Multi-scale interactions between internal waves and rotationally modified vortices

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In rotating and density stratified fluids such as the ocean and atmosphere, dynamics can span a wide range of scales and dynamical regimes, from wave breaking on a beach, to circulation around entire ocean basins, and everything in-between. At large scales, the flow is dominated by rotational forces and the stabilising effect of density stratification, leading to slowly varying, rotationally constrained, horizontal flow - an example being atmospheric weather systems. This flow is in a state of near-balance between the Coriolis force due to the Earth's rotation and horizontal pressure gradients. However, at small scales, the effects of rotation and stratification are negligible, and the flow is characterised by 3D turbulence. In this project, I will study the interactions between two classes of fluid dynamical processes that occur at the intermediate scales between large-scale balanced motion and small-scale turbulence, and are therefore modified, but not constrained, by rotation: internal waves and rotationally modified vortices.Internal waves are ubiquitous in stratified flows, including the ocean and atmosphere. They overlap in scale with rotationally modified vortices for which both inertial forces and rotation are of comparable importance, termed 'submesoscale' in the ocean and 'mesoscale' in the atmosphere. Although internal waves and rotationally modified vortices have received considerable attention in recent years, their interactions are still not well understood. Here, I propose to study the way in which internal waves and rotationally modified vortices interact, including how energy is transferred between them, and how they might affect each other's generation, lifecycle, and eventual decay.These interactions will be investigated for three different flow scenarios using a theoretical framework and high-resolution numerical simulations. The modelling will be idealised and simplified, allowing me to isolate the key processes at play, whilst being motivated by real interactions that occur in the ocean and atmosphere. Oceanic observations will be used to verify results.This project is motivated by the growing consensus that internal waves and rotationally modified vortices couple large- and small- scale dynamics. Capturing this effect is a key challenge in developing the next generation of climate models, since small scales provide an essential sink of energy from the large scale flow. Whilst larger scale, balanced, flows will soon be fully resolved in climate models, rotationally modified vortices and internal waves are at the frontier of climate parameterisations, and will continue to be relevant to the UK's capability in the prediction of climate for decades to come.