INTERACTION OF VORTICES WITH TOPOGRAPHY

不规则的地形是一个普遍的海洋特征，出现在海底的形状，沿着海岸线，在连接海岸和深渊的架子和斜坡上。在地形附近经常观测到具有相当大变异性和增强混合的强喷流，这意味着大陆架和斜坡、山脊和海山施加了强烈的海洋动力影响。过去的研究已经说明了涡旋-地形相互作用的复杂性，其中经常产生较小尺度的涡旋；也就是说，地形催化了中尺度场的正向级联，并可能提供重要的消散途径。海洋涡旋与大陆架和斜坡的相互作用是变介质中波浪-涡旋相互作用的一个更普遍的问题。这里的一个关键参数是陆架宽度与涡旋大小的比值，这个比值通常很小。为了建立适当的数学模型，并阐明基本的物理机制，我们提出了一个深入的研究强涡旋在封闭陆架地形附近的演变。第一阶段，当涡旋从公海接近冰架时，将从理论上进行分析，以确定由接近的涡旋所迫使的海岸困波。由于要正确描述大陆架断裂深水侧附近陡峭大陆坡上的海洋动力学，需要考虑斜压效应，因此我们建议在深海区使用双层模型，在海洋深度小于界面深度的浅海区使用正压模型。这种正压-斜压模式的结合应该能捕捉到沿海地区当前变率的最基本因素，这些因素目前还相对未被探索。下一阶段，高位涡量的陆架水在陆架上平流进入公海，在强涡周围形成涡片。随后的卷起成较小尺度的气旋涡旋将使用特定的方程集来进行数值研究，该方程集捕获了基本的动力学过程。分析结果将与一系列相关参数的数值模拟和观测数据进行比较。我们的总体目标是建立一个涡架相互作用过程的数学模型，该模型可以充分描述狭窄地形附近的变率和混合。

Irregular topography is a prevalent ocean feature, appearing in the shape of the ocean bottom, along the coastline, and on the shelves and slopes that connect the coast to the deep abyss. Strong jet-like currents, with considerable variability and enhanced mixing, are often observed near topography, implying that the continental shelves and slopes, ridges and seamounts exert a strong dynamical oceanic influence. Past studies have illustrated the complicated nature of vortex-topography interaction in which smaller-scale vortices are often produced; thatis, topography catalyzes a forward cascade in the mesoscale fields and may provide important routes to dissipation.The interaction of an ocean vortex with the continental shelf and slope is one aspect of a more general problem about wave-vortex interactions in a variable medium. A crucial parameter here is the ratio of the shelf width to the vortex size, which is typically small. In order to develop adequate mathematical models, and to clarify the basic physical mechanisms, we propose a thorough investigation of the evolution of a strong vortex in the vicinity of confined shelf-like topography. The first stage, when the vortex approaches the shelf from the open ocean, will be analyzed theoretically to determine the coastally-trapped waves forced by an approaching eddy. Since a proper description of ocean dynamics over a steep continental slope adjacent to the deep-water side of a shelf-break requires baroclinic effects to be taken into account, we propose using a two-layer model in the deep area matched with a barotropic model in the shallow area, where the ocean depth is smaller than the interface depth. Such a combination of a barotropic-baroclinic model should capture the most essential elements of current variability in the littoral zone, which remain presently relatively unexplored.At the next stage, the on-shelf advection of shelf water with high potential vorticity into the open ocean results in the development of a vortex sheet around the intense eddy. The subsequent rolling-up into smaller-scale cyclonic vortices will be studied numerically using a certain equation set which captures the essential dynamical processes. The results of the analysis will be compared with numerical simulations and observational data for a range of the relevant parameters. Our general aim is to construct a mathematical model for the process of vortex-shelf interaction, which can provide an adequate description of variability and mixing near confined topography.