Theoretical studies in the nonlinear dynamics of ocean currents, eddies and waves

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The ocean is a highly nonlinear turbulent caldron of ocean currents, eddies and waves that span time scales from minutes to years and space scales from centimetres to thousands of kilometres. Many of the physical processes observed in the ocean are not yet fully understood in terms of fundamental geophysical fluid dynamics. Discovering and deciphering the detailed dynamics of the ocean has the potential to make a profound impact on our ability to understand and predict the full range of dynamical responses that can occur as the environmental "drivers" of ocean physics change over time.  ******My long-term research objective is focused on discovering new dynamics and developing new physical insights into the fundamental nonlinear geophysical fluid mechanics of ocean currents, eddies and waves and to apply this new knowledge to understand existing and to predict new complex ocean flows. My research program exploits innovative theoretical models, mathematical analysis and computational simulations to describe and explain nonlinear oceanographic dynamical processes from the sub-mesoscale (e.g., internal gravity waves) to the mesoscale (e.g., baroclinic instability and eddy dynamics) to the basin scale (e.g., abyssal ocean circulation theory). Another objective of my research program is to predict where new or interesting physical oceanographic processes may be occurring in order to motivate further specific observational or numerical studies. I will address these objectives by:******1. Within the context of my research into abyssal ocean currents, I will (i) solve the important problem of the non-hydrostatic mixed Kelvin Helmholtz-frictional destabilization of abyssal overflows paying particular attention to describing the downslope flow, mixing and internal gravity wave generation properties; (ii) describe and clarify the role of baroclinic vortex stretching in the generation of surface-intensified mesoscale eddies associated with abyssal overflows; (iii) describe and clarify the role of dissipation and internal waves in the cross equatorial flow of abyssal ocean currents paying particular attention to predicting where in the equatorial Atlantic ocean these mixing processes are occurring,    ***2. Within the context of my research into nonlinear baroclinic instability, I will solve the very important and challenging problem of determining the nonlinear evolution of wave packets at the point of marginal stability when the background flow exhibits time variability. This research has the potential to make a groundbreaking advance in our understanding of the dynamics of nonlinear baroclinic waves and their role in large-scale mixing. ******I will be training three MSc and two PhD students. In addition to making high-quality research contributions, my students learn highly desirable skills in formulating tractable research questions, logical reasoning, team work and computer programing and simulation.**