Abstract: Firstly, wave breaking will be classified in a mostly descriptive way. Secondly, wave motion can be divided according to depth of water: shallow and deep. A division can thus be made into hyperbolic and dispersive wave models as limiting systems. Thirdly, we begin with an investigation of the shallow water equations, including a model of wave breaking, numerical results and challenges. Finally, we explore new (numerical) models of mixed hyperbolic- elliptic type for waves in deeper water, based on Luke's variational principle, and extensions thereof. Throughout, we will use in-house (live) experiments, including a mini-beach with wave-sand dynamics and the bore-soliton-splash; for purposes of visualisation, but also for fun and as reality check. The wider relevance of this work for our water-swept "nether lands" will become evident.
