Small-Scale Structure of Turbulence

通过数值求解Navier-Stokes方程，研究了湍流的小尺度结构。为了节省计算时间和内存容量，对速度场施加了高度对称性。主要研究了以下五个主题。(1)湍流的小尺度结构我们实现了微尺度雷诺数200的充分发展的湍流<similar or equal>。证实了Kolmogorov相似性在能谱中成立。在惯性范围内的能谱的Kolmogorov幂律与Kolmogorov常数1.8观察。发现表征湍流间歇结构的速度导数和能量耗散率的概率密度分布具有与大尺度运动无关的普遍形式c（2）能量衰减律首次在数值模拟中定量证实了实验观察到的、湍流统计理论描述的能量幂律。(3)我们发现，当雷诺数增加时，由定常外力激励的速度场经历了以下一系列的转变：定常-&gt;单周期-&gt;双周期-&gt;三周期-&gt;混沌运动。(4)我们发现当雷诺数超过一个临界值时，会发生发电机效应，通过发电机效应，动能被转换成磁能。在统计平衡态下，动能谱和磁能谱服从幂律。(5)涡流管的再连接为了研究湍流理论中的重要物理量之一螺旋度的动力学性质，我们对打结涡流管进行了数值模拟。螺旋度在无粘极限下是守恒的。在涡旋重联过程中观察到一种新的现象，称为桥接现象。

The small-scale structure of turbulence was investigated by solving the Navier-Stokes equation numerically. The high-symmetry was imposed on the velocity field to save the computation time and the memory capacity. The following five subjects were mainly investigated.(1) Small-scale structure of turbulence We realized the fully developed turbulence with the micro-scale Reynolds number <similar or equal> 200. The Kolmogorov similarity was confirmed to hold in the energy spectrum. The Kolmogorov power law of the energy spectrum in the inertial range was observed with Kolmogorov constant 1.8. The probability density distribution of the velocity derivative and the energy dissipation rate, which characterize the intermittent structure of turbulence, were found to have nuiversal forms independent of the large-scale motive c(2) Energy decay law The power law of energy, which had been observed by experiments and preficted by statistical theories of turbulence, was confirmed quantitatively for the first time as numerical simulation.(3) Chaos in a Navier-Stokes flow We found that the velocity field which is excited by a steady external force undergoes the following series of transitions as the Reynolds number is increased: Steady -> simply periodic -> doubly periodic ->triply periodic -> chaotic motions.(4) MHD trubulence We found that the dynamo effect, by which the kinetic energy is converted into the magnetic energy, occurs when the Reynolds number exceeds a critical value. The kinetic and magnetic energy spectra obey power laws in the statistically equilibrium state.(5) Reconnection of vortex tubes In order to investigate the dynamics of thehelicity, which is one of the important quantities in the theory of turbulence we made a numerical simulation of a knotted vortex tube. The helicity was found to be conserved in the inviscid limit. A new phenomenon called BRIDGING was observed in the process of vortex reconnection.