The same set of experiments is modelled using a novel VoF numerical wave tank created using OpenFOAM. Lagrangian numerical results are validated against experiments and VoF computations and good agreement is demonstrated. Differences are observed only for a small region around the breaking crest.

Wave Propagation Models for Numerical Wave Tanks

“…These problems can be efficiently approached by much simpler Lagrangian models similar to the original model of Brennen and Whitney (1970). Recent examples of application of such a model include tsunami waves in a wave flume (Buldakov, 2013), violent sloshing in a moving tank (Buldakov, 2014) and evolution of breaking wave groups (Buldakov et al, 2019).…”

“…Later in this chapter we consider a two-dimensional fully Lagrangian finite-difference wave model. The model follows the approach of the early Lagrangian models originally introduced by Brennen and Whitney (1970) and was further developed in Buldakov (2013Buldakov ( , 2014 and Buldakov et al (2019). Before continuing, let us first examine some aspects of the Lagrangian description that affect the application of discrete numerical methods, such as finite differences.…”