High-Reynolds-number turbulence in a shear-free boundary layer: revisiting the Hunt-Graham theory
High-Reynolds-number turbulence in a shear-free boundary layer: revisiting the Hunt-Graham theory
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DOI：
10.1017/s0022112003004245
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发表时间：
2003-06-10
影响因子：
3.7
通讯作者：
Magnaudet, J
中科院分区：
文献类型：
--
作者：
Magnaudet, J
近年来，快速变形理论预测近不透水表面附近无剪切湍流的长期演化的能力受到了严重的质疑。然而，在高雷诺数下进行的实验和大涡模拟表明，二阶湍流统计量与Hunt&Graham(1978)阐述的理论的预测非常接近。为了澄清这一问题，进行了理论分析，以确定原始理论中没有考虑的涡旋修正的相对大小。通过对近地表涡度平衡的各种项的计算，结果表明，这一相对量级是湍流雷诺数的递减函数，这一论点与大多数已有的结果相一致。因此，Hunt&Graham理论似乎是一种前导阶近似，能够描述大雷诺数极限下无剪切边界层的短期和长期演化。然后推导出与该近似相对应的压力脉动的表达式，并得到近似的雷诺应力预算。这些预算被用来预测和讨论在时间衰减和空间衰减湍流中平坦表面附近的组元间能量传递的特征。与已有结果一致的是，预测表明，在前一种情况下，切向速度分量向法向分量传递能量，而在后一种情况下，它们通常从该分量获得能量。
The capability of rapid distortion theory to predict the long-time evolution of shearless turbulence close to an impermeable surface has been seriously questioned in recent years. However, experiments and large-eddy simulations performed at high Reynolds number show that second-order turbulence statistics follow closely the predictions of the theory elaborated by Hunt & Graham (1978). To clarify this issue, a theoretical analysis is carried out in order to determine the relative magnitude of the vortical corrections which were not taken into account in the original theory. By evaluating the various terms of the enstrophy balance in the near-surface region, it is shown that this relative magnitude is a decreasing function of the turbulent Reynolds number, an argument reconciling most existing results. Hence the Hunt & Graham theory appears to be a leading-order approximation capable of describing short- and longtime evolutions of shear-free boundary layers in the limit of large Reynolds number. The expression for the pressure fluctuation corresponding to this approximation is then derived and approximate Reynolds stress budgets are obtained. These budgets are used to predict and discuss the characteristics of the intercomponent energy transfer near a flat surface in both time-decaying and spatially decaying turbulence. In agreement with available results, predictions reveal that tangential velocity components transfer energy towards the normal component in the former case, while they generally receive energy from this component in the latter case.