The relative efficiencies of the entrainment of mass, momentum and kinetic energy from a turbulent background
The relative efficiencies of the entrainment of mass, momentum and kinetic energy from a turbulent background
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湍流背景中质量、动量和动能夹带的相对效率
DOI：
10.1017/jfm.2023.958
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发表时间：
2023
影响因子：
3.7
通讯作者：
Buxton O
中科院分区：
文献类型：
--
作者：
Buxton O
我们推导了动量和动能的夹带通量的表达式，相对于暴露在湍流背景下的湍流尾迹所夹带的质量通量。这些表达式包含了夹带速度与背景湍流波动之间的相关性。我们进行了高分辨率，同步粒子图像测速和平面激光诱导荧光实验，并观察到这些相关性在远尾迹中可以忽略不计，因此动量和动能被带入尾迹的相对效率与来自理想的非湍流背景的质量相同。在建模的背景下，这是一个有用的结果，因为夹带假设（Turner， J.流体力学）。（第173卷，1986年，第431-471页）仍然可以用来模拟动量和动能的夹带。然而，质量的夹带率在空间上是不同的，并且随背景湍流的特定性质而变化，因此这反过来又驱动了空间/背景湍流特定的动量/动能夹带率。相反，在近尾流中，虽然湍流背景的动量与理想的非湍流背景的相对质量效率相同，但动能却不是这样。由于背景波动与夹带速度之间的多个正的小值相关性的总和，动能的夹带比理想情况下更有效。这包括来自非湍流背景的夹带，其中在无旋转背景波动和夹带速度之间观察到很小的相关性。在湍流背景下，夹带速度具有柯尔莫哥洛夫速度标度。
We derive expressions relating the entrainment fluxes of momentum and kinetic energy, relative to the mass flux entrained into a turbulent wake exposed to a turbulent background. These expressions contain correlations between the entrainment velocity and the turbulent fluctuations within the background. We perform high-resolution, simultaneous particle image velocimetry and planar laser-induced fluorescence experiments, and observe these correlations to be negligible in the far wake, such that momentum and kinetic energy are entrained into the wake with the same relative efficiency to mass as from an idealised, non-turbulent background. This is a useful result in the context of modelling, since the entrainment hypothesis (Turner, J. Fluid Mech., vol. 173, 1986, pp. 431–471) can still be used to model the entrainment of momentum and kinetic energy. Nevertheless, the entrainment rate of mass is shown to vary spatially, and with the specific nature of the background turbulence, so this in turn drives a spatial/background-turbulence-specific entrainment rate of momentum/kinetic energy. Contrastingly, in the near wake, whilst momentum is entrained from a turbulent background with the same relative efficiency to mass as for an idealised non-turbulent background, this is not the case for kinetic energy. Owing to the sum of multiple positive, small-valued correlations between the fluctuations in the background and the entrainment velocity, kinetic energy is entrained more efficiently than in the idealised case. This includes entrainment from a non-turbulent background, where small correlations are observed between the irrotational background fluctuations and the entrainment velocity. Evidence is also presented that the entrainment velocity scales with the Kolmogorov velocity scale when the background is turbulent.
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