Scalings of Inverse Energy Transfer and Energy Decay in 3-D Decaying Isotropic Turbulence with Non-rotating or Rotating Frame of Reference

Abstract

Energy 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 E(κ)~κm in a range between κmin and κmax. The Taylor microscale Reynolds number Reλ and Rossby number Ro 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 m, κmin, κmax, Reλ and Ro. First, we demonstrate the validity of the simulation by confirming the quantitative dependence of the decay exponent n on the initial energy spectrum exponent m, at Reλ =255 and Ro=∞, varying the values of m, κmin and κmax. Second, at relatively low Reλ, 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 E(κ)~κσ depends on the initial spectrum exponent E(κ) ~ κm: if m<4, σ=m while if m≥4, σ=4; (ii) rotation alters the inverse energy transfer rate when Reλ≤255 and Ro≥0.8; (iii) the energy increase in large scale during inverse energy transfer exhibits a bell shape, the peak of which varies with Reλ and Ro.