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Error scaling of large-eddy simulation in the outer region of wall-bounded turbulence

机译：壁面湍流外部区域大涡模拟的误差标度

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We study the error scaling properties of large-eddy simulation (LES) in the outer region of wall-bounded turbulence at moderately high Reynolds numbers. In order to avoid the additional complexity of wall-modeling, we perform LES of turbulent channel flows in which the no-slip condition at the wall is replaced by a Neumann condition supplying the exact mean wall-stress. The statistics investigated are the mean velocity profile, turbulence intensities, and kinetic energy spectra. The errors follow (Δ/L)αReτγ, where Δ is the characteristic grid resolution, Reτ is the friction Reynolds number, and L is the meaningful length-scale to normalize Δ in order to collapse the errors across the wall-normal distance. We show that Δ can be expressed as the L2-norm of the grid vector and that L is well represented by the ratio of the friction velocity and mean shear. The exponent α is estimated from theoretical arguments for each statistical quantity of interest and shown to roughly match the values computed by numerical simulations. For the mean profile and kinetic energy spectra, α ≈ 1, whereas the turbulence intensities converge at a slower rate α < 1. The exponent γ is approximately 0, i.e. the LES solution is independent of the Reynolds number. The expected behavior of the turbulence intensities at high Reynolds numbers is also derived and shown to agree with the classic log-layer profiles for grid resolutions lying within the inertial range. Further examination of the LES turbulence intensities and spectra reveals that both quantities resemble their filtered counterparts from direct numerical simulation (DNS) data, but that the mechanism responsible for this similarity is related to the balance between the input power and dissipation rather than to filtering.
机译：我们研究了在中等雷诺数下壁边界湍流外部区域中大涡模拟（LES）的误差缩放特性。为了避免壁建模的额外复杂性，我们执行湍流通道流的LES，其中壁的无滑移条件由提供精确的平均壁应力的诺伊曼条件代替。研究的统计数据是平均速度曲线，湍流强度和动能谱。错误遵循 （ Δ / L ） α R e τ < mi>γ ，其中Δ是特征网格分辨率，Reτ是摩擦雷诺数，L是有意义的长度标度，用于归一化Δ以使其塌陷跨墙法线距离的误差。我们表明，Δ可以表示为网格矢量的L2-范数，并且L由摩擦速度和平均剪切力之比很好地表示。指数α是从理论论据中为每个感兴趣的统计量估计的，并显示为与数值模拟计算的值大致匹配。对于平均轮廓和动能谱，α≈1，而湍流强度以较慢的比率α<1收敛。指数γ大约为0，即LES解与雷诺数无关。高雷诺数下的湍流强度的预期行为也被推导出来，并显示出与经典对数层剖面图相一致的惯性范围内的网格分辨率。对LES湍流强度和光谱的进一步检查表明，这两个量都类似于直接数值模拟（DNS）数据中的滤波后的对应物，但是造成这种相似性的机制与输入功率和耗散之间的平衡有关，而不是与滤波有关。

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