  Turbulent-laminar banded patterns in plane Poiseuille flow are studied via
direct numerical simulations in a tilted and translating computational domain
using a parallel version of the pseudospectral code Channelflow. 3D
visualizations via the streamwise vorticity of an instantaneous and a
time-averaged pattern are presented, as well as 2D visualizations of the
average velocity field and the turbulent kinetic energy. Simulations for
Reynolds numbers descending from 2300 to 700 show the gradual development from
uniform turbulence to a pattern with wavelength 20 half-gaps near Re=1900, to a
pattern with wavelength 40 near Re=1300 and finally to laminar flow near
Re=800. These transitions are tracked quantitatively via diagnostics using the
amplitude and phase of the Fourier transform and its probability distribution.
The propagation velocity of the pattern is approximately that of the mean flux
and is a decreasing function of Reynolds number. Examination of the
time-averaged flow shows that a turbulent band is associated with two
counter-rotating cells stacked in the cross-channel direction and that the
turbulence is highly concentrated near the walls. Near the walls, the Reynolds
stress force accelerates the fluid through a turbulent band while viscosity
decelerates it; advection by the laminar profile acts in both directions. In
the center, the Reynolds stress force decelerates the fluid through a turbulent
band while advection by the laminar profile accelerates it. These
characteristics are compared with those of turbulent-laminar banded patterns in
plane Couette flow.
