Numerical calculations based on a recent version of the eddy-damped quasi-normal model (EDQNM-LMFA) are carried out for homogeneous isotropic turbulence (HIT) with the aim of investigating the dependency on the Reynolds number of second and third order velocity structure functions. The quantities investigated include the energy spectrum $E$, the non-linear energy transfer $T$ as well as the second ($S_2$) and third ($S_3$) order moments of the longitudinal velocity increment. Both free decaying HIT and (steady state) forced HIT are considered. The analysis of the structure functions for $R{e}_{\lambda }\in [50,10^6]$ indicates that, regardless of whether one considers decaying or forced HIT, the large scales affect $S_2$ and $S_3$ in the scaling range. In that range, forcing affects $S_2$ and $S_3$ differently. For forced HIT, $S_2∕{\left(\overline{ϵ}r\right)}^{2∕3}$ exhibits a distinct “bump” near the upper end of the scaling range while no such bump is seen for $S_3∕\left(\overline{ϵ}r\right)$. The latter quantity remains approximately constant for values of $r$ which extend to the scale corresponding to the forcing. For decaying HIT, there is no discernible bump in either $S_2∕{\left(\overline{ϵ}r\right)}^{2∕3}$ or $S_3∕\left(\overline{ϵ}r\right)$. The slope of $S_3$ in the scaling range approaches the theoretical value of 1, when $R{e}_{\lambda }$ is sufficiently large. However, at similar $R{e}_{\lambda }$, the slope of $S_2$ has not yet reached a constant for either decaying or forced HIT.

为了研究二阶和三阶速度结构函数对雷诺数的依赖性，基于最新版本的涡阻尼准正态模型（EDQNM-LMFA）进行了数值计算，用于均质各向同性湍流（HIT）。 。研究的数量包括能谱$E$，非线性能量转移 $Ť$ 以及第二个（${\mathrm{小号}}_{\mathrm{2个}}$）和第三个（${\mathrm{小号}}_3$）纵向速度增量的阶矩。自由衰减HIT和（稳态）强制HIT都被考虑了。的结构功能分析$\mathrm{[R}{Ë}_{\lambda }\in [50，\mathrm{1个}{0}^6]$ 表示，无论是考虑衰减还是强制HIT，大规模影响 ${\mathrm{小号}}_{\mathrm{2个}}$ 和 ${\mathrm{小号}}_3$在缩放范围内。在此范围内，强迫会影响${\mathrm{小号}}_{\mathrm{2个}}$ 和 ${\mathrm{小号}}_3$不一样。对于强制命中，${\mathrm{小号}}_{\mathrm{2个}}∕{（\overline{ϵ}\mathrm{[R}）}^{\mathrm{2个}∕3}$ 在缩放范围的上限附近显示出明显的“凹凸”，而对于 ${\mathrm{小号}}_3∕（\overline{ϵ}\mathrm{[R}）$。对于的值，后一个量保持近似恒定$\mathrm{[R}$延伸到与强迫相对应的比例。对于衰减的HIT，两者中都没有明显的颠簸${\mathrm{小号}}_{\mathrm{2个}}∕{（\overline{ϵ}\mathrm{[R}）}^{\mathrm{2个}∕3}$ 或者 ${\mathrm{小号}}_3∕（\overline{ϵ}\mathrm{[R}）$。的斜率${\mathrm{小号}}_3$ 在标度范围内接近1的理论值 $\mathrm{[R}{Ë}_{\lambda }$足够大。但是，类似$\mathrm{[R}{Ë}_{\lambda }$，斜率 ${\mathrm{小号}}_{\mathrm{2个}}$ 衰减或强制HIT尚未达到常数。