2018 EGU ABSTRACT

Two particle stochastic diffusion tracking
model and the anomalous diffusion

A probabilistic description of suspended
sediment transport:

advection, diffusion and random movement

Movements of suspended sediment particles is regarded as a
stochastic process due to the highly uncertain behaviors under the influence of
the flow velocity and the turbulent effect in the open channel flow. In the
study, a-state-of-the-art two particle stochastic diffusion particle tracking
model (two-particle SD-PTM) is proposed. Modified from the stochastic diffusion
particle tracking model (SD-PTM), two-particle SD-PTM takes the particle
correlation into consideration while modeling the random behaviors of the
suspended sediment particles. Affected by the large eddy turbulence, the two
particles (paired particles) have similar motion when they are in the vicinity
of each other. On the other hand, paired particles move independently when they
are far away from each other. The proposed two particle SD-PTM model are
validated against experimental concentration data.

In the study, suspended sediment particles transport is hypothesized
to possess Markovian property and follows the Fickian law. While the Markovian property
is validated and showing that the movements of suspended sediment transport is memoryless,
the Fickian hypothesis is rejected by the observed anomalous diffusions based
on the simulation results of ensemble variances of particle displacements. In
the streamwise direction, suspended particle motions change from normal
diffusion to superdiffusion. Transitions from minor superdiffusion to
subdiffusion of particle motions are discovered in the vertical direction. The deposition and resusprnsion of particle motions are the main results of the anomalous diffusions. Influence of C isshown in comparisons of one-particle SD-PTM and two-particle SD-PTM.

The anomalous diffusions can be attributed to resuspension and
deposition of particle movements. Correlations between particle motions are
also discussed in this study.

2017英翻中

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本研究的主要目的是描述地表水中泥沙顆粒的隨機運動，以及在常規和極端水流條件下，預測及量化泥沙濃度和傳輸率的變化及其不確定性。本研究受獲諾貝爾經濟學獎的經濟理論啟發，運用其創新的思想於河流水力學領域，能夠更好的描述在極端事件中，觀察到的隨機粒子跳躍擴散過程。其行為類似於在股票市場中，因為好消息或壞消息導致股票價值突然而且巨大的變化。我們假設自然地表水流中，在極端事件所造成流量突然變化的情況下，泥沙顆粒的行為會遵循能夠描述跳躍的連續時間的隨機過程(continuous-time stochastic process with jumps)。

此外，我們還提出了一個分析系統不確定性和風險評估的工具，來量化正常和極端流況下的沉積風險(risk of sedimentation)。

泥沙顆粒在水中的行為不僅遵循平均漂移流動的方向，而且也因為周圍紊流的關係，會產生擴散的現象。從這個觀點來看，在我們的研究中，粒子運動是一個隨機過程。由Langevin方程導出的隨機擴散粒子追踪模型（SD-PTM），其建立在隨機微分方程（SDE）上，強調了力學機制，能夠根據隨機方法和物理機制，模擬粒子軌跡隨機的特性。

在本研究中，提出了三項研究假設：

1.      在明渠流中，泥沙顆粒傳輸是無記憶的隨機過程（即具備馬爾可夫屬性）。

2.      粒子運動行為不一定遵循菲克定律（即粒子可能會異常擴散）。

3.      紊流對泥沙粒子運動的影響，可以在不同的空間和時間尺度上解釋。另外，氣候變遷對顆粒物運輸的影響，也可能是影響因素的一部分。

本研究提出了不同層次的隨機擴散粒子追蹤模型(SD-PTMs)，它們考慮了氣候變遷、不同時空尺度下的紊流，以及粒子相互作用/相關性對粒子運動行為的影響。本研究期望能夠利用系綜統計，更深入地以機率描述顆粒運動行為。而本研究所提出的模型，其結果將以系綜平均速度和泥沙濃度與實驗數據進行驗證。

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The primary goals of this research are to characterize the stochastic movement of sediment particles in surface water and to scientifically quantify the variation and uncertainty of flow and sediment concentration and transport rate predictions in both regular and extreme flow conditions. 

