二维湍流外力尺度影响的格子Boltzmann方法研究

发布时间：2018-04-22 07:22

本文选题：二维湍流 + 外力尺度　；参考：《水动力学研究与进展A辑》2016年01期

【摘要】：该文基于格子Boltzmann方法,研究系统外力尺度kmax/kf对二维湍流的能谱和统计行为的影响。考虑了两种系统外力(高斯力和Kolmogorov力)和三种外力尺度max/fk k。在不存在线性摩擦力情况下,验证了描述二阶涡量结构函数与能谱关系的Benzi理论。研究表明:当外力尺度kmax/kf逐渐增大时,Kolmogorov外力情况下的二阶涡量结构函数与能谱之间的关系逐渐符合Benzi理论。在存在线性摩擦力情况下,出现能谱双能级。随着外力尺度kmax/kf逐渐增大,Kolmogorov外力情况下的直接惯性区能谱逐渐接近Kraichnann理论。在两种系统外力情况下涡量场和速度场的概率分布函数(PDF)具有指数尾迹,与Falkovich和Lebedev理论预测的结果一致。PDF随着kmax/kf增加有更大的峰度(Kurtosis),这意味着在直接级联惯性区具有更强的间歇性。
[Abstract]:Based on the lattice Boltzmann method, the effects of external force scale kmax/kf on the energy spectrum and statistical behavior of two-dimensional turbulence are studied. Two kinds of external forces (Gao Si force and Kolmogorov force) and three kinds of external force scale max/fk k are considered. In the absence of linear friction, the Benzi theory describing the relationship between the second order vorticity structure function and the energy spectrum is verified. The results show that the relationship between the second order vorticity structure function and the energy spectrum is consistent with the Benzi theory when the external force scale kmax/kf increases gradually. In the presence of linear friction, there are two energy levels in the energy spectrum. With the increase of the external force scale kmax/kf, the energy spectrum of the direct inertial region in the case of the external force is closer to that of the Kraichnann theory. The probability distribution function (PDF) of vorticity field and velocity field has exponential wake under two kinds of external forces. The results are consistent with the results predicted by Falkovich and Lebedev theory. PDFs have greater kurtosis with the increase of kmax/kf, which means that there is a stronger intermittency in the direct cascade inertial region.
【作者单位】：上海大学上海市应用数学和力学研究所;
【基金】：自然科学基金项目(91441104) 上海市优秀学术带头人计划(11XD1402300)~~
【分类号】：O357.5

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