Small-Scale Structure of Turbulence

小尺度湍流结构

基本信息

批准号：
61540279
负责人：
KIDA Shigeo
金额：
$ 1.15万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1986
资助国家：
日本
起止时间：
1986 至 1987
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61540279/
关键词：
Turbulence Numerical Simulation High-Symmetry Intermittency MHD Turbulence Dynamo Reconnection カオス特異性

项目摘要

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.

通过数值求解纳维-斯托克斯方程来研究湍流的小尺度结构。对速度场施加高度对称性以节省计算时间和存储容量。主要研究了以下五个课题。 (1)湍流的小尺度结构实现了微尺度雷诺数<相似或等于>200的充分发展的湍流。在能谱上证实了柯尔莫哥洛夫相似性成立。惯性范围内能谱的柯尔莫哥洛夫幂律被观测到，柯尔莫哥洛夫常数为1.8。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，被发现具有与大尺度动机无关的通用形式 c(2) 能量衰减定律能量的幂律，它有通过实验观察到并通过湍流统计理论预测，首次通过数值模拟定量地证实了这一点。（3）纳维-斯托克斯流中的混沌我们发现，由稳定的外部激励激发的速度场随着雷诺数的增加，力会经历以下一系列转变：稳态->简单周期->双周期->三周期->混沌运动。 (4)MHD湍流我们发现发电机效应，动能为当雷诺数超过临界值时，就会转化为磁能。在统计平衡状态下，动能谱和磁能谱均服从幂律。 (5)涡管重联为了研究湍流理论中重要物理量之一螺旋度的动力学，我们对涡流管进行了数值模拟。打结涡流管。发现螺旋度在无粘极限内保持不变。在涡旋重联过程中观察到一种称为桥接的新现象。