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存储容量，对速度场施加了高度对称性。主要调查了以下五个主题。(1)湍流的小尺度结构我们实现了微尺度雷诺数<相似或等于bbb200的充分发展的湍流。在能谱中证实了柯尔莫哥洛夫相似性。在柯尔莫哥洛夫常数为1.8时，观测到惯性范围内能谱的柯尔莫哥洛夫幂律。速度导数和能量耗散率的概率密度分布具有与大尺度动机无关的普遍形式。(2)能量衰减规律。由实验观察到的、由湍流统计理论预测的能量幂定律，首次通过数值模拟得到了定量的证实。(3) Navier-Stokes流的混沌现象我们发现，受定常外力激励的速度场随着雷诺数的增加，经历了如下一系列的跃迁：定常->单周期->双周期->三周期->混沌运动。我们发现，当雷诺数超过某一临界值时，会发生将动能转化为磁能的发电机效应。动力学能谱和磁能能谱在统计平衡状态下服从幂律。(5)涡流管的重新连接为了研究涡流理论中一个重要的量——螺旋度的动力学特性，我们对一个有结的涡流管进行了数值模拟。发现螺旋度在无粘极限下是守恒的。在涡旋重联过程中发现了一种新的现象，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.