Interaction of Oceanic Vortices with Steep Topography

不规则地形是一种普遍存在的海洋特征，它以海底的形状出现，沿着海岸线，以及连接海岸和深渊的陆架和斜坡上。在地形附近经常观察到强烈的急流，具有相当大的变异性和增强的混合，这意味着大陆架和斜坡、海脊和海山对海洋产生了强大的动力影响。过去的研究已经阐明了涡旋-地形相互作用的复杂性，在这种相互作用中，往往会产生较小尺度的涡旋；即，地形催化了中尺度场中的前向级联，并可能提供重要的消散途径。海洋涡旋与大陆架和陆坡的相互作用是可变介质中更一般的波涡相互作用问题的一个方面。在海洋环境中，一个关键参数是大陆架宽度与涡旋大小的比率，这通常是很小的。为了发展足够的数学模型，并阐明基本的物理机制，我们提议对受限陡峭地形附近的强涡的演变进行彻底的调查。由于要正确描述与陆架折断的深水侧相邻的陡峭大陆斜坡上的海洋动力学，需要考虑斜压效应，因此我们将在深区使用一种新的双层数值模式，并在浅区使用正压模式，那里的海洋深度小于界面深度。这种正压-斜压模式的组合捕捉到了海岸带最基本的海流变化要素，这些要素目前仍相对未被开发。以往的研究表明，陆架上具有高位涡的陆架平流进入开阔海洋，导致在强烈的初级涡旋周围形成涡旋层。随后卷起成小尺度气旋涡旋将用我们的数值模式和等高线动力学方法进行数值研究，这两种方法一起有望捕捉到基本的动力过程。我们的研究结果将与其他相关参数的数值模拟和观测数据进行比较。我们的总体目标是深入了解涡架相互作用的过程，这可以为有限地形附近的可变性和混合提供充分的描述。

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; that is, 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 in the oceanic context 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 steep topography. 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 will use a novel two-layer numerical 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 barotropic-baroclinic models captures the most essential elements of current variability in the littoral zone, which remain presently relatively unexplored.Previous studies have indicated that 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 primary eddy. The subsequent rolling-up into smaller-scale cyclonic vortices will be studied numerically using both our numerical model and contour dynamics methods which together can be expected to capture the essential dynamical processes. The results of our study will be compared with other numerical simulations and observational data for a range of the relevant parameters. Our general aim is to obtain a deep understanding of the process of vortex-shelf interaction, which can provide an adequate description of variability and mixing near confined topography.