Variational Linear Problems in Wave–Obstacle Interaction

We discuss the problem of the steady two-dimensional flow past fixed disturbances in an open channel of finite depth. We consider different types of obstacles: submerged or surface-piercing bodies and localized perturbations of a horizontal bottom. By a special variational approach, we prove the unique solvability of the linearized problem for supercritical velocities of the unperturbed flow. We also discuss extensions of the variational method to the limit case of a submerged beam and to subcritical velocities.