Large-box DNS of a turbulent channel at $Re_\tau \approx 2000$

A DNS of a turbulent channel has been performed at $Re_{\tau}\approx2000$ in a computational box of dimensions $(8\pi\times 2\times 3\pi)h$, using dealiased Fourier expansions in $x-z$, and compact finite differences in $y$. The results broadly confirm lower $Re_\tau$'s, but there is enough scale separation to distinguish some features of the logarithmic layer. At $y^+=15$ the $u$-spectrum has a wall-streak component whose length is $\lambda_x^+=300-5000$ and $\lambda_z sim\lambda_x^{1/3}$, and an outer one with $\lambda_x/h=2-10$ and $\lambda_z \sim\lambda_x$. The former peaks near the wall, and the latter moves outwards across the logarithmic layer as $\lambda_x$ increases. The intensities of the transverse velocity fluctuations collapse well with other Reynolds numbers when expressed in wall units, although the spanwise velocity has an unsuspected near-wall peak. The mean velocity has almost a decade of logarithmic profile. The streamwise velocity fluctuations have a short $k^{-1}$ spectral range, but they don't collapse in wall units.