  A turbulent-laminar banded pattern in plane Couette flow is studied
numerically. This pattern is statistically steady, is oriented obliquely to the
streamwise direction, and has a very large wavelength relative to the gap. The
mean flow, averaged in time and in the homogeneous direction, is analysed. The
flow in the quasi-laminar region is not the linear Couette profile, but results
from a non-trivial balance between advection and diffusion. This force balance
yields a first approximation to the relationship between the Reynolds number,
angle, and wavelength of the pattern. Remarkably, the variation of the mean
flow along the pattern wavevector is found to be almost exactly harmonic: the
flow can be represented via only three cross-channel profiles as U(x,y,z) =
U_0(y) + U_c(y) cos(kz) + U_s(y) sin(kz). A model is formulated which relates
the cross-channel profiles of the mean flow and of the Reynolds stress. Regimes
computed for a full range of angle and Reynolds number in a tilted rectangular
periodic computational domain are presented. Observations of regular
turbulent-laminar patterns in other shear flows -- Taylor-Couette,
rotor-stator, and plane Poiseuille -- are compared.
