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Analysis of multifractal natures in turbulence based on the dynamics of fine-scale coherent structures

基于精细尺度相干结构动力学的湍流多重分形性质分析

基本信息

批准号：
12834007
负责人：
TOH Sadayoshi
金额：
$ 2.37万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

It has shown that two dimensional Boussinesq turbulence has characteristics similar to those of three- dimensional Navier-Stokes turbulence. In particular, the existence of both cascade process and fine-scale coherent structures suggests that turbulence should be maintained by some universal mechanism. We believe that these results will contribute to the fundamental understanding of turbulence considerably. The main results are the following:1. The fine scale coherent structures formed by T vorticity have been found and defined.We found that strings-like temperature shocks maintained by the balance of stretching and dissipation are regarded as fine scale coherent structures in 2D Boussinesq turbulence, which have a life time longer than the characteristic times of small scales and quite long correlation length. These characters of fine-scale coherent structures are quite similar to those in 3D Navier-Stokes turbulence. Moreover it is shown that these structures are approximated by anal … More ytic solutions corresponding to the Burgers' vortex layer.2. The role of fine scale coherent structures in turbulence diffusion has been understood partially.We have shown that although fine scale coherent structures have quite long correlation length, they essentially contribute to the relative turbulent diffusion in a sense pf Kolmogorov scaling. This means that fine scale coherent structures play an important role even in lower order characteristics of turbulence.3. The result suggesting the existence of finite time singularity has been obtained.We developed a high resolution scheme in which new meshes are piled up at local regions where finer spatial resolution is required : adaptive mesh refinement method. With this scheme we have obtained the result suggesting the existence of finite-time singularity in ideal two dimensional Boussinesq system.The singularity seems to be triggered by a self-similar instability of a fine scale coherent structure. This suggests that even in the invisid limit structures become unstable and then characteristics of turbulence might be different from those accepted presently. Less

结果表明，二维Boussinesq湍流具有与三维Navier-Stokes湍流相似的特征。特别是，级联过程和细尺度相干结构的存在表明湍流应该是由某种普遍机制维持的。我们相信，这些结果将有助于对湍流的基本理解。主要研究结果如下：1.发现并定义了由T涡度形成的细尺度相干结构，发现在二维Boussinesq湍流中，由拉伸和耗散平衡维持的弦状温度激波是细尺度相干结构，它的寿命比小尺度的特征时间长，关联长度也很长。细尺度相干结构的这些特征与三维Navier-Stokes湍流中的特征十分相似。此外，它表明，这些结构是近似的分析 ...更多信息对应于Burgers涡层的对称解。细尺度相干结构在湍流扩散中的作用已得到部分理解，我们指出，虽然细尺度相干结构具有相当长的相关长度，但它们在Kolmogorov标度意义下对相对湍流扩散有实质贡献。这意味着即使在较低阶的双折射特性中，精细尺度相干结构也起着重要的作用.我们发展了一种高分辨率格式，在需要更高空间分辨率的局部区域堆积新的网格：自适应网格加密方法。利用该方案，我们得到了理想二维Boussinesq系统存在有限时间奇异性的结果，该奇异性似乎是由细尺度相干结构的自相似不稳定性触发的。这表明，即使在无粘极限结构变得不稳定，然后湍流的特性可能是不同的，从目前接受的。少