懸浮載傳輸中的記憶效應:序率泥砂力學分析架構發展芻議

Incorporating the particle memory effect under the impact of turbulence structures into suspended sediment transport analysis: Toward a novel random walk model

10.6342/NTU201803968

黃世勳

懸浮載運輸 ； 紊流擴散 ； 隨機漫步理論 ； 記憶效應 ； 紊流的時間尺度 ； suspended sediment transport ； turbulent diffusion ； random walk theory ； memory effect ； temporal scale of turbulence motion

臺灣大學土木工程學研究所學位論文

2018年

碩士

蔡宛珊

英文

在地貌發育過程模擬、水庫壽命評估等分析領域裡，明渠流中的懸浮載運輸都佔有一席之地。一般水利應用將其視為擴散現象，並使用移流擴散方程式(the advection-diffusion equation)進行模擬。移流擴散方程式能良好的表現平均泥沙濃度剖面，但其中最重要的參數——擴散係數(the diffusion coefficient)——往往需要藉由參數率定來取得。率定過程和泥沙顆粒在渠道中的移動無關，也不涉及紊流的流況，使得工程師在模擬懸浮載運輸時難以隨物理機制變化而調整擴散係數。 以隨機漫步理論(random walk theory)為基礎的隨機擴散粒子追蹤模型(the Stochastic Diffusion Particle Tracking Model)描繪擴散現象中粒子的移動路徑，為研究擴散係數和泥沙顆粒運動之間的關係開啟一扇大門。然而此一模型仍舊以移流擴散方程式為基礎。泥沙整體的擴散程度依循擴散係數的大小改變，模擬中泥沙顆粒移動速度的統計特性卻並不一定符合實際的物理現象。 本研究提出二隨機過程，逐步揭示單一懸浮泥沙顆粒的運動和整體懸浮載擴散之間的關係。第一部分將跳躍過程(the jump process)加入原先的維納過程(the Weiner process)，模擬近底床流體結構對於泥沙運輸的影響。模擬的結果顯現隨機漫步模型考量紊流時間尺度的必要性。第二部分則從由序率模型中記憶效應的角度切入，探討數學上隨機漫步模型考量紊流時間尺度時的擴散行為。最後，本研究建議將以此為基礎提出的隨機過程作為其後研究中模型發展的軸心。

In the conventional analysis, suspended sediment transport is regarded as an advection-diffusion process, called turbulent diffusion, which is driven mainly by turbulence. A fairly good estimate of long-term average sediment concentration can be obtained using the advection-diffusion equation. This governing equation is widely applied for the simulation of morphology development, assessment of reservoir lifespan and so on. In hydraulic engineering, the diffusion coefficient is typically calibrated against the data, but the calibration of the diffusion coefficient is not based on the movement of particles, so the estimation of this parameter is a “black box”. Random walk theory provides a way to simulate the probabilistic trajectory of sediment particles in turbulent diffusion; however, the provided sample path may not be consistent with other physical properties of interest, such as velocity fluctuations of the sediment particles because the currently random walk model is based on the advection-diffusion equation: The second statistical moment of particle displacement is proportional to time and the spreading rate depends on the diffusion coefficient. To fill the gap between simulated particle velocity and the real flow velocity, and to explain the linkage between single particle movement and evolution of sediment concentration, two random walk-based models are proposed in this study. At first, the jump process is introduced in the stochastic diffusion particle tracking model to delineate the influence of two flow structures, called ejection and sweep events, in the near wall region on suspended sediment transport. The results of simulation demonstrate that the temporal scale of flow structures plays an important role in carrying sediment particles in suspension. Then, the mathematical impact of including the temporal scale of turbulence coherent structures in the random walk-based model is discussed in terms of memory effect. A novel stochastic process is proposed to analyze the relationship between the probability properties of turbulence velocity and the spreading behavior of the fluid particles. Based on the proposed stochastic process, an improved random walk model of suspended sediment transport is suggested.

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