Vortical Structure of Turbulent Shear Flows Studied by Vortex Dynamics Simulation

1.用涡团方法模拟了圆角正方形涡环的演化过程，得到了三维无粘涡运动的动力学不变量真正守恒的变形规律。模拟表明，不变量是守恒的，直到它们发生灾难性的增加。发现动能是讨论不变量守恒性最严格的判据。出现灾变行为的时间随着涡团中心半径的增大和转角曲率半径的增大而增大。得到并讨论了涡环的拓扑演化过程。摘要对长短轴比为b…的两条平行直线段由两个相同半径的半圆连接而成的拟椭圆涡环的变形进行了涡动力学模拟。根据高宽比的不同，变形有四种基本模式：周期轴切换；轴切换后分裂成两个涡环；分裂成两个涡环而不切换轴；分裂成三个涡环而不切换轴。最后两种模式预计将导致进一步的轴线切换，并最终在较短的时间内分裂成两个涡环。流动可视化实验证实了这一点。对多个圆形涡环的相互作用进行了无粘涡动力学模拟，得到了部分符合Kolmogorov-5/3幂定律的功率谱。在相同的波数范围内，拟能谱相当于均匀湍流中的耗散谱，具有部分1/3幂定律。这项研究是第一批显示-5/3功率谱的研究之一，这是由于几个而不是许多涡环的无粘性相互作用的结果。-5/3幂定律的波数范围与涡环的个数和初始构型有一定的关系，涡环中心半径越小，波数范围越宽。高涡度区域的均匀分布似乎是具有-5/3幂定律的必要条件。无粘涡运动的五个不变量，即总能量、总动量、总角动量、总螺旋度和总涡度，在与相应初始阀的偏差允许范围内保持不变，直到涡度趋于发散。采用涡团方法对倾斜圆盘周围的非定常分离流动进行了数值模拟，得到了从圆盘边缘分离形成的圆形涡环的三维旋涡结构演变。数值模拟结果表明，在垂直于来流方向的平面内，涡量等值线为旋涡尾迹的螺旋结构。较少

1. Evolution of square vortex rings with rounded corners was simulated by a vortex blob method, in which the connectivity of vortex filaments is not explicitly maintained, to obtain patterns of deformation and the exetnt to which dynamical invariants of the three-dimensional inviscid vortex motion are really conserved. The simulation showed that the invariants were conserved until their catastrophic increase took place. The kinetic energy was found to serve as the most stringent criterion to discuss the conservation of the invariants. The time when the catastrophic bahavior appeared increased with increasing radius of core of the vortex blobs and with increasing radius of curvature of the corners. Evolution of topology of the vortex rings was obtained and discussed.2. A vortex dynamics simulation was made on the deformation of pseudoelliptical vortex rings which consists of two parallel line segments connected by two semicircles of the same radius, the major-to-minor axis ratio being b … More etween 2 and 20. The deformation had four fundamental patterns depending on the aspect ratio : the periodic axis switching ; the splitting into two vortex rings after the axix switching ; the splitting into two vortex rings without the axis switching ; the splitting into three vortex rings without the axis switching. The last two patterns are expected to lead to further axis switching and eventual splitting into two vortex rings at larer times. This was confirmed by a flow visualization experiment.3. An inviscid vortex dynamics simulation of interaction of several circular vortex rings produced the power spectrum which had a part of the Kolmogorov -5/3 power law. The enstrophy spectrum, which is equivalent to the dissipation spectrum in homogeneous turbulence, had a part of the 1/3 power law in the same wavenumber range. This study is among the first to show the -5/3 power spectrum as a result of the inviscid interaction of several, not many, vortex rings. The wavenumber range of the -5/3 power law slightly depends on the number of the vortex rings and their initial configuration, being wider for smaller radius of core of the vortex rings. A uniform distribution of high-vorticity regions appears to be essential to have the -5/3 power law. Five invariants of the inviscid vortical motion, i. e. The total energy, total momentum, total angular momentum, total helicity and total vorticity were maintained constant within tolerable deviations from the corresponding initial valves until vorticity tends to diverge.4. The unsteady separated flow around an inclined circular disk was simulated by the vortex blob method to obtain the evolution of three-dimensional vortical structures from circular vortex rings formed by the separation from the edge of the disk. A spiral structure of the vortical wake was confirmed by the simulation in terms of the vorticity contour in planes normal to the direction of the approaching flow. Less