Direct numerical simulations of passive scalars with Pr>1 advected by turbulent flow
Direct numerical simulations of passive scalars with Pr>1 advected by turbulent flow
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DOI：
10.1017/s0022112097005727
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发表时间：
1997-07-25
影响因子：
3.7
通讯作者：
Yeung, PK
中科院分区：
文献类型：
--
作者：
Bogucki, D;Domaradzki, JA;Yeung, PK
对普朗特数Pr = 3、5和7的被动标量在三种低雷诺数湍流中平流进行了直接数值模拟。在Kolmogorov标度下，能谱是自相似的，并且表现出与许多其他研究一致的行为：最高雷诺数的短惯性范围和耗散范围内所有雷诺数的谱的普遍指数形式。在所有情况下，被动标量谱在Batchelor标度下坍缩成一条自相似曲线，并呈现k（-1）范围，随后呈指数下降。我们将Batchelor标度对低雷诺数流的适用性归因于能量耗散谱的普适性。波数的巴彻勒范围与实验观测大体一致，但小于经典估计所预测的范围。造成这种差异的原因是产生巴彻勒范围的速度尺度在最大能量耗散波数附近，比经典理论中使用的柯尔莫哥罗夫波数小一个数量级。将Batchelor和Kraichnan提出的两种不同的无源标量谱函数形式拟合到模拟结果中，发现Kraichnan模型与数据吻合较好，而Batchelor公式与数据存在系统偏差。讨论了这些差异对测量海洋航道能量和被动标量耗散率的实验程序的影响。
Direct numerical simulations of passive scalars, with Prandtl numbers Pr = 3, 5, and 7, advected by turbulence at three low Reynolds numbers were performed. The energy spectra are self-similar under the Kolmogorov scaling and exhibit behaviour consistent with many other investigations: a short inertial range for the highest Reynolds number and the universal exponential form of the spectrum for all Reynolds numbers in the dissipation range. In all cases the passive scalar spectra collapse to a single selfsimilar curve under the Batchelor scaling and exhibit the k(-1) range followed by an exponential fall-off. We attribute the applicability of the Batchelor scaling to our low-Reynolds-number flows to the universality of the energy dissipation spectra. The Batchelor range is observed for wavenumbers in general agreement with experimental observations but smaller than predicted by the classical estimates. The discrepancy is caused by the fact that the velocity scales responsible for the generation of the Batchelor range are in the vicinity of the wavenumber of the maximum energy dissipation, which is one order of magnitude less than the Kolmogorov wavenumber used in the classical theory. Two different functional forms of passive scalar spectra proposed by Batchelor and Kraichnan were fitted to the simulation results and it was found that the Kraichnan model agrees very well with the data while the Batchelor formula displays systematic deviations from the data. Implications of these differences for the experimental procedures to measure the energy and passive scalar dissipation rates in oceanographic hows are discussed.