Pharasi Hirdesh K, Kumar Krishna, Bhattacharjee Jayanta K
Department of Physics, Indian Institute of Technology, Kharagpur-721 302, India.
Harish-Chandra Research Institute, Allahabad-211 019, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Feb;89(2):023009. doi: 10.1103/PhysRevE.89.023009. Epub 2014 Feb 13.
We present results for entropy and kinetic energy spectra computed from direct numerical simulations for low-Prandtl-number (Pr < 1) turbulent flow in Rayleigh-Bénard convection with uniform rotation about a vertical axis. The simulations are performed in a three-dimensional periodic box for a range of the Taylor number (0 ≤ Ta ≤ 10(8)) and reduced Rayleigh number r = Ra/Ra(∘)(Ta,Pr) (1.0 × 10(2) ≤ r ≤ 5.0 × 10(3)). The Rossby number Ro varies in the range 1.34 ≤ Ro ≤ 73. The entropy spectrum E(θ)(k) shows bisplitting into two branches for lower values of wave number k. The entropy in the lower branch scales with k as k(-1.4 ± 0.1) for r>10(3) for the rotation rates considered here. The entropy in the upper branch also shows scaling behavior with k, but the scaling exponent decreases with increasing Ta for all r. The energy spectrum E(v)(k) is also found to scale with the wave number k as k(-1.4 ± 0.1) for r>10(3). The scaling exponent for the energy spectrum and the lower branch of the entropy spectrum vary between -1.7 and -2.4 for lower values of r (<10(3)). We also provide some simple arguments based on the variation of the Kolmogorov picture to support the results of simulations.
我们展示了通过直接数值模拟计算得到的熵谱和动能谱的结果，该模拟针对围绕垂直轴均匀旋转的低普朗特数（Pr < 1）瑞利 - 贝纳德对流中的湍流流动。模拟在三维周期盒中进行，泰勒数范围为（0 ≤ Ta ≤ 10(8)），折合瑞利数r = Ra/Ra(∘)(Ta,Pr)（1.0 × 10(2) ≤ r ≤ 5.0 × 10(3)）。罗斯比数Ro在1.34 ≤ Ro ≤ 73范围内变化。对于较低的波数k，熵谱E(θ)(k)显示出双峰分裂为两个分支。对于此处考虑的旋转速率，当r > 10(3)时，下分支中的熵与k的标度关系为k(-1.4 ± 0.1)。上分支中的熵也显示出与k的标度行为，但对于所有r，标度指数随Ta的增加而减小。当r > 10(3)时，还发现能量谱E(v)(k)与波数k的标度关系为k(-1.4 ± 0.1)。对于较低的r值（<10(3)），能量谱和熵谱下分支的标度指数在 -1.7和 -2.4之间变化。我们还基于柯尔莫哥洛夫图像的变化提供了一些简单的论据来支持模拟结果。
