二维湍流外力尺度影响的格子Boltzmann方法研究

Investigation of effect of force scale on two dimensional turbulence based on Lattice Boltzmann method

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。

The effect of force scale kmax/kf on energy spectrum and statistic behaviors of two dimensional turbulence is investigated based on Lattice Boltzmann method. The two form of two external force of the two dimensional turbulence（Gaussian force and Kolmogorov force） and three values of force scale are considered respectively. In the absent of linear friction force, the theoretic prediction by Benzi et al., which describes relationship of second vorticity structure function with energy spectrum, is estimated. Results show that, the relationships in case of Kolmogorov force are gradually close to the Benzi theory when the force scale becomes larger. Added to linear friction force, the double cascade of the two dimensional turbulence appears. Energy spectrums of direct cascade in case of Kolmogorov force are gradually close to the Kraichnann theory when the force scale increases. For two external forces, the PDF of longitudinal velocity increments and vorticity increments has an exponential tail in direction cascade. The exponential tail of the vorticity field consists with very recently theoretical prediction by Falkovich and Lebedev. The Kurtosis of PDF is lager as the force scale is larger, which means that the intermittency is higher.