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 引用本文: 周泽友. 二维衰减湍流的速度加速度结构函数[J]. 力学学报, 2020, 52(4): 1035-1044.
Zhou Zeyou. VELOCITY-ACCELERATION STRUCTURE FUNCTION IN TWO-DIMENSIONAL DECAYING TURBULENCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1035-1044.
 Citation: Zhou Zeyou. VELOCITY-ACCELERATION STRUCTURE FUNCTION IN TWO-DIMENSIONAL DECAYING TURBULENCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1035-1044.

## VELOCITY-ACCELERATION STRUCTURE FUNCTION IN TWO-DIMENSIONAL DECAYING TURBULENCE

• 摘要: 湍流场中二阶速度加速度结构函数 (velocity-acceleration structure function, VASF) 被认为与尺度间能量或者拟涡能的传递相关,其正负表明传递的方向. 三维湍流中,能量从大尺度向 小尺度传递,VASF 为负. 在二维湍流中,能量反向传递到大尺度,拟涡能正向传递到小尺度,因此理论上 VASF 无论在反向能量级串区还是在正向拟 涡能级串区均为正. 然而,相对于三维湍流中 VASF 的充分研究,二维湍流中 VASF 的正负性迄今尚无实验或数值模拟数据验证. 本文通过三维二维湍流中普适的公式推导,指出在空间非均匀湍流场中,VASF 除了尺度间传递,还受到非均匀项的影响. 一种常见的空间非均匀湍流场是在实验研究中常用的风洞或水洞中,湍流发生装置 (如栅格) 后的湍流. 该流场中,湍流强度随下游位置增大而逐渐衰减,这种衰减则带来空间上的非均匀性. 本文在基于竖直流动皂膜的二维衰减湍流场中,利用拉格朗日粒子追踪法测得在拟涡能级串区的 VASF,并分析各部分的影响. 结果表明,虽然尺度间传递项为正值,但由于衰减带来的非均匀项为负值,使得 VASF 的值为负,使之失去了表征拟涡能传递方向的意义. 因此,在类似风洞、水洞、水槽等衰减流场中对 VASF 的讨论不应忽略非均匀项. 最后对与 VASF 密切相关的弥散过程进行分析,发现后期弥散过程变慢是由于负的 VASF 导致.

Abstract: Second order velocity-acceleration structure function (VASF) is related to energy or enstrophy scale-to-scale transfer both in two-dimensional (2D) and three-dimensional (3D) turbulence, whose sign indicates the transfer direction. In 3D turbulence, energy transfers to smaller scale which results in negative VASF. In 2D turbulence, energy transfers to larger scale and enstrophy transfers to smaller scale, so the VASF are supposed to be positive in both inverse energy cascade range and direct enstrophy cascade range. However, comparing the abundant VASF researches in 3D turbulence, the sign of VASF in 2D turbulence is still lack of identification in neither experiment nor simulation. In this work, we give a general derivation which points out that apart from the scale-transfer term, the inhomogeneous term will also affect the VASF in spatial inhomogeneous turbulence. A commonly-used spatial inhomogeneous turbulence is that the turbulence below the turbulence generating device (such as comb) in wind tunnel or water tunnel. As flowing downstream, the turbulence intensity will decay, which brings the spatial inhomogeneity. We built a 2D decaying setup based on vertical soap-film flow, and performed particle tracking to measure VASF and its two components. Results show that the scale-transfer term is positive, but the inhomogeneous term is negative and dominates the VASF. As a result, the VASF is negative and lose its significance to identify the enstrophy transfers direction. Thus in similarly decaying turbulence, such as wind tunnel, water tunnel, sink et al., we shouldn't ignore the inhomogeneous term anymore. Finally, we discuss the dispersion process and find the slower dispersion is owing to the negative VASF.

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