二维湍流中的拉格朗日统计

LAGRANGIAN STATISTICS IN TWO DIMENSIONAL TURBULENCE

李东方

11649094

硕士

力学

万敏平

2018-06-05

2018-07-02

哈尔滨工业大学

深圳

二维湍流模型在理论研究、数值模拟和实验方面相比于三维流动都有很多优势，理论方面扩展湍流理论框架，数值方面可以进行更高精度的数值模拟，实验上更容易测量。本文使用欧拉和拉格朗日两种观点来研究二维湍流。使用 Fourier 谱方法求解欧拉速度场，在欧拉速度场上插值求解拉格朗日速度，插值方法为六阶拉格朗日插值。二维湍流中存在两个能量级串，能量逆级串与拟涡能直接级串，本文使用Fourier 谱方法对二维湍流进行直接数值模拟来得到欧拉场，计算统计量。统计量主要有动能能谱，能量通量与涡量场。分别模拟衰减湍流与加力湍流，通过这些统计量来研究这两个能量级串，从能谱，能量通量和涡量场演化这三个方面来研究二维湍流中的能量耗散。得到欧拉场之后，再进行拉格朗日湍流的模拟，在欧拉场上插值得到粒子的拉格朗日量。欧拉方法与拉格朗日方法是描述同一流动现象的不同方法，问题的本质相同，因此拉格朗日观点下的反映出的流动特性与欧拉观点为下反映出的流动特性是一致的，本文首先研究单个粒子在湍流场中的运动，关注粒子的轨迹和速度变化，结合欧拉场，来相互印证流动的特性，研究欧拉场混沌对流对粒子轨迹和速度的影响，而粒子的不规则螺旋运动也反映出湍流场的混沌和欧拉观点下的不同尺度的结构。最后研究在理论和实际应用中有重大意义的扩散现象，本文研究二维湍流中的流体质点的对扩散现象，主要研究逆能量级串中的对扩散，分析逆级串中粒子的扩散行为。分析对扩散过程中粒子间距的概率分布，概率分布随时间的变化，扩散率随时间的变化，与理论结果对比。

Two dimensional turbulence model has many advantages over three dimensional flow in theory, numerical simulation and experiment. It extend the theoretical framework of the turbulence, there are high resolution direct numerical simulation and it is easier to measure two turbulence in the experiment. In this paper, two perspectives of Euler and Lagrange are used to study two dimensional turbulence. The Fourier spectrum method is used to solve the Euler velocity field, and the Lagrangian velocity is interpolated on the Eulerian field. The interpolation method is the six order Lagrangian interpolation.In two-dimensional turbulence, there are two energy cascades, the inverse energy cascade and the direct enstrophy cascade. In this paper, we use the Fourier spectrum method to simulate the two dimensional turbulence directly to get the Euler field and calculate the statistics. The statistics mainly include the kinetic energy spectrum, the energy flux spectrum and the vorticity field, which describe the decaying turbulence and the forced turbulence respectively. This two energy cascades are studied by these statics, and the energy dissipation is studied from the three aspects in energy spectrum, energy flux spectrum and vorticity field evolution.After obtaining the Eulerian field, we start to simulate the Lagrangian turbulence and the Lagrangian quantity of the particle is interpolated in the Euler field. The Eulerian method and the Lagrangian method are the different methods to describe the same flow phenomenon. The essence of the problem is the same, so the flow characteristics reflected by the Lagrangian perspective and the flow characteristics reflected by the Euler perspective is same. In this paper, we first study the motion of single particles, including studying the trajectories and velocity changes of particles, combining the Eulerian field to verify the simulation results, and studying the influence of the Eulerian field's chaotic convection on the particle trajectories and velocity. And the irregular spiral motion of the particles also reflects the chaos of the turbulent field. The dispersion problem research is of great significance in theoretical and practical applications. In this paper, the diffusion of fluid particles in two-dimensional turbulence is studied, and the diffusion behavior of particles in different cascade is analyzed by the study of the above two cascade phenomena. Analyzing the probability distribution of the distance in the diffusion process, its change with the time, the change of the diffusion rate with time and comparing the results with them theoretical results.

二维湍流 直接数值模拟 拉格朗日湍流 湍流级串 对扩散

two dimensional turbulence direct numerical simulation Lagrangian turbulence turbulent cascade pair dispersion

中文

联合培养

南方科技大学

李东方. 二维湍流中的拉格朗日统计[D]. 深圳. 哈尔滨工业大学,2018.