The presentation is devoted to a theoretical analysis of the wavy liquid film falling down a vertical plate and sheared by the turbulent gas. We use the Navier-Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use the Benjamin-Miles approach where the liquid phase is a small disturbance for the turbulent gas flowand where we can linearize the gas phase governing equations. We compute the steady state traveling solutions over a wide range of variations of the liquid Reynolds number and gas superficial velocity. Branching from the basic solution with a smooth free surface, we found different "optimal" waves for a co-current gas flow. We carried out detailed comparison of the wave's characteristics with the traveling solutions of the counter-current gas flow. We obtain that the computed wavy regimes at high values of the co-current gas flow corresponds to "the small waves on the substrate" observed in experiments. We obtained also that the complicated structure of the bifurcation lines obtained for the gravity film flow exists for all values of the gas velocity in the case of the co-current flow. In the case of the counter-current flow and starting from some value of the gas velocity, there is only one family of waves.