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Navier-Stokes方程来研究湍流的小规模结构。高对称性施加在速度场上，以节省计算时间和内存能力。（1）湍流的小尺度结构我们意识到了完全发育的湍流，其微尺度雷诺数<相似或等于> 200。确认Kolmogorov的相似性在能源谱中存在。 kolmogorov常数1.8观察到惯性范围内能量谱的Kolmogorov功率定律。发现速度衍生物的概率密度分布和耗散速率的特征是湍流间歇性结构的特征，其具有刺激性形式，与大规模的动力c（2）能量衰减法独立于能源的能力法，通过实验和经过量子的统计学理论，该法被观察到了均等的均值（以均值为单位）。 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 价值。（5）重新连接涡流管以研究螺旋性的动力学，这是湍流理论中的重要数量之一，我们对打结的涡流管进行数值模拟。发现螺旋性在无粘性极限内是保守的。在涡旋重新连接过程中观察到了一种称为桥接的新现象。