On the plane problem of the flow around a submerged beam

A classical problem in hydrodynamics is the study of the plane stationary flow of a heavy fluid over submerged obstacles. Assuming the usual hypotheses, i.e., irrotational and divergence-free flow, nonviscous fluid and negligible surface tension, the velocity field can be described by a complex function, holomorphic in the domain occupied by the fluid; such a domain has rigid boundaries, where the “no-flow condition” is imposed, and a free boundary where, in addition, the nonlinear dynamical condition (Bernoulli condition) holds. When no obstacle is contained in the fluid, the only rigid boundary is a horizontal bottom and we have the well-known steady water-wave problem.