本研究的主要目的是描述地表水中泥沙顆粒的隨機運動。同時在常規和極端水流條件下, 預測及量化泥沙濃度和傳輸率的變化以及其不確定性。

The proposed work focuses on examining the applicability of an innovative idea inspired by a Nobel Prize winning economic theory to the field of fluvial hydraulics to better describe the stochastic particle jump diffusion process often observed in extreme events.

本研究受諾貝爾經濟學獎的經濟理論啟發，運用其創新的思想在河流水力學領域，能夠更好的描述在極端事件中，觀察到的隨機粒子跳躍擴散過程。

In analogy to large sudden changes in market value of stocks due to significant good or bad news, 
we hypothesize that the behavior of sediment particles in natural surface flows follows a continuous-time stochastic process with jumps in situations where it allows for abrupt discharges resulting from an extreme flow event such as flooding. 

其行為類似於在股票市場中，因為好消息或壞消息導致股票市場價值突然而且巨大的變化。我們假設自然地表水流中，在極端事件所造成流量突然變化的情況下，泥沙顆粒的行為會遵循能夠描述跳躍的連續時間的隨機過程(continuous-time stochastic process with jumps)。

Furthermore, a systematic uncertainty analysis and risk assessment tool is proposed to quantify the risk of sedimentation in both regular and extreme flows.

此外，我們還提出了一個分析系統不確定性和風險評估的工具，來量化正常和極端流況下的沉積風險(risk of sedimentation)。

A sediment particle in a flow is assumed to not only follow the mean drift flow direction, but also diffuse through the surrounding water due to turbulence. From this perspective, particle movement is regarded as a stochastic process in our study. 

泥沙顆粒在水中的行為不僅遵循平均漂移流動的方向，而且也因為周圍紊流的關係，會產生擴散的現象。從這個觀點來看，在我們的研究中，粒子運動是一個隨機過程。

Derived from the Langevin equation, the stochastic diffusion particle tracking model (SD-PTM) is able to simulate the random characteristics of particle trajectories based on stochastic methodologies and physical mechanisms, underscoring mechanics in the stochastic differential equations (SDEs). 

由Langevin方程導出的隨機擴散粒子追踪模型（SD-PTM），其建立在隨機微分方程（SDEs）上，強調了力學機制，能夠根據隨機方法和物理機制，模擬粒子軌蹟隨機的特性。

In the study, three research hypothesizes are proposed. 

在這項研究中，提出了三項研究假設。

(1)     Sediment particles transport in open channel flow is a memoryless stochastic process (i.e., Markovian property).  

在明渠流中，泥沙顆粒傳輸是無記憶的隨機過程（即具備馬爾可夫屬性）。

(2)     Particles may not necessarily follow the Fickian law (i.e., anomalous diffusion).

粒子可能不一定遵循菲克定律（即粒子可能會異常擴散）。

(3)     Impacts from turbulence on particle movement can be account for at various spatial and temporal scales.

 In addition, the impact of climate change on particle transport may be included as part of the contributing factors.

紊流對泥沙粒子運動的影響，可以在不同的空間和時間尺度上解釋。 另外，氣候變遷對顆粒物運輸的影響，也可能是影響因素的一部分。

This study proposed various levels of SD-PTMs, which take the impact of climate change, turbulences of different temporal and spatial scales, and the particle interaction/correlation into consideration.

本研究提出了不同層次的隨機擴散粒子追蹤模型(SD-PTMs)，它們考慮了氣候變遷、不同時空尺度的紊流，以及粒子相互作用/相關性對粒子運動行為的影響。

 A more in-depth probabilistic description of ensemble statistics of particle movement is expected to be acquired in this study. The proposed models will be validated against experimental data by ensemble mean velocity and sediment concentrations. 本研究期望能夠利用系綜統計，更深入得以機率描述顆粒運動行為。本研究所提出的模型，使用系綜平均速度和泥沙濃度與實驗數據進行驗證。