ABSTRACT Clustering of tracers floating on the ocean surface and evolving due to combined velocity fields consisting of a deterministic mesoscale component and a kinematic random component is analysed. The random component represents the influence of submesoscale motions. A theory of exponential clustering in random velocity fields is applied to characterise the obtained clustering scenarios in both steady and unsteady time-dependent mesoscale flows, as simulated by a comprehensive realistic, eddy-resolving, general circulation model for the Japan/East Sea. The mesoscale flow field abounds in transient eddy-like patterns modulating and branching the main currents, and the underlying time-mean flow component features closed recirculation zones that can entrap the tracer. The submesoscale flow component is modelled kinematically, as a divergent random velocity field with a prescribed correlation radius and variance. The combined flow induces tracer clustering, that is, the exponential growth of tracer density in patches with vanishing areas. The statistical topography methodology, which provides integral characteristics to quantify the emerging clusters, uncovers drastic dependence of the clustering rates on whether the mesoscale flow component is taken to be steady or time-dependent. The former situation favours robust exponential clustering, similar to the theoretically understood case of purely divergent and zero-mean random velocity. The latter situation, on the contrary, hinders exponential clustering due to significant advection of the tracer out of the nearly enclosed eddies, at the rate faster than the clustering rate.

中文翻译：

---

不稳定中尺度海洋场调制的发散随机流中的浮动示踪剂聚类

摘要分析了漂浮在海洋表面并由于由确定性中尺度分量和运动学随机分量组成的组合速度场而演化的示踪剂的聚类。随机分量代表亚尺度运动的影响。应用随机速度场中的指数聚类理论来表征稳定和不稳定的随时间变化的中尺度流中获得的聚类场景，如日本/东海的综合现实、涡旋分辨一般环流模型所模拟的那样。中尺度流场充斥着瞬态涡流模式，调制和分支主流，而潜在的时间平均流分量具有封闭的再循环区，可以捕获示踪剂。亚尺度流动分量以运动学方式建模，作为具有指定相关半径和方差的发散随机速度场。组合流引起示踪剂聚类，即具有消失区域的斑块中示踪剂密度的指数增长。统计地形方法提供了量化新兴集群的整体特征，揭示了集群率对中尺度流分量是稳定的还是时间依赖的严重依赖。前一种情况有利于稳健的指数聚类，类似于理论上理解的纯发散和零均值随机速度的情况。相反，后一种情况会阻碍指数聚类，因为示踪剂从几乎封闭的涡流中以比聚类速度更快的速度明显平流。