Scaling-law-based decomposition and Reynolds-number effects of wall-bounded turbulent motions
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摘要: 壁湍流广泛存在于自然界和工程中，对其深入研究和理解有助于发展新的计算模型和调控手段。湍流具有多尺度性，壁面带来的各向异性使得壁湍流多尺度运动更为复杂。本文探讨和总结了基于标度律的壁湍流运动分解方法：内–外分解方法和外区分解方法，其中内–外分解方法基于内区湍流运动的雷诺数无关性，而外区分解方法基于Townsend的附着涡标度律；讨论了分解后壁湍流运动统计特性的雷诺数效应，给出了内区湍流运动达到雷诺数无关和出现外区湍流运动的2个临界雷诺数。Abstract: Wall-bounded turbulence widely exists in nature and engineering, the in-depth study and understanding of which can help to develop new computational models and control methodology. Turbulence has multi-scale characteristics, and the anisotropy caused by the wall makes the multi-scale motions of wall turbulence more complex and challenging. This paper discusses and summarizes the scaling-law-based decomposition methods for wall-bounded turbulent motions, including inner-outer decomposition and outer decomposition. The inner-outer decomposition is based on the Reynolds-number independence of the inner turbulent motions, and the outer decomposition is based on the scaling laws of Townsend’s attached eddy hypothesis. Finally, the Reynolds number effect of the statistical characteristics of the wall turbulent motions after decomposition is discussed, and two critical Reynolds numbers are given for the inner turbulent motions to reach Reynolds number independence and for the appearance of the outer turbulent motions.
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图 1 槽道湍流的平均速度和湍动能（实线：平均速度；虚线：湍动能）
Figure 1. Profiles of mean streamwise flow velocity and turbulence kinetic energy of turbulent channel flows （solid lines: mean flow velocity; dashed lines: turbulence kinetic energy）
图 2 槽道湍流流向脉动速度预乘能谱图
Figure 2. Premultiplied spectra of streamwise velocity fluctuation
图 3 根据原始内–外分解模型得到的内区湍流运动脉动强度
Figure 3. Intensities of inner turbulent motions by the original inner-outer decomposition model
图 4 根据原始内–外分解模型得到的叠加和调制函数
Figure 4. The superimposition and modulation functions by the original inner-outer decomposition model
图 5 根据改进内–外分解模型得到的内区湍流运动脉动强度
Figure 5. The intensities of inner turbulent motions by the improved inner-outer decomposition model
图 6 根据改进内–外分解模型得到的叠加和调制函数
Figure 6. The superimposition and modulation functions by the improved inner-outer decomposition model
图 8 槽道和边界层湍流中的附着涡流向速度脉动
Figure 8. The streamwise velocity fluctuations of wall-attached eddies in channels and turbulent boundary layers
图 9 不同层级附着涡的尺寸及数密度
Figure 9. The size and population density of wall-attached eddies of different hierarchies
图 10 低雷诺数内区湍流运动脉动强度
Figure 10. The intensities of inner motions at low Reynolds numbers
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