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

海洋是由洋流、涡流和波浪组成的高度非线性的湍流大锅，时间尺度从几分钟到几年，空间尺度从厘米到数千公里。在海洋中观察到的许多物理过程在基本地球物理流体动力学方面还没有得到充分的了解。发现和破译海洋的更详细的动力学，有可能对我们理解和预测随着海洋物理的环境因素随着时间的推移而发生的全方位动态响应的能力产生深远的影响。 我的长期研究目标是发现新的动力学，发展对洋流、涡流和波浪的基本和非线性地球物理流体力学的新的物理见解，并将这一新知识应用于了解现有的和预测新的复杂的海洋流动。我的研究项目利用创新的理论模型、数学分析和计算模拟来描述和解释从亚中尺度(例如，重力内波)到中尺度(例如，斜压不稳定和涡旋动力学)到盆地尺度(例如，深海海洋环流理论)的非线性海洋动力学过程。我的研究计划的另一个主要目标是预测新的或有趣的物理海洋过程可能发生在哪里，以激励进一步的具体观测或数值研究。我将通过以下方式实现这些目标： 1.在我对深海洋流的研究范围内，我将(I)解决开尔文·赫姆霍尔茨(Kelvin Helmholtz)的非静力混合的重要问题--深海溢流的摩擦失稳，特别注意描述下坡流、混合和内部重力波的产生特性；(Ii)描述和澄清斜压涡旋和伸展的作用在与深海溢流有关的表面强化中尺度涡旋的产生中的作用；(Iii)描述和澄清耗散和内波在深海洋流越赤道流动中的作用，特别注意预测这些混合过程在赤道大西洋的什么地方发生。 2.在我对非线性斜压不稳定的研究背景下，我将解决一个非常重要和具有挑战性的问题--当背景气流表现出时间变化时，在边缘稳定点确定波包的非线性演化。这项研究为我们理解非线性斜压波的动力学及其在大范围混合中的作用提供了开创性的进展。 我将培训三名硕士和两名博士生。除了做出高质量的研究贡献外，我的学生还将学习在制定易于处理的研究问题、逻辑推理、团队合作以及计算机编程和模拟方面非常令人满意的技能。

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.