拉格朗日速度演化的连续时间随机游动
Continuous Time Random Walks for the Evolution of Lagrangian Velocities
摘要：
基于流向质点速度的随机松弛过程，提出了一种求解定常非均质流中拉格朗日速度演化的连续时间随机游走（CTRW）方法。这种方法描述了在一个特征空间尺度上的速度的持久性，不像经典的随机游走方法，其模型在一个特征时间尺度上的持久性。我们首先建立欧拉和拉格朗日速度之间的关系，沿流线等距和等时线采样，在瞬态和稳态条件下。在此基础上，我们开发了一个空间连续的CTRW方法的拉格朗日速度的时空动力学。虽然经典的CTRW配方具有非平稳的拉格朗日速度统计，所提出的方法量化的拉格朗日速度统计的演变在平稳和非平稳条件下。我们提供了显式表达式的拉格朗日速度统计，并确定的平均粒子速度，速度协方差和粒子色散的行为。我们发现强烈的拉格朗日相关性和异常色散的速度分布，这是尾部向低速度以及显着的差异取决于初始条件。开发的CTRW方法预测拉格朗日粒子动力学从任意初始条件的基础上的欧拉速度分布和特征相关尺度。
英文摘要：
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of the mean particle velocity, velocity covariance and particle dispersion. We find strong Lagrangian correlation and anomalous dispersion for velocity distributions which are tailed toward low velocities as well as marked differences depending on the initial conditions. The developed CTRW approach predicts the Lagrangian particle dynamics from an arbitrary initial condition based on the Eulerian velocity distribution and a characteristic correlation scale.
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