WAVE MOTIONS ON A LIQUID LAYER FALLING ALONG A VERTICAL WALL

An equation which governs wave motions of a thin layer of a viscous fluid falling along a vertical wall is derived on the assumptions that a thickness of the layer varies slowly and that a surface tension is essential. When the thickness upstream is larger than that downstream, there exists a state in which the wave propagates downwards with a constant shape of the surface, while in the other cases no such a state exists. The former state is found to be stable, and in the latter the waves decay out. Numerical calculations for the initial value problem support these results. © 1969, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.