Eddy viscosity-based and regularization-based subgrid-scale (SGS) models are quantitatively assessed for large eddy simulations (LES) of stratified Taylor–Green vortex (TGV). LES calculations using the dynamic Smagorinsky, Leray- $$\alpha$$ α , LANS- $$\alpha$$ α and Clark- $$\alpha$$ α models are conducted using a pseudo-spectral formulation on a $$128^{3}$$ 128 3 grid and using $$\alpha =\frac{1}{160}$$ α = 1 160 (for all the regularization models) for Froude number, $$Fr_0=\frac{{\mathcal {U}}}{{{\mathcal {N}}}{{\mathcal {L}}}}=1$$ F r 0 = U N L = 1 , and Reynolds number, $$Re_{0}= \frac{\mathcal {U L} }{\nu }=1600$$ R e 0 = U L ν = 1600 . Results are compared in detail with in-house direct numerical simulation (DNS) calculations. Validation of the formulation is carried out through grid-dependent studies using grids of $$64^3$$ 64 3 , $$128^3$$ 128 3 and $$256^3$$ 256 3 , $$\alpha$$ α (regularization parameter)-dependent studies using $$\alpha$$ α values of $$\frac{1}{40}, \frac{1}{80}, \frac{1}{160}$$ 1 40 , 1 80 , 1 160 and $$\frac{1}{320}$$ 1 320 , and comparisons with previously published results Remmler and Hickel, 2012, of the same problem. Various quantities including turbulent kinetic energy ( tke ), turbulent potential energy ( tpe ), Q -criteria based vortical structures, potential & total energy spectra, and horizontal & vertical energy fluxes in the respective directions, are analyzed to understand the capability of the various LES models in predicting the development of stratified turbulence. Results showed that all the SGS model predictions were very similar to each other with Smagorinsky and Leray displaying the lowest and highest errors, respectively, in comparison to DNS. The effect of $$Fr_0$$ F r 0 was also studied through additional LES calculations at $$Fr_0=0.5$$ F r 0 = 0.5 and 0.16, again using the dynamic Smagorinsky and regularization models and comparing various parameters including tke , tpe and energy spectra to DNS. Decay rates of tke and tpe decreased and turbulence was significantly suppressed with decrease in $$Fr_0$$ F r 0 . At these lower $$Fr_0$$ F r 0 , all the SGS model predictions were almost identical to each other and compared extremely well with the DNS results.

中文翻译：

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分层泰勒-格林涡旋大涡模拟 (LES) 的 SGS 模型评估

基于涡粘性和基于正则化的亚网格尺度 (SGS) 模型被定量评估为分层泰勒-格林涡旋 (TGV) 的大涡模拟 (LES)。使用动态 Smagorinsky、Leray- $$\alpha$$ α 、LANS- $$\alpha$$ α 和 Clark- $$\alpha$$ α 模型的 LES 计算是使用 $$128^ 上的伪光谱公式进行的{3}$$ 128 3 网格并使用 $$\alpha =\frac{1}{160}$$ α = 1 160（对于所有正则化模型）对于 Froude 数，$$Fr_0=\frac{{\mathcal {U}}}{{{\mathcal {N}}}{{\mathcal {L}}}}=1$$ F r 0 = UNL = 1 和雷诺数，$$Re_{0}= \frac {\mathcal {UL} }{\nu }=1600$$ R e 0 = UL ν = 1600 。结果与内部直接数值模拟 (DNS) 计算进行了详细比较。使用$$64^3$$$64 3 的网格通过网格相关研究进行配方的验证，$$128^3$$ 128 3 和 $$256^3$$ 256 3 ，$$\alpha$$ α（正则化参数）相关研究，使用 $$\alpha$$ α 值的 $$\frac{1}{1}{ 40}, \frac{1}{80}, \frac{1}{160}$$ 1 40 , 1 80 , 1 160 和 $$\frac{1}{320}$$ 1 320 ，以及与之前的比较Remmler 和 Hickel，2012 年发表了相同问题的结果。包括湍流动能 (tke)、湍流势能 (tpe)、基于 Q 准则的涡结构、势能和总能谱以及各个方向的水平和垂直能量通量在内的各种量被分析，以了解各种能力LES 模型预测分层湍流的发展。结果表明，所有 SGS 模型预测都非常相似，Smagorinsky 和 ​​Leray 分别显示最低和最高误差，与 DNS 相比。还通过在 $$Fr_0=0.5$$F r 0 = 0.5 和 0.16 处的额外 LES 计算研究了 $$Fr_0$$ F r 0 的影响，再次使用动态 Smagorinsky 和正则化模型并比较各种参数，包括 tke 、 tpe和能谱到 DNS。随着$$Fr_0$$F r 0 的降低，tke 和tpe 的衰减率降低，湍流得到显着抑制。在这些较低的 $$Fr_0$$ F r 0 下，所有 SGS 模型预测几乎彼此相同，并且与 DNS 结果进行了非常好的比较。随着$$Fr_0$$F r 0 的降低，tke 和tpe 的衰减率降低，湍流得到显着抑制。在这些较低的 $$Fr_0$$ F r 0 下，所有 SGS 模型预测几乎彼此相同，并且与 DNS 结果进行了非常好的比较。随着$$Fr_0$$F r 0 的降低，tke 和tpe 的衰减率降低，湍流得到显着抑制。在这些较低的 $$Fr_0$$ F r 0 下，所有 SGS 模型预测几乎彼此相同，并且与 DNS 结果进行了非常好的比较。