Energy Spectra of Higher Reynolds Number Turbulence by the DNS with up to $12288^3$ Grid Points

Large-scale direct numerical simulations (DNS) of forced incompressible turbulence in a periodic box with up to $12288^3$ grid points have been performed using K computer. The maximum Taylor-microscale Reynolds number $R_\lambda$, and the maximum Reynolds number $Re$ based on the integral length scale are over 2000 and $10^5$, respectively. Our previous DNS with $R_\lambda$ up to 1100 showed that the energy spectrum has a slope steeper than $-5/3$ (the Kolmogorov scaling law) by factor $0.1$ at the wavenumber range ($k\eta<0.03$). Here $\eta$ is the Kolmogorov length scale. Our present DNS at higher resolutions show that the energy spectra with different Reynolds numbers ($R_\lambda>1000$) are well normalized not by the integral length-scale but by the Kolmogorov length scale, at the wavenumber range of the steeper slope. This result indicates that the steeper slope is not inherent character in the inertial subrange, and is affected by viscosity.