AN IDEAL FLUID JET IMPINGING ON AN UNEVEN WALL

The two-dimensional free-surface problem of an ideal jet impinging on an uneven wall is studied using complex-variable and transform techniq ues. A relation between the flow angle on the free surface and the wal l angle is first obtained. Then, by using a Hilbert transform and the generalized Schwarz-Christoffel transformation technique, a system of nonlinear integro-differential equations for the how angle and the wal l angle is formulated. For the case of symmetric flow, a compatibility condition for the system is automatically satisfied. In some special cases, for instance when the wall is a wedge, the problem reduces to t he evaluation of several integrals. Moreover, in the case of a jet imp inging normally on a hat wall, the classical result is recovered. For the asymmetric case, a relation is obtained between the point in the r eference zeta-plane which corresponds to the position of the stagnatio n point in the physical plane, the flow speed and the shape of the wal l. The solution to a linearized problem is given, for comparison. Some numerical solutions are presented, showing the shape of the free surf ace corresponding to a number of different wall shapes.