Dr Ricardo Lopes-Barros (Loughborough University) gives a research seminar at the School of Mathematics, UEA. The talk is on “Large amplitude mode-2 internal solitary waves in three-layer flows”. The abstract is below.

We consider a strongly nonlinear long wave model for large amplitude internal waves in a three-layer flow bounded above and below by rigid boundaries. The model extends the two-layer Miyata-Choi-Camassa (MCC) model (Miyata 1988; Choi & Camassa 1999) and is able to describe the propagation of long internal waves of both the first and second baroclinic modes. Solitary-wave solutions of the model are shown to be governed by a Hamiltonian system with two degrees of freedom. Emphasis is given to the solitary waves of the second baroclinic mode (mode-2) and their strongly nonlinear characteristics that fail to be captured by weakly nonlinear models. In asymptotic limits relevant to oceanic applications and previous laboratory experiments, it is shown that, after choosing relevant physical parameters, large amplitude mode-2 waves with single-hump profiles can be described by the solitary wave solutions of the MCC model, originally developed for mode-1 waves in a two-layer system. As a result of the richness of the dynamical system with two degrees of freedom, in the case when the density stratification is weak and the density transition layer is thin, new classes of mode-2 solutions, characterized by multi- humped wave profiles of large amplitude, are also found. In contrast with the classical solitary-wave solutions described by the MCC equation, such multi-humped solutions cannot exist for a continuum set of wave speeds for a given layer configuration. Our analytical predictions based on asymptotic theory are then corroborated by a numerical study of the full dynamical system.