基于单颗粒受力的均匀推移质颗粒对流和扩散特征

Advection and diffusion characteristics for uniform bed load particles from a semi-mechanistic model accounting for forces exerted on individual particles

为揭示均匀推移质颗粒对流和扩散特性的控制因素,建立了间歇郎之万方程模型。该模型可在单颗粒尺度充分考虑颗粒的受力特性,模拟颗粒随机、间歇运动过程。通过该模型引入不同的停时分布,对模拟的大量单颗粒运动过程进行统计,从而研究均匀颗粒在大的时空尺度上的对流和扩散特征。结果表明,对于均匀颗粒,受颗粒速度分布的窄尾性限制,即便单步步长是长尾分布,也不一定产生超扩散,扩散特性由停时分布的尾部特征决定,不同分布的停时可导致欠扩散、超扩散和正常扩散。进一步与已有的、复杂程度不同的随机模型进行对比,表明忽略单步时间将影响颗粒的扩散(二阶)特性,但不影响颗粒的对流(一阶)特性,类似地可以推广到更普遍规律,即所研究随机发生的统计矩阶数越高,需要的模型越复杂。

An episodic Langevin equation,which could account for forces exerted on individual particles and simulate stochastic and episodic motion characteristics of particles,is developed in order to reveal the control factor of normal or anomalous advection and diffusion characteristics for uniform particles. Using a model embedded with different distributed resting times,we study advection and diffusion characteristics by analyzing the statistical data of a large number of simulated particle trajectories. The results reveal that for uniform particles,because of the constraint of thintailed velocities of active particles,super-diffusion does not necessarily occur,even if their step lengths are heavy tailed. Diffusion characteristics are determined by the tail of resting times; for heavy-tailed resting times,sub-,normal,and super diffusion could all occur. The proposed semi-mechanistic model is further compared with other stochastic models,and the step time is ignored as it could result in right advection but wrong diffusion characteristics,which could be generalized for studying stochastic variables,i. e.,the higher the moment of the studied stochastic variables,the more complex the model.