從單顆粒受力到群體運動特征的推移質研究
發(fā)布時間：2018-12-15 08:11
【摘要】：推移質運動的隨機性一直是泥沙研究的難點和熱點，這種運動的隨機性歸根結底是由顆粒受力的不確定性導致的。顆粒受力的不確定性使得在中小尺度上，顆粒運動與否，運動的速度、單步步長、單步時間和停時等特征均具有隨機性，而中小尺度上這些變量的隨機性導致了顆粒群體在大的時空尺度上的擴散。 本文主要針對顆粒以滾動和滑動為主要運動形式的推移質運動。通過統(tǒng)計力學的方法，從單顆粒受力出發(fā)，將顆粒受力分解為確定性部分和隨機部分，從而建立了描述單顆粒動力學的郎之萬方程，并由此推導得到了描述顆粒速度概率密度函數（Probability density function, PDF）的�？恕绽士朔匠蹋瑥亩鴮晤w粒受力與顆粒群體速度的統(tǒng)計特征結合了起來。在此基礎上，將停時引入到郎之萬方程中，模擬了大量顆粒間歇性的運動過程，探討了顆粒群體在大的時空尺度上體現的對流和擴散特征。并分析了沙質床面和卵石夾沙床面的動態(tài)演化特征。 福克—普朗克方程的定態(tài)解析解給出的速度PDF與實驗資料符合較好，均表現出類指數分布（正向速度與負向速度的PDF均按指數衰減），該解從理論上解釋了這種類指數分布是由單顆粒受力引起的，即庫倫摩擦力和隨機力導致了這種類指數分布，而沿水流方向的確定性的時均力使得分布產生了偏態(tài)。 通過郎之萬方程直接模擬單顆粒速度序列，提取單步運動過程，得到了單步步長和單步時間的關系，與實驗資料符合較好，均表現出單步步長與單步時間的5/3冪律關系，體現了單步步長和單步時間是相關聯的。 郎之萬方程雖然較準確地描述了運動顆粒的動力學特性，但難以描述顆粒靜止時的受力狀態(tài)，導致這種困難的主要原因是摩擦力在速度為0時的多值性。因此，在速度為0時引入不同分布的停時，模擬了顆粒在大的時空尺度上的正常/奇異對流和擴散特征。結果表明，對于均勻顆粒，由于顆粒速度是窄尾分布，即便單步步長是長尾分布，，也不一定產生超擴散，擴散特性由停時分布的尾部特征決定，不同分布的停時可導致欠擴散、超擴散和正常擴散。忽略單步時間不影響顆粒的對流特性，但影響顆粒的擴散特性。對于非均勻顆粒群體，因為不再滿足隨機變量的同分布假定，因此由顆粒非均勻性產生的長尾分布將導致與均勻顆粒的長尾分布完全不同的對流和擴散特征，在大的時空尺度上，非均勻顆粒群體總是出現彈道運動，這對應的不是奇異擴散，而是確定性的沿程分選過程。
[Abstract]:The randomness of bed load motion is always a difficult point and hot spot in sediment research. The randomness of this motion is caused by the uncertainty of particle force in the final analysis. The uncertainty of particle force makes the characteristics of particle motion, velocity, single step length, single step time and stop time are all random in small and medium scale, such as moving or not, moving speed, single step length, single step time and stopping time, etc. The randomness of these variables leads to the diffusion of the particle population on the large scale of time and space. This paper focuses on the bedload motion in which rolling and sliding are the main motion forms of particles. By means of statistical mechanics, starting from the single particle force, the particle force is decomposed into deterministic part and random part, and the Langzhiwan equation describing the dynamics of single particle is established. The Fokk-Planck equation describing the probability density function of particle velocity (Probability density function, PDF) is derived, and the statistical characteristics of single particle force and particle population velocity are combined. On this basis, the stopping time is introduced into the Langzhiwan equation, the intermittent motion process of a large number of particles is simulated, and the convection and diffusion characteristics of the particle population on a large space-time scale are discussed. The dynamic evolution characteristics of sand bed and gravel bed are analyzed. The steady state analytical solution of Fokk-Planck equation shows that the velocity PDF is in good agreement with the experimental data, and both show exponential distribution (the PDF of forward velocity and negative velocity decay exponentially). The solution theoretically explains that this kind of exponential distribution is caused by a single particle force, that is, Coulomb friction and random force lead to this kind of exponential distribution, and the deterministic time-averaged force along the direction of water flow causes the distribution to be skewed. By directly simulating single particle velocity series by Lang Zhiwan equation, the single step motion process is extracted, and the relationship between single step length and single step time is obtained, which is in good agreement with experimental data, and shows the 5 / 3 power law relation between single step length and single step time. It shows that the single step length and the single step time are related. Although the Langzhiwan equation accurately describes the dynamic characteristics of moving particles, it is difficult to describe the mechanical state of particles when they are still. The main reason for this difficulty is the multivalue of friction force when the velocity is zero. Therefore, the normal / singular convection and diffusion characteristics of particles on a large space-time scale are simulated when different distributions are introduced when the velocity is zero. The results show that, for homogeneous particles, the velocity of particles is narrow tail distribution, even if the single step size is long tail distribution, it is not necessarily superdiffusion. The diffusion characteristics are determined by the tail characteristics of the stopping time distribution, and the stop time of different distributions can lead to underdiffusion. Superdiffusion and normal diffusion. Ignoring the single step time does not affect the convection characteristics of the particles, but affects the diffusion characteristics of the particles. For the heterogeneous particle population, because the assumption of the same distribution of random variables is no longer satisfied, the long tail distribution generated by the particle heterogeneity will lead to convection and diffusion characteristics completely different from the long tail distribution of uniform particles. In large space-time scale, there is always ballistic motion in non-uniform particle population, which corresponds to not singular diffusion, but deterministic separation along the path.
