Turbulent Poiseuille \& Couette flows at high $Re$

We present the results of direct numerical simulation (DNS) of high $Re$ turbulent Poiseuille and Couette flows. Couette flow has been simulated with a streamwise ($x$) domain that is 100$\pi\delta$ long at Reynolds number up to $Re_\tau \approx 500$. In addition Poiseuille flow simulations up to $Re_\tau \approx 5200$ were performed (Lee \& Moser, {\it J. Fluid Mech.}, {\bf 774}, 2015). In Couette flow, extremely large scale motions, which are approximately 50$\pi\delta$ long in the $x$-direction with very strong intensity, have been observed. In this presentation we will focus on a comparison between these two flows in terms of the vorticity-velocity co-spectra, which are interesting because of the relationship between the Reynolds stress and the velocity-vorticity correlation ($\partial_y \langle u'v' \rangle = \langle w'\omega_y' \rangle - \langle v'\omega_z' \rangle$). Also considered will be the spectra of the turbulent transport term in the evolution equation for the turbulent kinetic energy. In both (co)-spectra it is shown that the difference between the two flows at high $Re$ are primarily at large scales.