Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45365420190601Scalings of Inverse Energy Transfer and Energy Decay in 3-D Decaying Isotropic Turbulence with Non-rotating or Rotating Frame of Reference6396461384510.22055/jacm.2018.26826.1361ENRouChenDepartment of Mechanical & Energy Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USAWhitneyYuDepartment of Mechanical & Energy Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USAYoushengXuSchool of Light Industry, Zhejiang University of Science and Technology, Hangzhou 310023, ChinaLuodingZhuDepartment of Mathematical Sciences, Indiana University-Purdue University Indianapolis, IN 46202, USAJournal Article20180821Energy development of decaying isotropic turbulence in a 3-D periodic cube with non-rotating or rotating frames of reference is studied through direct numerical simulation using GPU accelerated lattice Boltzmann method. The initial turbulence is isotropic, generated in spectral space with prescribed energy spectrum <em>E(κ)~κ<sup>m</sup></em> in a range between <em>κ<sub>min</sub></em> and <em>κ<sub>max</sub></em>. The Taylor microscale Reynolds number <em>Re<sub>λ</sub></em> and Rossby number <em>Ro</em> are introduced to characterize the inertial, viscous, and rotational attributes of the system. The focus of this study is on the scalings of early inverse energy transfer and late energy decay in the development of turbulent energy under various conditions through combinations of <em>m, κ<sub>min</sub>, κ<sub>max</sub>, Re<sub>λ</sub></em> and <em>Ro</em>. First, we demonstrate the validity of the simulation by confirming the quantitative dependence of the decay exponent <em>n</em> on the initial energy spectrum exponent <em>m</em>, at <em>Re<sub>λ</sub> </em>=255 and <em>Ro</em>=∞, varying the values of <em>m, κ<sub>min</sub></em> and <em>κ<sub>max</sub></em>. Second, at relatively low <em>Re<sub>λ</sub></em>, the decay exponent for different initial spectra statistically fall in respective ranges, all of which agree well with the corresponding analytical predictions. Third, we quantitatively investigate the 3-D inverse energy transfer. Our findings include (i) the exponent of inverse energy transfer spectrum <em>E(κ)~κ<sup>σ</sup></em> depends on the initial spectrum exponent <em>E(κ) ~ κ<sup>m</sup></em>: if <em>m<</em>4, <em>σ=m</em> while if <em>m≥</em>4, <em>σ</em>=4; (ii) rotation alters the inverse energy transfer rate when <em>Re<sub>λ</sub>≤</em>255 and <em>Ro≥</em>0.8; (iii) the energy increase in large scale during inverse energy transfer exhibits a bell shape, the peak of which varies with <em>Re<sub>λ</sub></em> and <em>Ro</em>.https://jacm.scu.ac.ir/article_13845_4a1abed345a435381af1e0afb7afb238.pdf