  In light of some recent experiments on quasi two-dimensional (2D) turbulent
channel flow we provide here a model of the ideal case, for the sake of
comparison. The ideal 2D channel flow differs from its 3D counterpart by having
a second quadratic conserved variable in addition to the energy, and the latter
has an inverse rather than a direct cascade. The resulting qualitative
differences in profiles of velocity, V, and energy, K, as a function of the
distance from the wall are highlighted and explained. The most glaring
difference is that the 2D channel is much more energetic, with K in wall units
increasing logarithmically with the Reynolds number $\Ret$ instead of being
$\Ret$-independent in 3D channels.
