基于κ_sgs与θ_sgs²输运的中性大气边界层大涡模拟

Large-Eddy Simulation of Neutral Atmospheric Boundary Layer Based on κ_sgs and θ_sgs² Transports

摘要: 大气边界层(ABL)中标量的仿真对于掌握大气中温度、湿度等的分布，污染物的扩散规律及预测雨水的生成等均具有重要意义。大涡模拟(LES)是当前ABL湍流仿真的主要方法，其关键是如何利用解析尺度的速度场和标量场信息构建亚网格(SGS)应力模型和通量模型。对于ABL湍流这一典型的高雷诺数条件下的非各向同性湍流，以Boussinesq假设为出发点构建的粘性SGS模型存在先验误差较大、后验耗散过强等许多问题。本研究引入一种新的非线性SGS通量模型，该模拟不预先假设能量的传输方向，基于速度和标量的梯度计算SGS通量的结构(矢量分量的相对大小)，且摈弃局部平衡假设，采用动力学方程考虑能量反传，预测SGS通量强度的动态演化过程。研究采用一个中性ABL基准工况，通过与已有的理论预测和各种流动统计的对比进行系统的考察来对模型进行评估，同时也与传统粘性SGS模型的表现进行比较。具体地，当LES达到统计稳定后，我们重点关注了在不同网格条件下模型对无量纲速度梯度、无量纲标量梯度、能谱及流场结构等的预测结果。结果表明，除了可以获取可靠的流场结构，相比传统粘性SGS模型，新模型对无量纲梯度预测的准确度有明显提升，且对湍流能谱的预测有显著改善。此外，我们讨论了新模型预测效果提升的原因，相较于传统粘性SGS模型存在耗散较强的问题，新模型采用动态非线性的建模方法，可以预测ABL湍流中能量的逆向输运，并更好地捕捉小尺度的涡旋。

Abstract: The simulation of scalars in the atmospheric boundary layer (ABL) is of great significance for understanding the distribution of temperature, humidity, and other factors in the atmosphere, as well as the diffusion patterns of pollutants and the prediction of rain generation. Large-Eddy Simulation (LES) is currently the main method for ABL turbulence simulation, and the key is how to construct sub-grid-scale (SGS) stress model and flux model by using the velocity and scalar field information of analytic scale. For ABL turbulence, a typical non-isotropic turbulence under high Reynolds number conditions, the viscous SGS model based on the Boussinesq hypothesis has many problems, such as large prior errors and strong posterior dissipation. This study introduces a new nonlinear SGS flux model, which simulates the structure of SGS flux (relative magnitude of vector components) based on velocity and scalar gradients without assuming the direction of energy transfer. In addition, the local equilibrium hypothesis is discarded, and kinetic equations are adopted to consider the reverse energy transfer and predict the dynamic evolution of SGS flux intensity. The study used a neutral ABL benchmark operating condition and systematically evaluated the model by comparing it with existing theoretical predictions and various flow statistics, as well as comparing its performance with traditional viscous SGS models. Specifically, when LES reaches statistical stability, we focus on the prediction results of the model for dimensionless velocity gradient, dimensionless scalar gradient, energy spectrum, and flow field structure under different grid conditions. The results show that in addition to obtaining reliable flow field structure, compared with the traditional viscous SGS model, the new model significantly improves the accuracy of dimensionless gradient prediction and turbulence energy spectrum prediction. In addition, we discussed the reasons for the improved prediction performance of the new model. Compared with the traditional viscous SGS model, which has a strong dissipation problem, the new model adopts a dynamic nonlinear modeling method, which can predict the reverse energy transport in ABL turbulence and better capture small-scale vortices.