  We prove the existence of steady \emph{space quasi-periodic} stream
functions, solutions for the Euler equation in vorticity-stream function
formulation in the two dimensional channel ${\mathbb R}\times [-1,1]$. These
solutions bifurcate from a prescribed shear equilibrium near the Couette flow,
whose profile induces finitely many modes of oscillations in the horizontal
direction for the linearized problem. Using a Nash-Moser implicit function
iterative scheme, near such equilibrium we construct small amplitude, space
reversible stream functions slightly deforming the linear solutions and
retaining the horizontal quasi-periodic structure. These solutions exist for
most values of the parameters characterizing the shear equilibrium. As a
by-product, the streamlines of the nonlinear flow exhibit Kelvin's cat eye-like
trajectories arising from the finitely many stagnation lines of the shear
equilibrium.
