Kramer W, Keetels G H, Clercx H J H, van Heijst G J F
Fluid Dynamics Laboratory, Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Aug;84(2 Pt 2):026310. doi: 10.1103/PhysRevE.84.026310. Epub 2011 Aug 10.
Statistical properties of forced two-dimensional turbulence generated in two different flow domains are investigated by numerical simulations. The considered geometries are the square domain and the periodic channel domain, both bounded by lateral no-slip sidewalls. The focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no-slip boundaries. The scaling exponents of the velocity and the vorticity structure functions are compared to the classical Kraichnan-Batchelor-Leith (KBL) theory, which assumes isotropy, homogeneity, and self-similarity for turbulence scales between the forcing and dissipation scale. Our investigation reveals that in the interior of the flow domain, turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range, but it is weakly intermittent. However, the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the KBL theory predicts. Near the walls the turbulence is strongly anisotropic at all flow scales.
通过数值模拟研究了在两个不同流动区域中产生的强迫二维湍流的统计特性。所考虑的几何形状是方形区域和周期性通道区域，两者均由横向无滑移侧壁界定。重点在于直接涡量级串范围以及在无滑移边界存在的情况下统计特性如何变化。将速度和涡量结构函数的标度指数与经典的克莱奇南 - 巴彻勒 - 利思（KBL）理论进行比较，该理论假设在强迫和耗散尺度之间的湍流尺度具有各向同性、均匀性和自相似性。我们的研究表明，在流动区域内部，对于涡量级串范围，湍流在统计上可被视为各向同性且局部均匀，但具有弱间歇性。然而，涡量结构函数的标度表明能谱的斜率比KBL理论预测的更陡。在壁面附近，所有流动尺度下的湍流都是强烈各向异性的。
