Statistical physical Study of Anomalous Diffusion Phenomena in Inviscid Fluid.

无粘流体中反常扩散现象的统计物理研究。

基本信息

批准号：
06640508
负责人：
OKAMOTO Hisao
金额：
$ 1.34万
依托单位：
Kochi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06640508/
关键词：
two-dimensional decaying turbulence anomalous diffusion anomalous transport turbulent transport nonlinear open system scaling law eddy viscosity coefficient scaling exponent 非平衡開放系 2次元非粘性流体カルマン渦

项目摘要

Due to the progress of a computer technology, several properties of nonlinear-nonequilibrium systems are clarified. Since then the studies of nonlinear dynamics on the bases of dissipative dynamical system were started and encouraged for Japanese scientists, particularly, physicists, mathematicians, biologists, chemists, engineers, geologists and even for socialists.The goal of our study is to construct a statistical physical theory of anomalous diffusion phenomena in an inviscid fluid. By making use of sufficient computer resources, we have performed successfully theoretical formulation and direct computer simulation of the two-dimensional decaying turbulence. In the turbulence, it is known there are three stages in the temporal developement of the vortices. In the first stage, fluid self-organizes into a set of coherent vortices. Once the coherent vortices emerge, the second stage begins. In the second stage, the coherent vortices governs dynamics of the system. When they become close, within a critical distance, same sign vortices merge and become a larger vortex. A pair of opposite-sign vortices ultimately construct a dipole structure. In the final stage, the dipole structure decays diffusively. In the present study, we clarified the scaling law hold in the second stage. We also succeeded to formulate a theory to the scaling exponent xi and decided the numerical value of xi that is consistent with the result of numerical simulations.

由于计算机技术的进展，阐明了非线性 - 非核系统的几种属性。从那时起，对日本科学家，特别是物理学家，数学家，生物学家，化学家，工程师，地质学家，甚至针对社会主义者的目的，对非线性动力学的研究开始并鼓励了耗散动力学系统的基础。通过利用足够的计算机资源，我们已经成功地进行了理论配方，并直接对二维衰减的湍流进行了直接的计算机模拟。在湍流中，已知涡流的时间发展中有三个阶段。在第一阶段，流体自组织成一组相干涡流。一旦相干涡流出现，第二阶段就开始了。在第二阶段，连贯的涡流控制系统的动力学。当它们接近时，在临界距离内，相同的标志涡流合并并成为更大的涡流。一对相反的涡旋最终构建了偶极子结构。在最后阶段，偶极子结构扩散地衰减。在本研究中，我们阐明了第二阶段的规模定律。我们还成功地为缩放指数XI制定了理论，并决定了XI的数值，这与数值模拟的结果一致。