Kolmogorov’s similarity turbulence theory in a Lagrangian frame is assessed with new direct numerical simulations of isotropic turbulence with and without hyperviscosity, which attain higher Reynolds numbers than previously available. It is demonstrated that hyperviscous simulations can be used to accurately predict the second order Lagrangian velocity structure function (LVSF-2) in the inertial range, by using an original new procedure. The results strongly support Kolmogorov’s Lagrangian similarity assumption and allow the universal constant of LVSF-2 to be computed with a new level of confidence with C0=7.4±0.2.

中文翻译：

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重新审视 Kolmogorov 的拉格朗日相似定律

Kolmogorov 在拉格朗日坐标系中的相似性湍流理论通过具有和不具有高粘度的各向同性湍流的新直接数值模拟进行评估，获得比以前可用的雷诺数更高的雷诺数。结果表明，通过使用原始的新程序，高粘性模拟可用于准确预测惯性范围内的二阶拉格朗日速度结构函数（LVSF-2）。结果强烈支持 Kolmogorov 的拉格朗日相似性假设，并允许以新的置信水平计算 LVSF-2 的通用常数，C0=7.4±0.2。