Abstract
This paper deals With long nonlinear waves on a film flow of a viscous fluid down an inclined uneven wall. A system of equations for the free surface is derived to the first order accuracy of the shallow water parameter. When the derivative expansion method is applied to this system, it is shown that a fluctuation on the nonparallel basic steady flow is perturbed from that on the corresponding steady flow down a plane wall inclined at the same angle owing to the ununiformity of the basic flow. The linear stability of the basic flow is identical with that for the plane wall case. Near the upper branch of the neutral curve, the flow on the uneven wall is found to be supercritically stable and long waves of equilibrium amplitude are complicatedly perturbed from the corresponding waves for the plane wall case.
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