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The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

机译:湍流管道中间层的流向湍流强度

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摘要

The spectral model of Perry et al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199) predicts that the integral length scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale’s variation to be more realistic while keeping with the Townsend–Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high-Reynolds-number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high-Reynolds-number data by Hultmark et al. (Phys. Rev. Lett., vol. 108, 2012, 094501; J. Fluid Mech., vol. 728, 2013, pp. 376–395). Townsend’s (The Structure of Turbulent Shear Flows, 1976, Cambridge University Press) production–dissipation balance and the finding of Dallas et al. (Phys. Rev. E, vol. 80, 2009, 046306) that, in the intermediate layer, the eddy turnover time scales with skin friction velocity and distance to the wall implies that the logarithmic derivative of the mean flow has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmark et al. (Phys. Rev. Lett., vol. 108, 2012, 094501; J. Fluid Mech., vol. 728, 2013, pp. 376–395). The same approach also predicts that the logarithmic derivative of the mean flow has a logarithmic decay at distances to the wall larger than the position of the outer peak. This qualitative prediction is also supported by the aforementioned data.
机译:佩里等人的光谱模型。 (J. Fluid Mech。,第165卷,1986年,第163-199页)预测,积分长度比例会随着距中间层壁的距离而非常缓慢地变化。在保持Townsend-Perry附着的涡旋谱的同时,使积分长度标度变化更真实的唯一方法是在比该谱小的波数处向模型添加新的波数范围。这种必要的添加还可以解释中间层中湍动能的高雷诺数外峰。根据Hultmark等人的极高雷诺数数据,获得了该外峰的解析表达式。 (Phys。Rev. Lett。,第108卷,2012年,094501; J。Fluid Mech。,第728卷,2013年,第376-395页)。汤森(《湍流剪切流的结构》,1976年,剑桥大学出版社)生产—耗散平衡以及达拉斯等人的发现。 (Phys.Rev.E,vol.80,2009,046306),在中间层中,涡流周转时间与皮肤摩擦速度和与壁的距离成比例,意味着平均流量的对数导数在与湍动能位于同一位置。这可以从Hultmark等人的数据中看出。 (Phys。Rev. Lett。,第108卷,2012年,094501; J。Fluid Mech。,第728卷,2013年,第376-395页)。相同的方法还预测,平均流量的对数导数在距壁的距离大于外峰位置的距离处具有对数衰减。上述数据也支持这种定性预测。

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