LANS-α的高湍流解及其LES势
Highly turbulent solutions of LANS-alpha and their LES potential
摘要：
我们计算的拉格朗日平均Navier-Stokes α模型（LANS）显着更高的雷诺数（Re 8300）比以前完成的解决方案。这允许充分的尺度分离，以观察纳维尔-斯托克斯（NS）惯性范围，然后是第二LANS惯性范围。对三阶结构函数标度的分析支持预测的l^3标度;它对应于能谱的k^（-1）标度。能谱本身显示了一个不同的标度，即k^1。后一种光谱与子滤波器尺度中没有拉伸是一致的，这是由于在LANS的推导中采用泰勒冻结假设作为闭合。这两个缩放被证明是共存于不同的空间部分的流动。在能谱中，l^3（E（k）k^（-1））标度比k^1次显性，但l^3标度是直接能量级联的原因，因为没有内部自由度的运动不可能产生级联。我们验证了预测的LANS吸引子的大小从这种缩放。从这一点上，我们给出了一种方法，无论是到达网格独立的解决方案，局域网，或获得一个制定的LES最佳的上下文中的阿尔法模型。完全收敛的网格无关LANS可能不是NS方程的直接数值模拟的最佳近似，因为最小误差是截断误差和由于使用LANS而不是原始方程引起的近似误差之间的平衡。此外，LANS的小尺度行为有助于减少恒定能量下的通量，导致大α的能谱较浅。这些小尺度的特征并不妨碍LANS正确地再现高Re流的湍流特性。
英文摘要：
We compute solutions of the Lagrangian-Averaged Navier-Stokes alpha-model (LANS) for significantly higher Reynolds numbers (up to Re 8300) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes (NS) inertial range followed by a 2nd LANS inertial range. The analysis of the third-order structure function scaling supports the predicted l^3 scaling; it corresponds to a k^(-1) scaling of the energy spectrum. The energy spectrum itself shows a different scaling which goes as k^1. This latter spectrum is consistent with the absence of stretching in the sub-filter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of LANS. These two scalings are conjectured to coexist in different spatial portions of the flow. The l^3 (E(k) k^(-1)) scaling is subdominant to k^1 in the energy spectrum, but the l^3 scaling is responsible for the direct energy cascade, as no cascade can result from motions with no internal degrees of freedom. We verify the prediction for the size of the LANS attractor resulting from this scaling. From this, we give a methodology either for arriving at grid-independent solutions for LANS, or for obtaining a formulation of a LES optimal in the context of the alpha models. The fully converged grid-independent LANS may not be the best approximation to a direct numerical simulation of the NS equations since the minimum error is a balance between truncation errors and the approximation error due to using LANS instead of the primitive equations. Furthermore, the small-scale behavior of LANS contributes to a reduction of flux at constant energy, leading to a shallower energy spectrum for large alpha. These small-scale features, do not preclude LANS to reproduce correctly the intermittency properties of high Re flow.
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