Multi-scale interactions between internal waves and rotationally modified vortices

在海洋和大气等旋转和密度分层的流体中，动力学可以跨越广泛的尺度和动力体系，从海滩上的波浪破碎到整个海洋盆地的环流，以及介于两者之间的一切。在大尺度上，气流受旋转力和密度分层的稳定作用支配，导致缓慢变化的、旋转受限的水平气流——大气天气系统就是一个例子。由于地球自转而产生的科里奥利力和水平压力梯度之间的流动处于接近平衡的状态。然而，在小尺度上，旋转和分层的影响可以忽略不计，流动的特征是三维湍流。在这个项目中，我将研究两类流体动力学过程之间的相互作用，这两类流体动力学过程发生在大尺度平衡运动和小尺度湍流之间的中间尺度上，因此受到旋转的修正，但不受其约束：内波和旋转修正涡。内波在分层流中普遍存在，包括海洋和大气。它们在尺度上与旋涡重叠，其中惯性力和旋转都相当重要，在海洋中称为“亚中尺度”，在大气中称为“中尺度”。虽然近年来内波和旋变涡受到了相当多的关注，但它们之间的相互作用仍然没有得到很好的理解。在这里，我建议研究内波和旋转修正涡流相互作用的方式，包括它们之间的能量传递方式，以及它们如何影响彼此的产生、生命周期和最终衰减。这些相互作用将在三种不同的流动情况下使用理论框架和高分辨率数值模拟进行研究。建模将被理想化和简化，使我能够隔离发挥的关键过程，同时受到海洋和大气中发生的真实相互作用的激励。海洋观测将用于验证结果。这个计划的动机是越来越多的共识，即内波和旋转修正涡耦合大尺度和小尺度动力学。捕捉这种效应是开发下一代气候模式的一个关键挑战，因为小尺度提供了大尺度流的基本能量汇。虽然更大规模、平衡的气流很快就会在气候模式中得到完全解决，但旋转修正的涡旋和内波是气候参数化的前沿，并将继续与英国未来几十年的气候预测能力相关。

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.