Local behaviour of an inviscid flow from a uniform channel over a sharp- crested weir (Q1111842)

A local analysis is presented for determining an approximate shape of the free surfaces of an inviscid flow from a uniform channel over a sharp- crested weir as well as speed of the flow along those free surfaces. Using the conformal mapping to map the region of flow in the normalized complex potential plane onto the upper half-plane, and following Carter's method [\textit{D. S. Carter}, J. Math. Mech. 10, 441-449 (1961; Zbl 0096.421)] we found a valid solution in a sufficiently small neighbourhood of a common end point between the fixed and the free boundaries, also for a far downstream, in terms of a parameter t of the upper half-plane.