Direct numerical simulation for incompressible channel flow at $Re_\tau = 5200$

High-resolution direct numerical simulation (DNS) of wall-bounded canonical channel flow at $Re_\tau = 5200$ is performed. The computational domain is $8\pi\delta \times 2\delta \times 3\pi\delta$ with $10240 \times 1536 \times 7680$ grid points in streamwise($x$), wall-normal direction($y$), and spanwise($z$) directions, respectively. Fourier spectral method($x$, and $z$) and B-splines($y$) are used for the the computation of derivatives. In this presentation we demonstrate that the simulation exhibits several features of high Reynolds number wall-bounded turbulence. The value of von K\'{a}rm\'{a}n constant appears to be $\kappa$ = 0.384 in the region of $y^+$=300 $\sim$ $y$=$0.2\delta$ where the mean velocity profile shows logarithmic variation. Also, distinct inner($\lambda _x^+$= 800, $\lambda _z^+$= 120) and outer($\lambda _x$= 8$\delta$, $\lambda _z$= $\delta$) peaks in one-dimensional premultiplied spectra of the velocity variance are observed. Finally, the $k_x^{-1}$ region is observed in the range of $y^+$= $120\sim 150$ and $k_x$= $6 \sim 10$.