Dynamical Systems Methods for Waves in Fluids: Stability, Breaking and Mixing

Abstract

In this thesis, we investigate the problem of density stratified interfacial flows of immiscible fluids in the shallow water limit. We focus our attention on the two-and-a-half- and three-layer flows, with and without the so-called Boussinesq approximation which requires small density differences. The governing equations are carefully derived and the dynamics of their solutions are studied from both analytical and numerical points of view, particularly the issues of modal decomposition and whether a solution maintains hyperbolicity (i.e. wave-like behaviour) or not. New explicit criteria for transition to the elliptic regime are provided using dynamical systems techniques. The existence of invariant hyperbolic regions is proven and examples are constructed using the so-called simple waves. In addition, the mixing and entrainment phenomena are discussed and modelled for the case of a two-layer shallow water flow. Extensions and future work are suggested at the end.

Date of Award	22 Nov 2018
Original language	English
Awarding Institution	University of Bath
Sponsors	Conselho Nacional de Desenvolvimento Cientifico e Tecnologico
Supervisor	Paul Milewski (Supervisor)