SIAM Review, Volume 62, Issue 4, Page 781-816, January 2020.
Uncertainties in velocity data are often ignored when computing Lagrangian particle trajectories of fluids. Modeling these as noise in the velocity field leads to a random deviation from each trajectory. This deviation is examined within the context of small (multiplicative) stochasticity applying to a two-dimensional unsteady flow operating over a finite time. These assumptions are motivated precisely by standard availability expectations of realistic velocity data. Explicit expressions for the deviation's expected size and anisotropy are obtained using an Itô calculus approach, thereby characterizing the uncertainty in the Lagrangian trajectory's final location with respect to lengthscale and direction. These provide a practical methodology for ascribing spatially nonuniform uncertainties to predictions of flows, and also provide new tools for extracting fluid regions that remain robust under velocity fluctuations.

中文翻译：

---

随机敏感性：用于非恒定流的可计算拉格朗日不确定性测度

SIAM评论，第62卷，第4期，第781-816页，2020年1月。
在计算流体的拉格朗日粒子轨迹时，通常会忽略速度数据的不确定性。将它们建模为速度场中的噪声会导致每个轨迹的随机偏差。在适用于在有限时间内运行的二维非定常流动的小（乘性）随机性的背景下检查此偏差。这些假设正是由实际速度数据的标准可用性期望所激发的。使用Itô演算方法可获得偏差的预期大小和各向异性的明确表达式，从而表征拉格朗日轨迹最终位置相对于长度尺度和方向的不确定性。这些为将空间非均匀性不确定性归因于流量预测提供了一种实用的方法，