Communications and forum: A cybernetic approach to the problem of cusp free‐surface flow caused by a line sink on a sloping bottom

In the present paper we investigate a two dimensional potential flow produced by a submerged sink of fluid of infinite depth located at the vertex on a sloping bottom. We considered the cusp configuration. Both the effects of the acceleration of gravity g and the surface tension T are included in the free surface condition. We computed numerically the solutions via a series tuncation method for different values of the angle γ(0≤γ<π/2). The numerical computation shows that there exist two critical values μ˜ and μ_min of the importance measure of surface tension μ for all values of γ(0≤γ<π/2). When μ→∞, the results of Craya, Hocking, Tuck, Vanden‐Broeck and Keller are reproduced and confirmed.