标题： 三层地理流中单极涡旋与孤立地形特征的相互作用 显示英文标题

标题： Interaction of a monopole vortex with an isolated topographic feature in a three-layer geophysical flow

摘要： 在一个三层准地转分析模型框架内，该模型基于地球物理流的$f$平面，由单极涡旋与孤立地形特征相互作用诱导出拉格朗日平流问题被研究。 我们关注两种不同情况：单极涡旋位于上层或中层。 在底层，存在一个 δ 函数形式的地形特征，在背景流的作用下，其附近会生成一个闭合回流区域。 这个回流区域延伸到中层和上层，并扮演着地形涡旋的角色。 单极涡旋与地形涡旋之间的相互作用导致流体质点复杂的包括混沌的平流。 我们表明，模型参数——即单极涡旋和地形涡旋的强度和初始位置、各层深度和密度，负责形成各种不同的平流模式。 尽管这些模式相当复杂，但可以区分出两个主要过程，它们主导了流体质点的平流。 第一个过程是系统相空间结构随时间的变化，因此在地形涡旋的闭合区域内，会出现周期性的非闭合粒子路径，使粒子离开地形涡旋。 第二个过程是由单极涡旋与地形之间非定常相互作用引起的混沌平流。 显示英文摘要

摘要： In the frame of a three-layer quasi-geostrophic analytical model of a $f$-plane geophysical flow, Lagrangian advection being induced by the interaction of a monopole vortex with an isolated topographic feature is addressed. Two different cases when the monopole locates either within the upper or the middle layer are of our interest. In the bottom layer, there is a delta function topographic feature, which generates a closed recirculation region in its vicinity due to the background flow. This recirculation region extends to the middle and upper layers, and it plays the role of a topographic vortex. The interaction between the monopole and the topographic vortex causes complex, including chaotic, advection of fluid particles. We show that the model's parameters, namely, the monopole and topographic vortices' strengths and initial positions, the layers' depths and densities are responsible for the diverse advection patterns. While the patterns are rather complicated, however, one can single out two major processes, which mostly govern fluid particle advection. The first one is the variation in time of the system's phase space structure, so that within the closed region of the topographic vortex, there appear periodically unclosed particle pathways by which the particles leave the topographic vortex. The second one is chaotic advection that arises from the nonstationarity of the monopole-topography interaction.