Loughborough University is a top-ten rated university in England for research intensity (REF2014) and an outstanding 66% of the work of Loughborough’s academic staff who were eligible to be submitted to the REF was judged as ‘world-leading’ or ‘internationally excellent’, compared to a national average figure of 43%. In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career. The study of internal waves has important applications in geophysical fluid dynamics and theoretical oceanography. This PhD project could contribute to a better understanding of the threats such waves may pose to the Arctic environment, and a more complete description of higher baroclinic mode waves and their ability to efficiently trap and transport particles. The PhD student will acquire expertise in the areas of nonlinear waves, applied dynamical systems, asymptotic analysis, mathematical modelling, and scientific computation. The PhD student will join an internationally recognised group working on linear and nonlinear waves, and mathematical modelling at the Department of Mathematical Sciences. Large amplitude internal waves have been observed frequently in coastal oceans through in situ measurements and satellite images. The importance of this geophysical phenomenon has been increasingly appreciated, as it is believed to be responsible for a significant fraction of the mixing that must exist to maintain the observed ocean circulation. Weakly nonlinear models have been extensively used to study internal waves and, among them, the KdV model has stood for many years as the ‘‘canonical’’ equation for the evolution of these waves. However, to allow a more accurate description, higher-order nonlinear models may be required, as wave amplitudes are often large and comparable to the thickness of the well- mixed upper layer. This research will further develop the mathematical understanding of the proposed nonlinear models for internal waves, and improving them by considering more realistic situations where two-dimensional effects, vorticity, and multiple interfaces are present. The hydrodynamic stability issues associated with the propagation of internal waves will also be addressed, and links between weakly and strongly nonlinear regimes will be investigated.