Free surface flow over an obstacle. Theoretical study of the fluvial case (Q1599220)

This paper is devoted to a free boundary value problem for harmonic functions in a strip-like domain. Free boundary condition is the Bernoulli equation. This statement corresponds to a steady flow of an ideal fluid over an obstacle lying on the bottom of a stream. The main result concerns existence and uniqueness of the solution for a sufficiently small Froude number \(F=u_0/\sqrt{gy_0}\) of the flow. Here \(u_0\) is the value of velocity, \(g\) is the downward acceleration due to the gravity and \(y_0\) is the height of a channel at infinity.