A numerical comparison of velocity-based and strain-based Lagrangian-history turbulence approximations
A numerical comparison of velocity-based and strain-based Lagrangian-history turbulence approximations
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基于速度和基于应变的拉格朗日历史湍流近似的数值比较
DOI：
10.1017/s0022112079000343
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发表时间：
1979
影响因子：
3.7
通讯作者：
R. Kraichnan
中科院分区：
文献类型：
--
作者：
J. Herring;R. Kraichnan
本文对二维和三维各向同性湍流的简化拉格朗日历史直接相互作用（ALHDI）近似（Kraichnan 1966）和基于应变的简化拉格朗日历史直接相互作用（SBALHDI）近似（Kraichnan & Herring 1978）进行了数值积分，并与实验数据进行了比较。在三维中等雷诺数下，与Orszag和Patterson（1972）的计算机模拟比较表明，ALHDI在耗散范围内给出了数值上过量的能量传递，而SBALHDI近似在所有范围内都显示出令人满意的精度。在二维情况下，这两种近似值都与Herring等人（1974）的模拟值相当一致，ALHDI近似值显示出两者在低波数时更好的精度。在高波数下，SBALHDI近似再次比ALHDI近似传递更少的能量，但效果不如三维中显著，并且两条曲线跨越数据。这两种近似的高雷诺数三维积分与Grant，Stewart & Moilliet（1962）的潮汐通道惯性和耗散范围数据很好地吻合，SBALHDI近似比ALHDI近似得到更大的Kolmogorov常数值。应变效率之间的差异在高波数的两个近似和这种差异对维数的依赖性的起源表现出的应用到拉伸的小尺度的对流被动标量场。在三维空间中，SBALHDI近似在Batchelor（1959）的k−1光谱范围内给出的常数值明显大于ALHDI近似，并且与实验更符合。Batchelor常数的SBALHDI值满足吉布森（1968）下界，而ALHDI值不满足。
The abridged Langrangian-history direct-interaction (ALHDI) approximation (Kraichnan 1966) and the strain-based abridged Lagrangian-history direct-interaction (SBALHDI) approximation (Kraichnan & Herring 1978) are integrated numerically for isotropic turbulence in two and three dimensions and compared with data. At moderate Reynolds numbers in three dimensions, comparison with the computer simulations by Orszag & Patterson (1972) shows that the ALHDI gives numerically excessive energy transfer in the dissipation range while the SBALHDI approximation displays satisfactory accuracy in all ranges. In two dimensions, both approximations are in reasonable agreement with the simulations of Herring et al. (1974), the ALHDI approximation showing the better accuracy of the two at low wavenumbers. At high wavenumbers the SBALHDI approximation again transfers less energy than the ALHDI approximation but the effect is less marked than in three dimensions and the two curves straddle the data. High Reynolds number integrations of both approximations in three dimensions agree well with the tidal-channel inertial- and dissipationrange data of Grant, Stewart & Moilliet (1962), the SBALHDI approximation yielding a somewhat larger value of Kolmogorov's constant than the ALHDI approximation. The origin of the difference in straining efficiency between the two approximations at high wavenumbers and of the dependence of this difference on dimensionality is exhibited by application to the stretching of small scales of a convected passive scalar field. In three dimensions the SBALHDI approximation gives markedly larger values of the constant in Batchelor's (1959) k−1 spectrum range than the ALHDI approximation and is in better agreement with experiment. The SBALHDI values of Batchelor's constant satisfy Gibson's (1968) lower bound while the ALHDI values do not.