论文标题
基于少数轨迹的客观流量测量
Objective Flow Measures Based on Few Trajectories
论文作者
论文摘要
稀疏的轨迹数据由较少数量的轨迹组成，因此无法重建基础速度场。最近，已经引入了仅基于单个轨迹的流动行为的方法：轨迹拉伸指数（TSE）检测双曲线（拉伸）行为和轨迹角速度（TRA）以检测椭圆形（旋转）行为。在本文中，我们分析了这些方法，尤其表明它们与文献中所主张的相反 - 在扩展相空间中不是客观的。此外，我们介绍了仅基于少数轨迹的旋转行为的第一个客观度量：至少3分，而至少4分为3D。对于此度量，称为轨迹涡度（TRV） - 我们表明它是客观的，可以通过两种独立的方式引入：通过不稳定的方法，并考虑相对旋转张量。我们将TRV应用于许多构建和真实的轨迹数据集，包括在大西洋中漂流浮标，Midge Swarm跟踪数据和模拟涡流街。
Sparse trajectory data consist of a low number of trajectories such that the reconstruction of an underlying velocity field is not possible. Recently, approaches have been introduced to analyze flow behavior based on a single trajectory only: trajectory stretching exponent (TSE) to detect hyperbolic (stretching) behavior, and trajectory angular velocity (TRA) to detect elliptic (rotation) behavior. In this paper, we analyze these approaches and in particular show that they are -- contrary to what is claimed in the literature -- not objective in the extended phase space. Furthermore, we introduce the first objective measure of rotation behavior that is based on only few trajectories: at least 3 in 2D, and at least 4 in 3D. For this measure -- called trajectory vorticity (TRV) -- we show that it is objective and that it can be introduced in two independent ways: by approaches for unsteadiness minimization and by considering the relative spin tensor. We apply TRV to a number of constructed and real trajectory data sets, including drifting buoys in the Atlantic, midge swarm tracking data, and a simulated vortex street.
