  Reduced-order models were derived for plane Couette flow using Galerkin
projection, with orthonormal basis functions taken as the leading
controllability modes of the linearised Navier-Stokes system for a few low
wavenumbers. Resulting Galerkin systems comprise ordinary differential
equations, with a number of degrees of freedom ranging from 144 to 600, which
may be integrated to large times without sign of numerical instability. The
reduced-order models so obtained are also found to match statistics of direct
numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy,
despite a truncation of orders of magnitude in the degrees of freedom of the
system. The present models offer thus an interesting compromise between
simplicity and accuracy in a canonical wall-bounded flow, with relatively few
modes representing coherent structures in the flow and their dominant dynamics.
