三维湍流风沙运动的大涡模拟及沙漠地貌的数值模拟
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摘要
本文采用大涡模拟方法和小球运动方程及内置边界条件等方法，进行了三维湍流风沙跃移运动和三维沙波纹演化过程的数值模拟，主要研究工作和结果如下：
我们研制的三维拟谱法与内置边界方法和风沙运动模型相结合的大涡模拟算法和程序适合于模拟三维风沙跃移运动和三维沙波纹的形成。通过对单颗沙粒的跃移轨迹和单宽输沙率的数值模拟，验证了程序的可靠性。
在研究单颗沙粒的跃移运动中，使用单向模型对单颗沙粒在不同受力情况下的运动轨迹进行分析后，发现重力和空气阻力是沙粒所受到的最重要的两个作用力。此外，静电力对沙粒运动轨迹的影响要明显大于空气升力，Magnus力的影响主要由沙粒角速度决定，当角速度很小时，其影响可以忽略，当角速度很大时，其影响非常显著。并且对单向和双向模型得到的单颗沙粒跃移轨迹进行比较后，发现在双向耦合模型情况下沙粒跃移的距离近一些，这是由于沙粒对风有了阻碍作用。
在沙粒群体跃移运动中，静电力对沙粒的平均速度以及风沙流结构都有明显影响，空气升力则影响微小；沙粒沿Y轴的运动速度不易受到Z轴方向受力的影响，即使这个力很大。计算得到风沙流结构分为三层：线性增加层；饱和层；当高度超过饱和层时，输沙量很快下降的下降层。这与实验结果一致。并且静电力对饱和层的高度有明显影响。
在湍流风沙跃移运动和蠕移运动的共同作用下得到三维沙波纹的演化过程，最终收敛的沙波纹迎风坡平缓，背风坡陡峭，这与自然形成的沙波纹的形态是一致的。在数值模拟中还再现了三维沙波纹的自我修复过程，这从另一个方面说明了我们的数值模拟方法和所采用的跃移、蠕移模型等是合理的，可以反映沙波纹演化过程中的典型自组织特征。分析了沙波纹对三维湍流风场的影响，发现沙波纹地形的出现和发展使得湍流风场在法向有着更强烈的能量交换，揭示了湍流起沙的机理。沙波纹与地表湍流脉动涡量间有着明显的对应关系，这有助于我们解释沙波纹的形成机理。
In this thesis, numerical simulation of three dimensional turbulent aeolian motion and the formation of sand ripples under three dimensional turbulent wind are carried out. The main work and resuls are as follows:
A large-eddy simulation program for three dimensional aeolian motion and sand ripples under three dimensional turbulent wind is obtained, which combines the three dimensional pseudo-spectrum method and the method of immersed boundary and models of three dimensional aeolian motion. The reliability and verification of the code is vertified with the trajectory of single particle and the sand flux per width with others numerical and experimental results.
In the motion of single particle, we analyze the trajectories in one-way model when different force act on single particle, and discuss the influence of each force on trajectories of particle, the results show that gravity and aerodynamic drag are the most important forces, electrostatic force play a more important role than lift force. The influence of Magnus force is determined by the angular speed of particle, therefore when the angular speed is small, the influence can be neglected. Because the partcles obstructs the wind, so that the saltation length of single particle obtained by the one-way model is slightly larger than that of by the tow-way model.
In the motion of large amount of sand particles, electrostatic force plays a more important role than lift force in the average velocity of particles and the structure of aeolian motion. The average velocity of particles in Y direction is hardly affected by the force in Z direction, even this force is quite large. Furthermore, we find the aeolian sand flow is divided into three layers: linearly increasing layer, saturation layer and decrease layer, according to the amount of transportation of sands, which is agreed with experimental results.
The evolution process of three dimensional sand ripples is obtained, with the models of saltation and creep, the resulting form of sand ripples has the feature of sand ripplrs in the nature, i.e., the slope of lee side is steeper than the slope of up-wind side. Furthermore,
我们研制的三维拟谱法与内置边界方法和风沙运动模型相结合的大涡模拟算法和程序适合于模拟三维风沙跃移运动和三维沙波纹的形成。通过对单颗沙粒的跃移轨迹和单宽输沙率的数值模拟，验证了程序的可靠性。
在研究单颗沙粒的跃移运动中，使用单向模型对单颗沙粒在不同受力情况下的运动轨迹进行分析后，发现重力和空气阻力是沙粒所受到的最重要的两个作用力。此外，静电力对沙粒运动轨迹的影响要明显大于空气升力，Magnus力的影响主要由沙粒角速度决定，当角速度很小时，其影响可以忽略，当角速度很大时，其影响非常显著。并且对单向和双向模型得到的单颗沙粒跃移轨迹进行比较后，发现在双向耦合模型情况下沙粒跃移的距离近一些，这是由于沙粒对风有了阻碍作用。
在沙粒群体跃移运动中，静电力对沙粒的平均速度以及风沙流结构都有明显影响，空气升力则影响微小；沙粒沿Y轴的运动速度不易受到Z轴方向受力的影响，即使这个力很大。计算得到风沙流结构分为三层：线性增加层；饱和层；当高度超过饱和层时，输沙量很快下降的下降层。这与实验结果一致。并且静电力对饱和层的高度有明显影响。
在湍流风沙跃移运动和蠕移运动的共同作用下得到三维沙波纹的演化过程，最终收敛的沙波纹迎风坡平缓，背风坡陡峭，这与自然形成的沙波纹的形态是一致的。在数值模拟中还再现了三维沙波纹的自我修复过程，这从另一个方面说明了我们的数值模拟方法和所采用的跃移、蠕移模型等是合理的，可以反映沙波纹演化过程中的典型自组织特征。分析了沙波纹对三维湍流风场的影响，发现沙波纹地形的出现和发展使得湍流风场在法向有着更强烈的能量交换，揭示了湍流起沙的机理。沙波纹与地表湍流脉动涡量间有着明显的对应关系，这有助于我们解释沙波纹的形成机理。
In this thesis, numerical simulation of three dimensional turbulent aeolian motion and the formation of sand ripples under three dimensional turbulent wind are carried out. The main work and resuls are as follows:
A large-eddy simulation program for three dimensional aeolian motion and sand ripples under three dimensional turbulent wind is obtained, which combines the three dimensional pseudo-spectrum method and the method of immersed boundary and models of three dimensional aeolian motion. The reliability and verification of the code is vertified with the trajectory of single particle and the sand flux per width with others numerical and experimental results.
In the motion of single particle, we analyze the trajectories in one-way model when different force act on single particle, and discuss the influence of each force on trajectories of particle, the results show that gravity and aerodynamic drag are the most important forces, electrostatic force play a more important role than lift force. The influence of Magnus force is determined by the angular speed of particle, therefore when the angular speed is small, the influence can be neglected. Because the partcles obstructs the wind, so that the saltation length of single particle obtained by the one-way model is slightly larger than that of by the tow-way model.
In the motion of large amount of sand particles, electrostatic force plays a more important role than lift force in the average velocity of particles and the structure of aeolian motion. The average velocity of particles in Y direction is hardly affected by the force in Z direction, even this force is quite large. Furthermore, we find the aeolian sand flow is divided into three layers: linearly increasing layer, saturation layer and decrease layer, according to the amount of transportation of sands, which is agreed with experimental results.
The evolution process of three dimensional sand ripples is obtained, with the models of saltation and creep, the resulting form of sand ripples has the feature of sand ripplrs in the nature, i.e., the slope of lee side is steeper than the slope of up-wind side. Furthermore,
引文
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