Abstract. The Eulerian point of view is the traditional theoretical and numerical tool to describe fluid mechanics. Some modern computational fluid dynamics codes allow for the efficient simulation of particles, in turn facilitating a Lagrangian description of the flow. The existence and persistence of Lagrangian coherent structures in fluid flow has been a topic of considerable study. Here we focus on the ability of Lagrangian methods to characterize mixing in geophysical flows. We study the instability of a strongly non-linear double-jet flow, initially in geostrophic balance, which forms quasi-coherent vortices when subjected to ageostrophic perturbations. Particle clustering techniques are applied to study the behavior of the particles in the vicinity of coherent vortices. Changes in inter-particle distance play a key role in establishing the patterns in particle trajectories. This paper exploits graph theory in finding particle clusters and regions of dense interactions (also known as subclusters). The methods discussed and results presented in this paper can be used to identify mixing in a flow and extract information about particle behavior in coherent structures from a Lagrangian point of view.

中文翻译：

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粒子聚类和子聚类作为混合地球物理流的代理

摘要。欧拉观点是描述流体力学的传统理论和数值工具。一些现代计算流体动力学代码允许对粒子进行有效模拟，从而促进对流动的拉格朗日描述。流体流动中拉格朗日相干结构的存在和持久性一直是大量研究的主题。在这里，我们关注拉格朗日方法表征地球物理流中混合的能力。我们研究了强非线性双射流的不稳定性，最初处于地转平衡状态，当受到地转扰动时会形成准相干涡流。粒子聚类技术用于研究粒子在相干涡流附近的行为。粒子间距离的变化在建立粒子轨迹模式方面起着关键作用。本文利用图论来寻找粒子簇和密集相互作用区域（也称为子簇）。本文中讨论的方法和结果可用于识别流动中的混合，并从拉格朗日的角度提取有关相干结构中粒子行为的信息。