  On its way to turbulence, plane Couette flow - the flow between
counter-translating parallel plates - displays a puzzling steady oblique
laminar-turbulent pattern. We approach this problem via Galerkin modelling of
the Navier-Stokes equations. The wall-normal dependence of the hydrodynamic
field is treated by means of expansions on functional bases fitting the
boundary conditions exactly. This yields a set of partial differential
equations for the spatiotemporal dynamics in the plane of the flow. Truncating
this set beyond lowest nontrivial order is numerically shown to produce the
expected pattern, therefore improving over what was obtained at cruder
effective wall-normal resolution. Perspectives opened by the approach are
discussed.
