湍流边界层外区相干结构的三维波模型

A 3-D WAVE MODEL FOR THE COHERENT STRUCTURES IN THE OUTER REGION OF A TURBULENT BOUNDARY LAYER

根据流动稳定性理论，提出了一种三维波模型来描述湍流边界层外区大尺度相干结构．计算所得流线图和等涡量线图较罗纪生，周恒（１９９３）的二维波模型更符合实验结果．说明该三维模型能够较好地反映湍流边界层外区大尺度相干结构的物理特征．

Based on the theory of hydrodynamic instability, a new theoretical model containing a 2-D wave and a pair of 3-D waves was proposed for the coherent structures in the outer region of a turbulent boundary layer. In calculation, we assumed that the Reynolds stresses induced by small-scale eddies acting on the large-scale eddies can be expressed by eddy viscosity model, where the complex eddy viscosity is used to embody the lag of the stresses to the deformation of large--scale eddies. According to the experiments that the scale of the coherent structures in the streamwise is about 26, the streamwise wave number of the waves is chosen as 2π/λ = 3.14. At present, there have been no experimental results about the spanwise wave number. In this paper, several cases with different spanwise numbers were computed. The results showed that both the streamlines and the isovorticity lines obtained were in good agreement with those of experimental observations only when the spanwise number of 3-D wave was about half of the streamwise number. The streamlines and isovorticity lines for four different Reynolds numbers R = 11800, 19005, 47949 and 84427 were calculated. The results agree with the experimental results much better than those by 2-D wave model. It is can concluded that large-scale coherent structures in the outer region of a turbulent boundary layer can be described by the unstable wave model. The 3-D model proposed in this paper can correctly describe the physical mechanism of the coherent structures in the outer region of a turbulent boundary layer.