相干结构和非均匀性在近场湍流尺度间能量传递中的作用
The role of Coherent Structures and Inhomogeneity in Near-Field Inter-Scale Turbulent Energy Transfers
摘要：
我们使用DNS来研究尺度间和空间间的能量交换在近场的湍流尾流的正方形棱柱的KHMH方程的速度场的三重分解占准周期性的旋涡脱落。KHMH的定向平均项在平均流平面和几何中心线上计算。我们考虑$2$和$8$之间的位置乘以棱镜的宽度$d$。平均流产生动能，供给旋涡脱落相干结构。反过来，这些结构转移能量的随机波动在所有的长度尺度$r$从泰勒长度$λ$ $d$和主导空间湍流传输的两点随机湍流波动。Alves Portela等人发现取向平均的非线性尺度间转移速率$Π^{a}$与$r$近似无关。在距离正方形棱镜$x_{1}=2d$的距离处的范围$λ\le r \le 0.3d$中，对于这种近似恒定性，需要相干结构的尺度间转移贡献。然而，Alves Portela et.（2017）主要是由于随机波动。即便如此，在$x_1=8d$处的范围$λ\le r\le d$内，$-Π^a$与湍流耗散率$\varepsilon$的接近需要相干结构的贡献。空间不均匀性也对$Π^a$有直接和明显的贡献，如果没有它，在近场流中$-Π^a/\varepsilon$接近1的恒定性是不可能的。最后，压力-速度项也是KHMH的重要贡献者，特别是在尺度r大于约$0.4d$的情况下，并且当取向平均值被提升时，似乎与纯随机非线性尺度间转移速率相关。
英文摘要：
We use DNS to study inter-scale and inter-space energy exchanges in the near-field of a turbulent wake of a square prism in terms of the KHMH equation written for a triple decomposition of the velocity field accounting for the quasi-periodic vortex shedding. Orientation-averaged terms of the KHMH are computed on the plane of the mean flow and on the geometric centreline. We consider locations between $2$ and $8$ times the width $d$ of the prism. The mean flow produces kinetic energy which feeds the vortex shedding coherent structures. In turn, these structures transfer energy to the stochastic fluctuations over all length-scales $r$ from the Taylor length $λ$ to $d$ and dominate spatial turbulent transport of two-point stochastic turbulent fluctuations. The orientation-averaged non-linear inter-scale transfer rate $Π^{a}$ which was found to be approximately independent of $r$ by Alves Portela et. al. (2017) in the range $λ\le r \le 0.3d$ at a distance $x_{1}=2d$ from the square prism requires an inter-scale transfer contribution of coherent structures for this approximate constancy. However, the near-constancy of $Π^a$ at $x_1=8d$ which was also found by Alves Portela et. al. (2017) is mostly due to stochastic fluctuations. Even so, the proximity of $-Π^a$ to the turbulence dissipation rate $\varepsilon$ in the range $λ\le r\le d$ at $x_1=8d$ requires contributions of the coherent structures. Spatial inhomogeneity also makes a direct and distinct contribution to $Π^a$, and the constancy of $-Π^a/\varepsilon$ close to 1 would not have been possible without it either in this near-field flow. Finally, the pressure-velocity term is also an important contributor to the KHMH, particularly at scales r larger than about $0.4d$, and appears to correlate with the purely stochastic non-linear inter-scale transfer rate when the orientation average is lifted.
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