Flow of liquid down an inclined plane at high Reynolds numbers

The stability of the flow of a layer of incompressible liquid with a free surface down an inclined plane under the force of gravity is investigated for the case of large Reynolds and Froude numbers. The amplitudes of the perturbations which lead to a non-linear problem are found. Problems with initial data are formulated, as well as the boundary value problems with conditions on a moving wall. It is shown that four characteristic zones appear in the field of flow in a transverse direction, changing successively from one to the next. It is noted that the proposed scheme enables one to study detached flows with recirculation zones. The scheme constructed here resembles in many ways the pattern of flow past a plate on which a boundary layer is developed with selfinduced pressure.