【學位授予單位】：清華大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TV142.2
本文編號：2380315
[Abstract]:The randomness of bed load motion is always a difficult point and hot spot in sediment research. The randomness of this motion is caused by the uncertainty of particle force in the final analysis. The uncertainty of particle force makes the characteristics of particle motion, velocity, single step length, single step time and stop time are all random in small and medium scale, such as moving or not, moving speed, single step length, single step time and stopping time, etc. The randomness of these variables leads to the diffusion of the particle population on the large scale of time and space. This paper focuses on the bedload motion in which rolling and sliding are the main motion forms of particles. By means of statistical mechanics, starting from the single particle force, the particle force is decomposed into deterministic part and random part, and the Langzhiwan equation describing the dynamics of single particle is established. The Fokk-Planck equation describing the probability density function of particle velocity (Probability density function, PDF) is derived, and the statistical characteristics of single particle force and particle population velocity are combined. On this basis, the stopping time is introduced into the Langzhiwan equation, the intermittent motion process of a large number of particles is simulated, and the convection and diffusion characteristics of the particle population on a large space-time scale are discussed. The dynamic evolution characteristics of sand bed and gravel bed are analyzed. The steady state analytical solution of Fokk-Planck equation shows that the velocity PDF is in good agreement with the experimental data, and both show exponential distribution (the PDF of forward velocity and negative velocity decay exponentially). The solution theoretically explains that this kind of exponential distribution is caused by a single particle force, that is, Coulomb friction and random force lead to this kind of exponential distribution, and the deterministic time-averaged force along the direction of water flow causes the distribution to be skewed. By directly simulating single particle velocity series by Lang Zhiwan equation, the single step motion process is extracted, and the relationship between single step length and single step time is obtained, which is in good agreement with experimental data, and shows the 5 / 3 power law relation between single step length and single step time. It shows that the single step length and the single step time are related. Although the Langzhiwan equation accurately describes the dynamic characteristics of moving particles, it is difficult to describe the mechanical state of particles when they are still. The main reason for this difficulty is the multivalue of friction force when the velocity is zero. Therefore, the normal / singular convection and diffusion characteristics of particles on a large space-time scale are simulated when different distributions are introduced when the velocity is zero. The results show that, for homogeneous particles, the velocity of particles is narrow tail distribution, even if the single step size is long tail distribution, it is not necessarily superdiffusion. The diffusion characteristics are determined by the tail characteristics of the stopping time distribution, and the stop time of different distributions can lead to underdiffusion. Superdiffusion and normal diffusion. Ignoring the single step time does not affect the convection characteristics of the particles, but affects the diffusion characteristics of the particles. For the heterogeneous particle population, because the assumption of the same distribution of random variables is no longer satisfied, the long tail distribution generated by the particle heterogeneity will lead to convection and diffusion characteristics completely different from the long tail distribution of uniform particles. In large space-time scale, there is always ballistic motion in non-uniform particle population, which corresponds to not singular diffusion, but deterministic separation along the path.
【學位授予單位】：清華大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TV142.2
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